ADF ManualAmsterdam Modeling Suite 2019.3

www.scm.com

Nov 08, 2019

CONTENTS

1 General 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Functionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.2 Applicability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.3 Model Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.5 Technical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.6 Fragments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Basic atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Automatic mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.1.7 Slater-type basis sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 What’s new in ADF 2019 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 New features in ADF2019.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2 New features in ADF2019.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Feature List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.1 Model Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.2 Structure and Reactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.3 Spectroscopic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3.4 Charge transport properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3.6 Accuracy and Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Technical remarks, Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.4.1 Density functional theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.4.2 The Kohn-Sham MO model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.4.3 Basis functions and orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Cartesian function sets, spurious components . . . . . . . . . . . . . . . . . . . . . . . . . . 9Frozen core: Core Orbitals and Core Functions . . . . . . . . . . . . . . . . . . . . . . . . . 9Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Orthonormal basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Fragments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Summary of functions and orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.4.4 Fit functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.4.5 Three-step build-up of the bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.4.6 Transition State procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.5 Running the program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.5.1 Execution of ADF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.5.2 Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

TAPE21 and logfile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Standard output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

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File names during parallel runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2 Input and Output 172.1 Minimal input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.1.1 Shell script . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Structure of the Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.1 Units of length and angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.2 Including an external file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.3 Title, comment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.4 General remarks on input structure and parsing . . . . . . . . . . . . . . . . . . . . . . . . 192.2.5 Keys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.6 Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.2.7 Input parsing changes in ADF2018 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

New syntax for a few keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Strict parsing of input file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3 Structure of the Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.3.1 Job Characteristics on standard Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.3.2 Log file, TAPE21, TAPE13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3 Coordinates, Basis sets, Fragments 273.1 Atomic coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1.1 Cartesian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.1.2 Z-matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.1.3 Mixed Cartesian and Z-matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1.4 MOPAC format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1.5 Orientation of Local Atomic Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.1.6 ASCII Output Files with Atomic Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . 303.1.7 Symmetry Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2 Basis sets and atomic fragments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.2.1 STO basis sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.2.2 Available basis sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.2.3 The Basis Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.2.4 Automatic mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.2.5 Create mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.2.6 Ghost Atoms, Non-standard Chemical Elements . . . . . . . . . . . . . . . . . . . . . . . . 393.2.7 Nuclear Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.3 Molecular fragments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.3.1 Fragment mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.3.2 Fragment files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4 Model Hamiltonians 454.1 Electronic Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.1.1 Charge and Spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Spin: restricted vs. unrestricted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Unrestricted and Spin-Orbit Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Net Charge and Spin polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.1.2 Orbital occupations: electronic configuration, excited states . . . . . . . . . . . . . . . . . . 47Aufbau, smearing, freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Explicit occupation numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49CHARGE vs. IRREPOCCUPATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Create mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.1.3 Frozen core approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.1.4 Spin-polarized start-up potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Spin-flip method for broken symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

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Modify the starting potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.1.5 Unrestricted fragments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Prepared for bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.1.6 Simulated unrestricted fragments with key FRAGOCCUPATIONS . . . . . . . . . . . . . . 54

Prepared for bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54FRAGOCCUPATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.1.7 Remove Fragment Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.1.8 CDFT: Constrained Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . 56

4.2 Density Functionals (XC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.2.1 LDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.2.2 GGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.2.3 MetaGGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.2.4 Hartree-Fock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.2.5 Hybrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.2.6 Meta-Hybrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.2.7 Double-Hybrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.2.8 MP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.2.9 Range separated hybrids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

RangeSep + XCFun: Yukawa-range separated hybrids . . . . . . . . . . . . . . . . . . . . . 69Range-separated hybrids with LibXC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.2.10 Notes on Hartree-Fock and (meta-)hybrid functionals . . . . . . . . . . . . . . . . . . . . . 714.2.11 Notes on MP2 and double-hybrid functionals . . . . . . . . . . . . . . . . . . . . . . . . . 724.2.12 Model Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.2.13 Optimized effective potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.2.14 XCFun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754.2.15 LibXC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754.2.16 Dispersion corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

DFT-D4 functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78DFT-D3 functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78DFT-D functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79MM dispersion (old implementation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80dDsC: density dependent dispersion correction . . . . . . . . . . . . . . . . . . . . . . . . . 80DFT-ulg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80DFT-MBD functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.2.17 Self-Interaction Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.2.18 Post-SCF energy functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

GGA energy functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Meta-GGA and hybrid energy functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82Post Hartree-Fock energy functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.3 Relativistic effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.3.1 Pauli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.3.2 ZORA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854.3.3 X2C and RA-X2C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854.3.4 Spin-Orbit coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.4 Solvents and other environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864.4.1 COSMO: Conductor like Screening Model . . . . . . . . . . . . . . . . . . . . . . . . . . 864.4.2 SM12: Solvation Model 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.4.3 QM/MM: Quantum mechanical and Molecular Mechanics model . . . . . . . . . . . . . . . 964.4.4 Quild . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 974.4.5 DIM/QM: Discrete Interaction Model/Quantum Mechanics . . . . . . . . . . . . . . . . . . 97

DRF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Surface-enhanced response properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Input options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99EXTERNALS key for DRF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

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4.4.6 FDE: Frozen Density Embedding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Fragment-specific FDE options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Kinetic energy approximants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111General FDE options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Frozen Density Embedding with External Orthogonality . . . . . . . . . . . . . . . . . . . . 114FDE and (localized) COSMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Subsystem TDDFT, coupled FDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Restrictions and pitfalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

4.4.7 SCRF: Self-Consistent Reaction Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1174.4.8 VSCRF: Vertical Excitation Self-Consistent Reaction Field . . . . . . . . . . . . . . . . . . 1224.4.9 3D-RISM: 3D reference Interaction Site Model . . . . . . . . . . . . . . . . . . . . . . . . 126

4.5 Electric Field: Homogeneous, Point Charges, Polarizability . . . . . . . . . . . . . . . . . . . . . . 131

5 Structure and Reactivity 1335.1 Run Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

5.1.1 RunType control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1345.1.2 Nuclear Gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

5.2 Geometry Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1355.2.1 Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1355.2.2 Optimization strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

5.3 Transition State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1395.3.1 Transition State Reaction Coordinate (TSRC) . . . . . . . . . . . . . . . . . . . . . . . . . 140

5.4 Linear Transit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1415.4.1 Linear Transit (new branch) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1425.4.2 Linear Transit (old branch) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1435.4.3 Symmetry in a Linear Transit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

5.5 Intrinsic Reaction Coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1445.5.1 IRC start direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1455.5.2 Forward / Backward IRC paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

5.6 Climbing-Image Nudged Elastic Band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1465.6.1 Recommendations concerning the NEB method . . . . . . . . . . . . . . . . . . . . . . . . 147

5.7 Special Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1485.7.1 Initial Hessian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1485.7.2 Constrained optimizations, LT (new branch) . . . . . . . . . . . . . . . . . . . . . . . . . . 1485.7.3 Constrained optimizations, IRC, NEB, LT (old branch) . . . . . . . . . . . . . . . . . . . . 1505.7.4 Restrained optimizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1535.7.5 Symmetry versus constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

5.8 Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1545.8.1 Analytical Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1545.8.2 Numerical Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1575.8.3 Mobile Block Hessian (MBH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1585.8.4 Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Gibbs free energy change for a gas phase reaction . . . . . . . . . . . . . . . . . . . . . . . . 1605.8.5 Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1615.8.6 Isotope Shifts of Vibrational Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . 1625.8.7 Scanning a Range of Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1625.8.8 Moments of inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

6 Spectroscopic properties 1656.1 IR spectra, (resonance) Raman, VROA, VCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

6.1.1 IR spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1656.1.2 Raman scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1656.1.3 Raman Intensities for Selected Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . 1666.1.4 Resonance Raman: excited-state finite lifetime . . . . . . . . . . . . . . . . . . . . . . . . 168

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6.1.5 Resonance Raman: excited-state gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . 1686.1.6 VROA: (Resonance) vibrational Raman optical activity . . . . . . . . . . . . . . . . . . . . 1726.1.7 Vibrational Circular Dichroism (VCD) spectra . . . . . . . . . . . . . . . . . . . . . . . . . 1736.1.8 Vibrationally resolved electronic spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

6.2 Time-dependent DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1736.2.1 General remarks on the Response and Excitation functionality . . . . . . . . . . . . . . . . 1746.2.2 Analysis options for TDDFT (excitation energies and polarizabilities) . . . . . . . . . . . . 1776.2.3 Time-dependent Current DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Magnetic properties within TDCDFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1786.3 Excitation energies: UV/Vis, X-ray, CD, MCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

6.3.1 Excitation energies, UV/Vis spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179Tamm-Dancoff approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181Full XC kernel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181Plasmons in Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182Accuracy and other technical parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

6.3.2 Excitation energies for open-shell systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 1836.3.3 Spin-flip excitation energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1846.3.4 Select (core) excitation energies, X-ray absorption . . . . . . . . . . . . . . . . . . . . . . . 184

State selective optimization excitation energies . . . . . . . . . . . . . . . . . . . . . . . . . 185Modify range of excitation energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186Excitations as orbital energy differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187Quadrupole intensities in X-ray spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . 188

6.3.5 XES: X-ray emission spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1886.3.6 Excitation energies and Spin-Orbit coupling . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Perturbative inclusion of spin-orbit coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . 189Self-consistent spin-orbit coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190Highly approximate spin-orbit coupled excitation energies open shell molecule . . . . . . . . 191

6.3.7 CV(n)-DFT: Constricted Variational DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . 1926.3.8 TD-DFT+TB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1946.3.9 sTDA, sTDDFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1956.3.10 CD spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1966.3.11 MCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1976.3.12 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

NTO: Natural Transition Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200SFO analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201Charge-transfer descriptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

6.4 Excited state (geometry) optimizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2026.4.1 Nuclear gradients only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

6.5 Vibrationally resolved electronic spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2046.5.1 AH-FC: Adiabatic Hessian Franck-Condon . . . . . . . . . . . . . . . . . . . . . . . . . . 2046.5.2 VG-FC: Vertical Gradient Franck-Condon . . . . . . . . . . . . . . . . . . . . . . . . . . . 2056.5.3 FCF program: Franck-Condon Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2056.5.4 FCF example absorption and fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . 2086.5.5 FCF Example phosphorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

6.6 (Hyper-)Polarizabilities, ORD, magnetizabilities, Verdet constants . . . . . . . . . . . . . . . . . . . 2116.6.1 RESPONSE: (Hyper-)Polarizabilities, ORD . . . . . . . . . . . . . . . . . . . . . . . . . . 211

RESPONSE: Polarizabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211RESPONSE: Accuracy and convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212RESPONSE: Hyperpolarizabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213RESPONSE: Optical rotation dispersion (ORD) . . . . . . . . . . . . . . . . . . . . . . . . . 213

6.6.2 AORESPONSE: Lifetime effects, (Hyper-)polarizabilities, ORD, magnetizabilities, Verdetconstants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

AORESPONSE: Polarizabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214AORESPONSE: Technical parameters and expert options . . . . . . . . . . . . . . . . . . . 214

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AORESPONSE: Damped First Hyperpolarizabilities . . . . . . . . . . . . . . . . . . . . . . 215AORESPONSE: Damped Second Hyperpolarizabilities . . . . . . . . . . . . . . . . . . . . . 216AORESPONSE: ORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216AORESPONSE: magnetizabilities, Verdet constants, Faraday B term . . . . . . . . . . . . . 217AORESPONSE: Raman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217Applications of AORESPONSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

6.6.3 POLTDDFT: Damped Complex Polarizabilities . . . . . . . . . . . . . . . . . . . . . . . . 218UV/Vis spectra, CD spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219Reduced fit set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

6.6.4 Van der Waals dispersion coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220DISPER program: Dispersion Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

6.7 Ligand Field and Density Functional Theory (LFDFT) . . . . . . . . . . . . . . . . . . . . . . . . . 2226.7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2226.7.2 Input description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

6.8 NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2256.8.1 NMR Chemical Shifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

Important notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226Input options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

6.8.2 Paramagnetic NMR Chemical Shifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2316.8.3 NMR spin-spin coupling constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232Input file for CPL: TAPE21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234Running CPL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236Practical Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

6.9 ESR/EPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2416.9.1 ESR/EPR g-tensor and A-tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2416.9.2 ESR/EPR Q-tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2436.9.3 ESR/EPR Zero-field splitting (D-tensor) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

6.10 Nuclear Quadrupole Interaction (EFG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2446.11 Mössbauer spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

7 Transport properties 2477.1 Charge transfer integrals (transport properties) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

7.1.1 Charge transfer integrals with the TRANSFERINTEGRALS key . . . . . . . . . . . . . . . 2477.1.2 Charge transfer integrals with FDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

7.2 GREEN: Non-self-consistent Green’s function calculation . . . . . . . . . . . . . . . . . . . . . . . 2517.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2517.2.2 Wide-band-limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2537.2.3 Input options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2547.2.4 Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2557.2.5 GREEN with ADF-GUI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

8 Analysis 2578.1 Molecules built from fragments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2578.2 Bond energy analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

8.2.1 Bond energy details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2598.2.2 Notes on double-hybrid functionals and MP2 . . . . . . . . . . . . . . . . . . . . . . . . . 2608.2.3 Total energy evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2608.2.4 Interacting Quantum Atoms (IQA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

8.3 Localized Molecular Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2628.3.1 Perturbed Localized Molecular Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263

8.4 Advanced charge density and bond order analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2648.4.1 Charges, Populations, Bond orders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2648.4.2 ETS-NOCV: Natural Orbitals for Chemical Valence . . . . . . . . . . . . . . . . . . . . . . 265

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8.4.3 Adfnbo, gennbo: NBO analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267NBO analysis of EFG, NMR chemical shifts, NMR spin-spin coupling . . . . . . . . . . . . 268

8.4.4 QTAIM: Atoms in Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272Local, atomic, and non-local properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272ADF2AIM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274Aromaticity index with QTAIM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274

8.4.5 Conceptual DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275Global, atomic, and non-local descriptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275Domains of the dual descriptor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276

8.4.6 adf2damqt: DAMQT interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2788.4.7 FOD: fractional orbital density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

8.5 Controlling printed Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2798.5.1 Print / NoPrint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2798.5.2 Debug . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2838.5.3 Eprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2848.5.4 Eprint subkeys vs. Print switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2858.5.5 Other Eprint subkeys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2908.5.6 Reduction of output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

8.6 Results on Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2928.6.1 Electronic Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2938.6.2 Mulliken populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2938.6.3 Hirshfeld charges, Voronoi deformation density . . . . . . . . . . . . . . . . . . . . . . . . 2938.6.4 Multipole derived charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2948.6.5 Charge model 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2958.6.6 Bond order analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2958.6.7 Dipole moment, Quadrupole moment, Electrostatic potential . . . . . . . . . . . . . . . . . 2968.6.8 Fragments and Basis Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2968.6.9 MO analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2968.6.10 Bond energy analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

8.7 Densf: Volume Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2988.7.1 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2998.7.2 Result: TAPE41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

8.8 Dos: Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3118.8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3128.8.2 Mulliken population analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3138.8.3 Density of states analyses based on Mulliken population analysis . . . . . . . . . . . . . . . 3148.8.4 Generalizations of OPDOS, GPDOS, PDOS . . . . . . . . . . . . . . . . . . . . . . . . . . 3158.8.5 Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

8.9 VCD Analysis: VCDtools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3178.9.1 General Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3188.9.2 General Coupled Oscillator Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3188.9.3 Available options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

8.10 PyFrag: Activation Strain Model Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3208.10.1 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3208.10.2 Running PyFrag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3208.10.3 Specifying the Trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3208.10.4 Molecular Fragments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3208.10.5 ADF Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3208.10.6 Analysis Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

9 Accuracy and Efficiency 3239.1 Precision and Self-Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

9.1.1 SCF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323Main options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

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Energy-DIIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326Augmented Roothaan-Hall (ARH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

9.1.2 Numerical Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328Becke Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329Voronoi grid (deprecated) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330Atomic radial grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

9.1.3 Density fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3339.1.4 Hartree-Fock RI scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334

Old Hartree-Fock RI scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3359.1.5 MP2 scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3379.1.6 Dependency (basis set, fit set) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339

9.2 Basis Set Superposition Error (BSSE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3409.3 Control of Program Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

9.3.1 Limited execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3409.3.2 Skipping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3419.3.3 Ignore checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3419.3.4 Parallel Communication Timings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342

9.4 Technical Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3429.4.1 GPU Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3429.4.2 Memory usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3449.4.3 Direct SCF: recalculation of data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3449.4.4 Vector length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3459.4.5 Tails and old gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3459.4.6 Linearscaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3459.4.7 All Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3479.4.8 Full Fock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3479.4.9 Electrostatic interactions from Fit density . . . . . . . . . . . . . . . . . . . . . . . . . . . 3479.4.10 Save info . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

10 Restarts 34910.1 Restart files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34910.2 The restart key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35010.3 Structure of the restart file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

11 Recommendations and Troubleshooting 35511.1 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

11.1.1 Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35511.1.2 Electronic Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

Spin-unrestricted versus spin-restricted, Spin states . . . . . . . . . . . . . . . . . . . . . . . 35611.1.3 What basis set should I use in ADF? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

ZORA or non-relativistic calculation? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357Large or small molecule? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357Frozen core or all-electron? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358Diffuse functions needed? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358Normal or even-tempered basis? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359What accuracy do the basis sets give? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

11.1.4 Relativistic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36111.2 Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

11.2.1 License file corrupt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36111.2.2 Recover from Crash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36211.2.3 Memory Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36211.2.4 SCF troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36311.2.5 Geometry Optimization troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365

New Branch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366

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Old Branch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366Very short bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367

11.2.6 Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367Imaginary Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367Geometry-displacement numbers in the logfile are not contiguous . . . . . . . . . . . . . . . 368

11.2.7 Input ignored . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36811.2.8 SFO Populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36911.2.9 Error Aborts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36911.2.10 Warnings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369

12 ADF as an AMS engine 371

13 Appendices 37313.1 Basis set file format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

13.1.1 Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37313.1.2 Example of a basis set file: Calcium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37513.1.3 Extending a basis set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376

13.2 Elements of the Periodic Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37713.3 Multiplet States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

13.3.1 Multiplet energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38113.4 Dirac program: relativistic core potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38813.5 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390

13.5.1 Schönfliess symbols and symmetry labels . . . . . . . . . . . . . . . . . . . . . . . . . . . 39013.5.2 Molecular orientation requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391

13.6 Binary result files, KF browser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39213.6.1 TAPE21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392

Contents of TAPE21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393Using Data from TAPE21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411

13.6.2 TAPE13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41313.6.3 KF browser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

13.7 Error messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41313.8 Warnings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414

14 Examples 42714.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42714.2 Model Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428

14.2.1 Special exchange-correlation functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428Example: Asymptotically correct XC potentials: CO . . . . . . . . . . . . . . . . . . . . . . 428Example: Meta-GGA energy functionals: OH . . . . . . . . . . . . . . . . . . . . . . . . . . 430Example: Hartree-Fock: HI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436Example: B3LYP: H2PO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438Example: Long-range corrected GGA functional LCY-BP: H2O . . . . . . . . . . . . . . . . 440Example: Range-separated functional CAMY-B3LYP: H2O . . . . . . . . . . . . . . . . . . 441Example: Single point MP2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441Example: Water Dimer SOS-AO-PARI-MP2 . . . . . . . . . . . . . . . . . . . . . . . . . . 442Example: Single point B2GPPLYP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443Example: Water-MeOH - DODSCAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445Example: Grimme Molecular Mechanics dispersion-corrected functionals (DFT-D3-BJ) . . . 446Example: Density-Dependent Dispersion Correction (dDsC): CH4-dimer . . . . . . . . . . . 450Example: DFT-ulg Dispersion Correction: Benzene dimer T-shaped . . . . . . . . . . . . . . 451

14.2.2 ZORA and spin-orbit Relativistic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452Example: ZORA Relativistic Effects: Au2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 452Example: Spin-Orbit coupling: Bi and Bi2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 453Example: Spin-Orbit unrestricted non-collinear: Tl . . . . . . . . . . . . . . . . . . . . . . . 456

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Example: Excitation energies including spin-orbit coupling: AuH . . . . . . . . . . . . . . . 459Example: ZORA, X2C and RA-X2C: HgI2 = Hg + I2 . . . . . . . . . . . . . . . . . . . . . 460

14.2.3 Solvents, other environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461Example: COSMO: HCl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461Example: solvation model SM12: Acetamide . . . . . . . . . . . . . . . . . . . . . . . . . . 463Example: Electric Field, Point Charge(s): N2 and PtCO . . . . . . . . . . . . . . . . . . . . 464Example: 3D-RISM: Glycine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467Example: ReaxFF: ADF geometry optimization using ReaxFF forces . . . . . . . . . . . . . 469

14.2.4 FDE: Frozen Density Embedding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471Example: FDE: H2O in water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471Example: FDE freeze-and-thaw: HeCO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486Example: FDE energy: NH3-H2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492Example: FDE energy: unrestricted fragments: Ne-H2O . . . . . . . . . . . . . . . . . . . . 495Example: FDE geometry optimization: H2O-Li(+) . . . . . . . . . . . . . . . . . . . . . . . 497Example: Geometry optimization ICW FDE/sSDFT . . . . . . . . . . . . . . . . . . . . . . 499Example: FDE NMR shielding: Acetonitrile in water . . . . . . . . . . . . . . . . . . . . . . 501Example: FDE NMR spin-spin coupling: NH3-H2O . . . . . . . . . . . . . . . . . . . . . . 504Example: Subsystem TDDFT, coupled FDE excitation energies . . . . . . . . . . . . . . . . 508Example: FDE and COSMO: H2O-NH3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519Example: FDE and COSMO: H2O-NH3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

14.2.5 QM/MM calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52314.2.6 Quild: Quantum-regions Interconnected by Local Descriptions . . . . . . . . . . . . . . . . 52314.2.7 DIM/QM: Discrete Interaction Model/Quantum Mechanics . . . . . . . . . . . . . . . . . . 523

Example: DRF: H2O and H2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523Example: DRF: hyperpolarizability H2O in water . . . . . . . . . . . . . . . . . . . . . . . . 524Example: DRF: scripting tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533Example: DRF2: Polarizability N2 on Ag68 + H2O . . . . . . . . . . . . . . . . . . . . . . 535Example: CPIM: excitation energies N2 on silver cluster Ag68 . . . . . . . . . . . . . . . . . 542Example: CPIM: polarizability N2 on silver cluster Ag68 . . . . . . . . . . . . . . . . . . . 544Example: PIM: H2O on Ag2689 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551Example: PIM: Polarizability with local fields . . . . . . . . . . . . . . . . . . . . . . . . . . 552Example: PIM: optimization N2 on silver cluster Ag68 . . . . . . . . . . . . . . . . . . . . . 554Example: PIM: polarizability N2 on silver cluster Ag68 . . . . . . . . . . . . . . . . . . . . 557Example: PIM: Raman scattering N2 on silver cluster Ag68 . . . . . . . . . . . . . . . . . . 564Example: PIM: SEROA calculation N2 on silver cluster Ag68 . . . . . . . . . . . . . . . . . 566Example: PIM: Multipole Method N2 on silver cluster Ag1415 . . . . . . . . . . . . . . . . 569

14.3 Structure and Reactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59414.3.1 Geometry Optimizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594

Example: Geometry Optimization: H2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594Example: Restraint Geometry Optimization: H2O . . . . . . . . . . . . . . . . . . . . . . . 598Example: Constraint Geometry Optimization: H2O . . . . . . . . . . . . . . . . . . . . . . . 600Example: Initial Hessian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603Example: Geometry optimization with an external electric field or point charges: LiF . . . . . 606Example: Excited state geometry optimization with a constraint: CH2O . . . . . . . . . . . . 607

14.3.2 Transition States, Linear Transits, Intrinsic Reaction Coordinates . . . . . . . . . . . . . . . 608Example: LT, Frequencies, TS, and IRC: HCN . . . . . . . . . . . . . . . . . . . . . . . . . 608Example: Transition state search with the CINEB method: HCN . . . . . . . . . . . . . . . . 618Example: TS search using partial Hessian: C2H6 internal rotation . . . . . . . . . . . . . . . 620Example: Relativistic ZORA TS search: CH4 + HgCl2 CH3HgCl + HCl . . . . . . . . 622Example: TS reaction coordinate: F- + CH3Cl . . . . . . . . . . . . . . . . . . . . . . . . . 623Example: Constraint Linear Transit: H2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624Example: (non-)Linear Transit: H2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625

14.3.3 Total energy, Multiplet States, S2, Localized hole, CEBE . . . . . . . . . . . . . . . . . . . 626Example: Total Energy calculation: H2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626

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Example: Multiplet States: [Cr(NH3)6]3+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629Example: Calculation of S2: CuH+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633Example: Localized Hole: N2+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635Example: Broken spin-symmetry: Fe4S4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636Example: Core-electron binding energies (CEBE): NNO . . . . . . . . . . . . . . . . . . . . 637Example: Constrained DFT: H2O+ ... H2O . . . . . . . . . . . . . . . . . . . . . . . . . . . 641

14.4 Spectroscopic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64214.4.1 IR Frequencies, (resonance) Raman, VROA, VCD, Franck-Condon factors . . . . . . . . . 642

Example: Numerical Frequencies: NH3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642Example: Numerical Frequencies, spin-orbit coupled ZORA: UF6 . . . . . . . . . . . . . . . 645Example: Numerical Frequencies, accurate Hartree-Fock: H2O . . . . . . . . . . . . . . . . 648Example: Numerical Frequencies of an excited state: PH2 . . . . . . . . . . . . . . . . . . . 649Example: Analytic Frequencies: CN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651Example: Analytic Frequencies: CH4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652Example: Analytic Frequencies, scalar ZORA: HI . . . . . . . . . . . . . . . . . . . . . . . 652Example: Mobile Block Hessian (MBH): Ethanol . . . . . . . . . . . . . . . . . . . . . . . . 653Example: Mobile Block Hessian: CH4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655Example: Raman: NH3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656Example: Raman: HI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659Example: Resonance Raman, excited state finite lifetime: HF . . . . . . . . . . . . . . . . . 662Example: Resonance Raman, excited state gradient: Formaldehyde . . . . . . . . . . . . . . 663Example: Vibrational Raman optical activity (VROA): H2O2 . . . . . . . . . . . . . . . . . 664Example: Resonance VROA: H2O2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665Example: Vibrational Circular Dichroism (VCD): NHDT . . . . . . . . . . . . . . . . . . . . 667Example: Franck-Condon Factors: NO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667

14.4.2 Excitation energies: UV/Vis spectra, X-ray absorption, CD, MCD . . . . . . . . . . . . . . 670Example: Excitation energies and polarizability: Au2 . . . . . . . . . . . . . . . . . . . . . . 670Example: Excitation energies open shell molecule: CN . . . . . . . . . . . . . . . . . . . . . 671Example: Spin-flip excitation energies: SiH2 . . . . . . . . . . . . . . . . . . . . . . . . . . 673Example: TDHF excitation energies: N2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674Example: excitation energies CAM-B3LYP: Pyridine . . . . . . . . . . . . . . . . . . . . . . 677Example: CAMY-B3LYP excitation energies: H2O . . . . . . . . . . . . . . . . . . . . . . . 678Example: Full XC kernel in excitation energy calculation: H2O+ . . . . . . . . . . . . . . . 679Example: Use of xcfun in excitation energy calculations: H2O . . . . . . . . . . . . . . . . . 679Example: Core excitation energies: TiCl4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 680Example: X-Ray Absorption and Emission Quadrupole Oscillator strengths at the Cl K-edge:

TiCl4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686Example: (Core) Excitation energies including spin-orbit coupling: Ne . . . . . . . . . . . . 689Example: Excitation energies perturbative spin-orbit coupling: AgI . . . . . . . . . . . . . . 694Example: Excitation energies including spin-orbit coupling for open shell: PbF . . . . . . . . 694Example: Excited state geometry optimization: N2 . . . . . . . . . . . . . . . . . . . . . . . 695Example: Spin-flip excited state geometry optimization: CH2 . . . . . . . . . . . . . . . . . 697Example: Circular Dichroism (CD) spectrum: DMO . . . . . . . . . . . . . . . . . . . . . . 699Example: CD spectrum, hybrid functional: Twisted ethene . . . . . . . . . . . . . . . . . . . 700Example: MCD: H2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701Example: MCD including zero-field splitting: H2O . . . . . . . . . . . . . . . . . . . . . . . 702Example: CV(n)-DFT excitation energies: Formamide . . . . . . . . . . . . . . . . . . . . . 703Example: TD-DFT+TB excitation energies: beta-Carotene . . . . . . . . . . . . . . . . . . . 705Example: sTDA excitation energies: Adenine . . . . . . . . . . . . . . . . . . . . . . . . . . 708Example: sTDDFT excitation energies: Adenine . . . . . . . . . . . . . . . . . . . . . . . . 708Example: sTDA excitation energies RS functional: Bimane . . . . . . . . . . . . . . . . . . 709Example: sTDA excitation energies wB97: TCNE-Benzene . . . . . . . . . . . . . . . . . . 711

14.4.3 (Hyper-)Polarizabilities, dispersion coefficients, ORD, magnetizabilities, Verdet constants . 713Example: Polarizabilities including spin-orbit coupling: AgI . . . . . . . . . . . . . . . . . . 713

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Example: damped first hyperpolarizability: LiH . . . . . . . . . . . . . . . . . . . . . . . . . 713Example: damped second hyperpolarizability: LiH . . . . . . . . . . . . . . . . . . . . . . . 716Example: Verdet constants: H2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719Example: Dispersion Coefficients: HF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720Example: Optical Rotation Dispersion (ORD): DMO . . . . . . . . . . . . . . . . . . . . . . 721Example: ORD, lifetime effects (key AORESPONSE): DMO . . . . . . . . . . . . . . . . . 722Example: Polarizability: first order perturbed density . . . . . . . . . . . . . . . . . . . . . . 724Example: Hyperpolarizabilities of He and H2 . . . . . . . . . . . . . . . . . . . . . . . . . . 739Example: Damped Verdet constants: Propene . . . . . . . . . . . . . . . . . . . . . . . . . . 740Example: Static magnetizability: H2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 741Example: Dynamic magnetizability: H2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743Example: Time-dependent current-density-functional theory: C2H4: . . . . . . . . . . . . . . 744Example: Damped complex polarizabilities with POLTDDFT: Au10 . . . . . . . . . . . . . . 745

14.4.4 Ligand Field DFT (LFDFT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746Example: Ligand Field DFT: Co 2+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746Example: Ligand Field DFT: f-d transitions in Pr 3+ . . . . . . . . . . . . . . . . . . . . . . 747

14.4.5 NMR chemical shifts and spin-spin coupling constants . . . . . . . . . . . . . . . . . . . . 749Example: NMR Chemical Shifts: HBr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 749Example: NMR Chemical Shifts: HgMeBr . . . . . . . . . . . . . . . . . . . . . . . . . . . 751Example: NMR Chemical Shifts, SAOP potential: CH4 . . . . . . . . . . . . . . . . . . . . 754Example: NMR Nucleus-independent chemical shifts (NICS): PF3 . . . . . . . . . . . . . . 754Example: NMR with B3LYP: PF3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756Example: NMR Spin-spin coupling constants: C2H2 . . . . . . . . . . . . . . . . . . . . . . 759Example: NMR Spin-spin coupling constants, hybrid PBE0: HF . . . . . . . . . . . . . . . . 762Example: NMR Spin-spin coupling constants, finite nucleus: PbH4 . . . . . . . . . . . . . . 763

14.4.6 ESR/EPR g-tensor, A-tensor, Q-tensor, ZFS . . . . . . . . . . . . . . . . . . . . . . . . . . 767Example: ESR g-tensor, A-tensor, Q-tensor, D-tensor: HfV . . . . . . . . . . . . . . . . . . . 767Example: ESR g-tensor, A-tensor, self consistent spin-orbit coupling: VO . . . . . . . . . . . 769Example: ESR g-tensor, A-tensor, perturbative spin-orbit coupling: HgF . . . . . . . . . . . . 771Example: ESR spin-restricted and spin-unrestricted: TiF3 . . . . . . . . . . . . . . . . . . . 773Example: ESR, X2C and RA-X2C: PdH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 776Example: Zero-field splitting (ZFS), ESR D-tensor: NH . . . . . . . . . . . . . . . . . . . . 778Example: ZFS D tensor, including direct electron spin-spin part: Phenylnitrene . . . . . . . . 779

14.4.7 EFG, Mössbauer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 780Example: Mössbauer spectroscopy: Ferrocene . . . . . . . . . . . . . . . . . . . . . . . . . 780Example: Mössbauer with X2C: Hg compounds . . . . . . . . . . . . . . . . . . . . . . . . 783

14.5 Transport properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78514.5.1 Charge transfer integrals (transport properties) . . . . . . . . . . . . . . . . . . . . . . . . . 785

Example: Charge transfer integrals: AT base pair . . . . . . . . . . . . . . . . . . . . . . . . 785Example: Charge transfer integrals with FDE: water dimer . . . . . . . . . . . . . . . . . . . 787Example: Charge Recombination Calculation of Toluene and TCNE . . . . . . . . . . . . . . 798Example: XCDFT: Charge Separation of an ethylene dimer . . . . . . . . . . . . . . . . . . 813

14.5.2 Non-self-consistent Green’s function calculation . . . . . . . . . . . . . . . . . . . . . . . 826Example: DOS and transmission: Aluminium . . . . . . . . . . . . . . . . . . . . . . . . . . 826Example: Gold electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 829Example: Benzenedithiol junction: Wide-Band-Limit . . . . . . . . . . . . . . . . . . . . . . 833Example: Benzenedithiol junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835

14.6 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83814.6.1 Fragment orbitals, bond energy decomposition . . . . . . . . . . . . . . . . . . . . . . . . 838

Example: Compound Fragments: Ni(CO)4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 838Example: Fragments: PtCl4H2 2- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 841Example: Spin-unrestricted Fragments: H2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 843Example: Bond Energy analysis open-shell fragments: PCCP . . . . . . . . . . . . . . . . . 847Example: Analysis of NaCl using ionic fragments: Na+ and Cl- . . . . . . . . . . . . . . . . 852

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Example: Electron Pair bonding in NaCl: open shell fragments . . . . . . . . . . . . . . . . . 854Example: Bond Energy analysis meta-GGA, (meta-)hybrids: Zn2, Cr2, CrH . . . . . . . . . . 860Example: unrestricted EDA: Cu(C2H4)2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864Example: unrestricted fragments: CH3I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865Example: Spin-Orbit SFO analysis: TlH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 868Example: Activation Strain Model Analysis using PyFrag . . . . . . . . . . . . . . . . . . . 870

14.6.2 Localized orbitals, bond orders, charge analysis . . . . . . . . . . . . . . . . . . . . . . . . 871Example: (Perturbed) localized molecular orbitals in twisted Ethene . . . . . . . . . . . . . . 871Example: Charge model 5 (CM5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 872Example: Bond Orders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873

14.6.3 ETS-NOCV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875Example: NOCV: ethylene – Ni-diimina and H+ – CO . . . . . . . . . . . . . . . . . . . . . 875Example: NOCV: CH2 – Cr(CO)5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 880Example: NOCV: CH3 – CH3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 882

14.6.4 QTAIM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885Example: QTAIM Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885Example: QTAIM Reactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 886Example: IQA/QTAIM analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887Example: QTAIM Aromaticity indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 889

14.6.5 DOS: Density of states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 890Example: Density of States: Cu4CO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 890

14.6.6 Third party analysis software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 892Example: adf2aim: convert an ADF TAPE21 to WFN format (for Bader analysis) . . . . . . . 892Example: NBO analysis: adfnbo, gennbo . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893Example: NBO analysis: EFG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895Example: NBO analysis: NMR chemical shift . . . . . . . . . . . . . . . . . . . . . . . . . . 897Example: NBO analysis: NMR spin-spin coupling . . . . . . . . . . . . . . . . . . . . . . . 899Example: Multiple excited state gradients: H2O . . . . . . . . . . . . . . . . . . . . . . . . . 901Example: Calculation of overlap of primitive basis functions . . . . . . . . . . . . . . . . . . 902

14.7 Accuracy and Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90314.7.1 BSSE, SCF convergence, Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903

Example: Basis Set Superposition Error (BSSE): Cr(CO)5 +CO . . . . . . . . . . . . . . . . 903Example: Troubleshooting SCF convergence: Ti2O4 . . . . . . . . . . . . . . . . . . . . . . 908Example: Rescan frequencies: NH3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915

14.7.2 Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 916Example: Multiresolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 916

14.8 Scripting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91914.8.1 Prepare an ADF job and generate a report . . . . . . . . . . . . . . . . . . . . . . . . . . . 919

Example: Single point for multiple xyz files: Bakerset . . . . . . . . . . . . . . . . . . . . . 919Example: Basis set and integration accuracy convergence test: Methane . . . . . . . . . . . . 919Example: adfprep: Replace atom with ligand . . . . . . . . . . . . . . . . . . . . . . . . . . 920

14.9 List of Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 921

15 Required Citations 92715.1 General References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92715.2 Feature References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927

15.2.1 Coordinates, basis sets, fragments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92715.2.2 Geometry optimizations, transition states, and reaction paths . . . . . . . . . . . . . . . . . 92815.2.3 Model Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92815.2.4 Relativistic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92815.2.5 Solvents and other environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92915.2.6 Frequencies, IR Intensities, Raman, VCD . . . . . . . . . . . . . . . . . . . . . . . . . . . 93015.2.7 Time-Dependent DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93115.2.8 LFDFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934

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15.2.9 NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93415.2.10 ESR/EPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93515.2.11 Transport properties: Non-self-consistent Green’s function . . . . . . . . . . . . . . . . . . 93615.2.12 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93615.2.13 Accuracy and efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 937

15.3 External programs and Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 937

16 Keywords 939

Index 943

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CHAPTER

ONE

GENERAL

1.1 Introduction

ADF (Amsterdam Density Functional) is a Fortran program for calculations on atoms and molecules (in gas phaseor solution). It can be used for the study of such diverse fields as molecular spectroscopy, organic and inorganicchemistry, crystallography and pharmacochemistry. A separate program BAND is available for the study of periodicsystems: crystals, surfaces, and polymers. The COSMO-RS program is used for calculating thermodynamic propertiesof (mixed) fluids.

The underlying theory is the Kohn-Sham approach to Density-Functional Theory (DFT). This implies a one-electronpicture of the many-electron systems but yields in principle the exact electron density (and related properties) and thetotal energy.

If ADF is a new program for you we recommend that you carefully read the section Technical remarks, Terminology(page 7), which presents a discussion of a few ADF-typical aspects and terminology. This will help you to understandand appreciate the output of an ADF calculation.

ADF has been developed since the early 1970s (at that time called HFS, later AMOL, see also refs.123, mainly bythe two theoretical chemistry groups of, respectively, the Vrije Universiteit in Amsterdam ( http://www.chem.vu.nl/en/research/division-theoretical-chemistry/index.asp) and the University of Calgary, Canada. Other researchers havealso contributed. As a major research tool of these academic development groups, ADF is in continuous developmentand retains a firm basis in the academic world.

Maintenance and distribution of the commercial (export) version of the program is done by Software for Chemistry &Materials B.V. (SCM) ( http://www.scm.com), a company based in Amsterdam, formally split off from the theoreticalchemistry group in Amsterdam but practically still very much a part of it. Documentation such as User manuals,Installation instructions, Examples, Theoretical documents can be found at the SCM web site.

Publications based on research with ADF should include appropriate references to the program. We recommend thatreferences are made both to the program itself and to publications related to its development and structure. See theRequired Citations (page 927).

The installation of the Amsterdam Density Functional program package (ADF) is explained in the Installation manual.This User’s Guide describes how to use the program, how input is structured, what files are produced, and so on. Somespecial applications of ADF are described in the Examples (page 427).

Where references are made to the operating system (OS) and to the file system on your computer the terminology ofUNIX type OSs is used.

1 E.J. Baerends, D.E. Ellis and P. Ros, Self-consistent molecular Hartree-Fock-Slater calculations I. The computational procedure, ChemicalPhysics 2, 41 (1973) (https://doi.org/10.1016/0301-0104(73)80059-X)

2 E.J. Baerends and P. Ros, Evaluation of the LCAO Hartree-Fock-Slater method: Applications to transition-metal complexes, InternationalJournal of Quantum Chemistry 14, S12, 169 (1978) (https://doi.org/10.1002/qua.560140814)

3 G. te Velde, F.M. Bickelhaupt, E.J. Baerends, C. Fonseca Guerra, S.J.A. van Gisbergen, J.G. Snijders, T. Ziegler, Chemistry with ADF, Journalof Computational Chemistry 22, 931 (2001) (https://doi.org/10.1002/jcc.1056)

1

http://www.chem.vu.nl/en/research/division-theoretical-chemistry/index.asphttp://www.chem.vu.nl/en/research/division-theoretical-chemistry/index.asphttp://www.scm.comhttps://doi.org/10.1016/0301-0104(73)80059-Xhttps://doi.org/10.1016/0301-0104(73)80059-Xhttps://doi.org/10.1002/qua.560140814https://doi.org/10.1002/qua.560140814https://doi.org/10.1002/jcc.1056https://doi.org/10.1002/jcc.1056

ADF Manual, Amsterdam Modeling Suite 2019.3

The ADF package is in continuous development to extend its functionality and applicability, to increase its efficiencyand user-friendliness, and of course to correct errors. We appreciate comments and suggestions for improvement ofthe software and the documentation.

1.1.1 Functionality

• Single Point calculation

• Geometry Optimization

• Transition States

• Frequencies and thermodynamic properties

• Tracing a Reaction Path

• Computation of any electronic configuration

• Excitation energies, oscillator strengths, transition dipole moments, (hyper)polarizabilities, Van der Waals dis-persion coefficients, CD spectra, ORD, MCD, VCD, magnetizabilities, Verdet constants, using Time-DependentDensity Functional Theory (TDDFT)

• ESR (EPR) g-tensors, A-tensors, NQCCs

• NMR chemical shifts and spin-spin coupling constants

• Mössbauer spectroscopy

• Transport properties: charge transfer integrals, NEGF

• Various other molecular properties

• Treatment of large systems and environment by the QM/MM (Quantum Mechanics / Molecular Mechanics)hybrid approach.

1.1.2 Applicability

All elements of the periodic table can be used (Z = 1-118). For each of the elements, basis sets of different sizes areavailable, ranging from minimal to high quality. Special basis sets are provided for relativistic calculations within theZORA approach and for response calculations that require additional diffuse basis functions.

1.1.3 Model Hamiltonian

• A choice of Density Functionals, both for the Local Density Approximation (LDA), for the Generalized GradientApproximation (GGA), for (range-separated) hybrid functionals (not for all properties available), and for meta-GGA functionals (not for all properties available) are available.

• Spin: restricted or unrestricted

• Relativistic effects: scalar approximation and spin-orbit (double-group symmetry), using the (now recom-mended) ZORA or the (previously used) Pauli formalism, X2C

• Environment: Solvent Effects, Homogeneous Electric Field, Point Charges (Madelung Fields), QM/MMmethod, FDE

• Constrained Density Functional Theory

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1.1.4 Analysis

• Decomposition of the bond energy in ‘chemical’ components (steric interaction, Pauli repulsion, orbital interac-tions...)

• Natural orbitals for chemical valence (ETS-NOCV)

• Representation of data (Molecular Orbital coefficients, Mulliken Populations) in terms of the constituent chem-ical fragments in the molecule, along with the conventional representation in elementary basis functions

• Atomic charge determination by Hirshfeld analysis and by Voronoi analysis, multipole derived charges, alongwith the classical Mulliken populations, and Mayer bond orders

• QTAIM analysis based on local, atomic and non-local descriptors for bonding description.

• Conceptual DFT descriptors including global, atomic, non-local ones and a detailed analysis of the dual descrip-tor’s domains (predominantly electrophilic or nucleophilic regions).

• Bond energy decomposition based on the interacting quantum atoms (IQA) approach and using QTAIM real-space partition. Any atom-atom interaction can be evaluated and decomposed into electrostatic (ionic) andexchange (covalent) contributions.

• Localized molecular orbitals

1.1.5 Technical

• The implementation is based upon a highly optimized numerical integration scheme for the evaluation of matrixelements of the Fock operator, property integrals involving the charge density, etc. The code has been vectorizedand parallelized.

• Basis functions are Slater-Type Orbitals (STOs). A database is available with several basis sets for each atom inthe periodic table of elements.

• The Coulomb potential is evaluated via an accurate fitting of the charge density.

• A frozen core facility is provided for an efficient treatment of the inner atomic shells.

• Extensive use is made of point group symmetry. Most of the commonly encountered symmetry groups areavailable.

• Linear scaling techniques are used to speed up calculations on large molecules

1.1.6 Fragments

ADF has a fragment oriented approach: the poly-atomic system to be computed is conceptually built up from frag-ments, the molecular one-electron orbitals are calculated as linear combinations of fragment orbitals, and final analyzesof e.g. the bonding energy are in terms of fragment properties. The fragments may be single atoms or larger moieties.

When you compute a system in terms of its constituent fragments, these fragments must have been computed beforeand their properties must be passed on to the current calculation. This is done by attaching fragment files, whichcontain the necessary information. A fragment file is simply the standard result file of an ADF calculation on thatfragment.

When using Basic Atoms as fragments, you do not need to create the fragment files yourself. Instead, you may usethe Basis key, and ADF will create the required fragment files automatically. We therefore recommend this feature forstarting ADF users.

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Basic atoms

Obviously there must be a set of fundamental fragments that are not defined in terms of smaller fragments. ThereforeADF has two modes of execution: the normal mode, using fragments, and the create mode, in which a fundamentalfragment is generated. Such a fundamental fragment must be a single atom, spherically symmetric and spin-restricted(i.e. spin-𝛼 and spin-𝛽 orbitals are spatially identical, they are equally occupied, and fractional occupations are applied,if necessary, to distribute the electrons equally over symmetry-degenerate states). Such a fundamental fragment isdenoted a basic atom. The basic atoms are the smallest building blocks from which any ‘real’ calculations are started.

One should realize that the basic atoms are artificial objects that are convenient in the computational approach butthat do not necessarily represent real atoms very well (in fact, usually not at all). The bonding energy of a moleculewith respect to basic atoms, for instance, should be corrected for this discrepancy in order to get a decent comparisonagainst experimental data. See ref.4 for a discussion and for examples of applicable values.

A basic atom is computed in the conventional way. The one-electron orbitals are determined as linear combinations ofbasis functions; the frozen core approximation may be applied for the inner atomic states; a particular type of densityfunctional can be chosen, et cetera. You may have, for instance, different basic Copper atoms by using different basissets, by choosing different levels of frozen core approximations, or by applying different density functionals.

Automatic mode

If you are using ‘Basic Atom’ fragments only, you do not need to prepare the corresponding fragment files yourself.Instead, add the BASIS block key to the ADF input, and ADF will generate all the required fragment files for you. Thismakes your job scripts and ADF inputs simpler, it ensures that consistent options for the create runs and molecularruns are used, and you will be sure that the fragment files used have been created by the same release of ADF.

1.1.7 Slater-type basis sets

ADF uses Slater-Type Orbitals (STO’s) as basis functions. Slaters can display the correct nuclear cusp and asymptoticdecay.

𝑓(r) = 𝑌𝑙𝑚𝑟𝑛𝑒−𝜁𝑟

The center of the function is at a nucleus, the 𝑌𝑙𝑚 are spherical harmonics, and the exponential factor 𝜁 (zeta) deter-mines the long-range decay of the function.

ADF comes with a database of thoroughly tested basis set files, ranging in quality from single-zeta to quadruple-zetabasis sets with various diffuse and polarization functions. All-electron and frozen-core basis sets are available for allelements, including lanthanides and actinides. The frozen-core approximation can be used to considerably reduce thecomputation time for systems with heavy nuclei, in a controlled manner.

1.2 What’s new in ADF 2019

1.2.1 New features in ADF2019.3

In comparison to ADF 2019.1, the 2019.3 release offers the following new functionality:

• Model Hamiltonians

– MP2 (page 68) and double hybrid (page 65) energy calculations4 E.J. Baerends, V. Branchadell and M. Sodupe, Atomic reference-energies for density functional calculations, Chemical Physics Letters 265,481

(1997) (https://doi.org/10.1016/S0009-2614(96)01449-2)

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https://doi.org/10.1016/S0009-2614(96)01449-2https://doi.org/10.1016/S0009-2614(96)01449-2

ADF Manual, Amsterdam Modeling Suite 2019.3

– D4(EEQ) (page 78) dispersion correction by Grimme and coworkers

• Spectroscopy using ADF as an AMS engine (page 371)

– VG-FC vibrationally resolved electronic spectra via AMS

– VG-FC Resonance Raman via AMS

• Analysis

– Energy decomposition analysis with real unrestricted fragments (page 53)

• Accuracy and performance

– Improved the fit set for quality GOOD in the RI-HartreeFock scheme (page 334)

1.2.2 New features in ADF2019.1

In comparison to ADF 2018, the ADF 2019 release offers the following new functionality:

• Spectroscopy: AOResponse (page 214): Raman spectra in combination with spin-orbit coupling

• Restructured QTAIM section (page 272)

• New Conceptual DFT section (page 275) introducing extra reactivity descriptors (global, atomic and non-localones). A new option is dedicated to the analysis of the dual descriptor domains (predominantly electrophilic ornucleophilic regions).

• Optimize Spin Polarization (page 47)

• DRF gradients: expert option (page 97)

1.3 Feature List

1.3.1 Model Hamiltonians

• XC energy functionals and potentials (page 58)

– LDA (page 59), GGA (page 60), meta-GGA (page 62), model potentials (page 73)

– (meta-)hybrid (page 63), range-separated (page 69), double-hybrids (page 65)

– dispersion corrected (page 76)

• Relativistic effects (ZORA and spin-orbit coupling) (page 83)

• Solvents and other environments

– COSMO (page 86), SM12 (page 93), QM/MM , pdb2adf, DIM/QM (page 97), SCRF (page 117), FDE(page 107), 3D-RISM (page 126), QUILD

• Homogeneous electric field and point charges (page 131)

1.3.2 Structure and Reactivity

• Geometry Optimizations (page 135)

• Linear Transit (page 141), Transition States (page 139), CI-NEB (page 146), TSRC (page 140)

• Intrinsic Reaction Coordinate (page 144)

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• Excited state optimizations with TDDFT gradients (page 202)

Optimizations (page 135) can be done in Cartesian, internal, and delocalized coordinates. Various restraints (page 153)and constraints ( 1 (page 150), 2 (page 148)) can be imposed. Hessians (page 154) are available analytically for mostGGAs, and numerically otherwise. Preoptimization is possible with DFTB.

1.3.3 Spectroscopic properties

• Vibrational Spectroscopy

– IR frequencies and intensities (page 154)

– Mobile Block Hessian (MBH) (page 158), Vibrational Circular Dichroism (VCD) (page 172)

– Raman intensities (page 165)

– Resonance Raman from frequency-dependent polarizabilities (page 168) or excited state gradients(page 168)

– vibrational Raman optical activity (VROA) (page 171)

– Franck-Condon Factors (page 205)

• Excitation energies: UV/Vis spectra, X-ray absorption, CD, MCD (page 179)

– UV/Vis spectra, oscillator strengths (page 179), open shell excitations (page 183), spin-orbit coupled ex-citations (page 189)

– core excitations (page 184), Quadrupole oscillator strengths (page 188), XES (page 188)

– TD-DFT+TB (page 194), sTDA, sTDDFT (page 195)

– vibrationally resolved electronic spectra (page 205)

– excited state optimizations (page 202)

– CD spectra (page 179), MCD (page 197)

• (Hyper-)Polarizabilities, dispersion coefficients, ORD, magnetizabilities, Verdet constants (page 211)

– frequency-dependent (hyper)polarizabilities (page 211), lifetime effects (page 214)

– van der Waals dispersion coefficients (page 220)

– optical rotatory dispersion (ORD) (page 213)

– magnetizability (page 214)

– Verdet constants, Faraday terms (page 214)

• NMR

– chemical shifts (page 226)

– spin-spin couplings (page 232)

• ESR (EPR)

– g-tensors (g-factor) (page 241)

– A-tensor (hyperfine interaction) (page 241)

– zero-field splitting (ZFS, D-tensor) (page 241)

• Nuclear quadrupole interaction (EFG), ESR Q-tensor (page 244)

• Mössbauer (page 245), NRVS (page 246)

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1.3.4 Charge transport properties

• charge transfer integrals (page 247)

• Non-self-consistent Green’s function calculation (page 251)

1.3.5 Analysis

• Fragments (page 3)

• Bond energy decomposition (page 12), ETS-NOCV (page 265)

• Advanced charge density and MO analysis

– Mulliken (page 293), Multipole-derived charges (page 294)

– Hirshfeld charges, Voronoi deformation density (page 293), CM5 charges (page 295), FOD (page 278)

– bond orders: Mayer, Nalewajski-Mrozek (page 295)

– Bader (QT-AIM) (page 272), Conceptual DFT (page 275)

– NB0 6.0 (page 267)

– (partial) DOS (page 311)

• Molecular symmetry (page 9), Schönfliess symbols and symmetry labels (page 390)

1.3.6 Accuracy and Efficiency

• Slater-type basis sets (page 8)

– Z = 1 to 118, all electron, frozen-core, non-relativistic and relativistic (page 31)

– SZ, DZ, DZP, TZP, TZ2P, QZ4P, even-tempered, diffuse (page 31)

• Integration scheme (page 328)

• Parallelization (page 14)

• Linear scaling / distance cut-offs (page 345)

• Density fit (page 333) and frozen core approximation (page 9)

• SCF convergence: simple damping, DIIS, EDIIS, ADIIS, LISTi, ARH (page 324)

1.4 Technical remarks, Terminology

A few words about ADF as regards its technical setup and the names and abbreviations used in this manual. Referencesto these will be made in the discussion of output and print switches.

1.4.1 Density functional theory

The underlying theory of the ADF package is the Kohn-Sham approach to the Density-Functional Theory (DFT).Kohn-Sham DFT is an important first-principles computational method to predict chemical properties accurately andto analyze and interpret these in convenient and simple chemical terms.

The reasons for its popularity and success are easy to understand. In the first place, the DFT approach is in principleexact. In particular, the Kohn-Sham method implies a one-electron picture of the many-electron systems but yields

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in principle the exact electron density (and related properties) and the total energy. The exact exchange-correlation(XC) functional is unknown, but the currently