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Supplementary Information
Key Role of Higher Order Symmetry and Electrostatic Ligand Field Design in the Magnetic Relaxation of Low-coordinate Er(III) Complexes **
Saurabh Kumar Singh, Bhawana Pandey, Gunasekaran Velmurugan and Gopalan Rajaraman[a]
Electronic Supplementary Material (ESI) for Dalton Transactions.This journal is © The Royal Society of Chemistry 2017
Supplementary Information
Table S1. Selected structural-parameters of complex 1, 2, and 3.
Selected structural parameters Complex 1 Complex 2 Complex 3Er–N1 (Å) 2.23118 2.22287 2.24883
Er–N1 (Å) 2.25056 2.37436 2.24660
Er–N1 (Å) 2.24634 2.30658 2.24184
Er–Cl (Å) 2.52846 2.38642 2.5712
N1-Er–N2 () 115.2 111.01 117.6
N2-Er–N3 () 118.1 113.1 114.6
N1-Er–N3 () 115.3 116.1 116.9
Cl-Er–N1 () 102.7 108.2 100.6
Cl-Er–N2 () 101.9 102.9 101.1
Cl-Er–N3 () 100.3 102.9 101.5
N1-N2–N3–Er () 23.1 30.1 20.8
(Å) 0.45 0.61 0.43
Table S2. SHAPE computed minimal distortion from the ideal geometry in coordination number four. vTBPY stands for axially vacant trigonal bipyramid and T-4 stands for the tetrahedral geometry.
Selected structural parameters vTBPY-4 T-4Complex 1 2.103 0.381
Complex 2 2.425 0.185
Complex 3 2.069 0.423
Supplementary Information
Figure S1. SINGLE_ANISO computed principal magnetization orientation of each KDs of complex 1a.
Figure S2. SINGLE_ANISO computed principal magnetization orientation of the ground state KD of complex 1a with different level of theory. Red line represent computed orientation using BS1 basis set, Blue line represent using BS2 level of theory, green represent the computed orientation for complex 1a + 4 layers of point charge at BS1 level of theory.
12
34
8
7
5
6
Supplementary Information
Table S3. SINGLE_ANISO computed composition of wave functions of the ground J=15/2 of Er(III) for complex 1a,@BS1 level of theory
wave function 1 wave function 2 wave function 3 wave function 4 wave function 5mJ real imag real imag real imag real imag real imag
-15/2-13/2-11/2-9/2-7/2-5/2-3/2-1/21/23/25/27/29/211/213/215/2
-0.473976-0.0009150.000050-0.013635-0.0316960.012702-0.0109990.0023380.002682-0.0037830.000186-0.0007700.002117-0.000007-0.000105-0.000251
0.872206-0.006737-0.0227010.1052490.017402-0.005959-0.031893-0.0056020.002041-0.007150-0.0022890.0016050.0028150.000340-0.0014750.000000
-0.000120-0.001246-0.0003020.001463-0.001778-0.0021000.0044760.0005120.006038-0.0227710.0113000.030424-0.098987-0.0199700.0054820.992671
0.000220-0.000797-0.0001560.003205-0.000090-0.0009300.0067380.0033310.000621-0.024893-0.008315-0.019540-0.038274-0.0107960.0040200.000000
-0.000254-0.163976-0.0112380.0026090.0025110.0027680.0026770.013199-0.0075920.0036730.021540-0.042868-0.082305-0.0815510.543853-0.016042
-0.000282-0.0801320.0005640.013691-0.0104600.0001010.0081890.005050-0.044900-0.010280-0.0060060.018292-0.016334-0.0154990.8069340.000000
-0.010734-0.963583-0.0660840.067209-0.015089-0.009949-0.0051820.0384480.012584-0.0078770.0019270.0060930.0119210.007100-0.1692680.000380
-0.0119220.135742-0.0502370.050238-0.044098-0.0200270.009608-0.0244000.0064300.0034900.001990-0.008865-0.0072210.008729-0.0682460.000000
0.0000400.014311-0.015012-0.007141-0.008230-0.013600-0.0031220.0638770.0171990.032708-0.1193460.0580800.059220-0.935046-0.052116-0.018286
0.0000170.011408-0.017190-0.0068460.0189800.0044050.0036000.0044290.018321-0.007169-0.099343-0.082461-0.1520440.229346-0.0408250.000000
wave function 6 wave function 7 wave function 8 wave function 9 wave function 10-15/2-13/2-11/2-9/2-7/2-5/2-3/2-1/21/23/25/27/29/211/213/215/2
-0.0168430.063899-0.7719680.0046500.0213910.1486070.027335-0.0229750.0605610.001474-0.0108120.000191-0.0092430.0205200.017623-0.000044
-0.007120-0.017312-0.575306-0.1631030.098568-0.0450370.0193380.0101790.0207910.004532-0.0093520.0206870.003525-0.009989-0.0049360.000000
-0.005219-0.0122010.009863-0.0076370.0562180.015103-0.0532780.001772-0.0675070.106333-0.103145-0.1689460.8549880.0197330.0225960.116748
0.007829-0.0064070.003293-0.1113240.0008330.017742-0.080702-0.033833-0.0002260.2118150.0417450.1342600.2897260.1335650.0772290.000000
0.0647550.051728-0.100192-0.233146-0.2054220.091945-0.1172690.0372550.029134-0.037600-0.006386-0.0304890.088394-0.002731-0.0014360.009409
-0.0971440.061637-0.0905020.8721170.066109-0.062671-0.205961-0.0562960.017291-0.089094-0.0224070.0472400.0681010.0100330.0137060.000000
0.000193-0.000064-0.0408150.061817-0.2630790.193568-0.0021650.106315-0.2128370.0776060.146490-0.775375-0.068627-0.022836-0.0259270.009102
-0.000530-0.0286560.081526-0.0440850.0557810.1425300.134194-0.116110-0.131732-0.055664-0.2810060.066059-0.154238-0.034342-0.0589630.000000
0.003110-0.0465580.024475-0.121513-0.326979-0.3141440.078828-0.0510940.1454450.126860-0.0678250.1423020.0625520.0905650.026910-0.000564
-0.008555-0.0445110.033194-0.1171910.7061550.041675-0.053920-0.245036-0.0602510.043811-0.230615-0.228193-0.043037-0.0105070.009850-0.000000
wave function 11 wave function 12 wave function 13 wave function 14 wave function 15-15/2-13/2-11/2-9/2-7/2-5/2-3/2-1/21/23/25/27/29/211/213/215/2
-0.0001770.0225670.0187780.052401-0.056177-0.4393280.103641-0.0099840.1809670.068969-0.503922-0.361758-0.0431060.0154650.0204660.005739
0.000105-0.003423-0.110080-0.024496-0.208492-0.441623-0.1899720.002476-0.134358-0.1459890.135878-0.031791-0.068540-0.113853-0.0264720.000000
-0.0049290.031135-0.071589-0.0019240.294439-0.502412-0.1340030.2242430.0098430.1863070.1511830.058521-0.0575530.072502-0.021137-0.000206
0.0029390.012256-0.0898710.080946-0.2125680.141360-0.0900720.022726-0.0029860.110093-0.6043050.2078460.0057960.0849330.0086170.000000
-0.0005240.0015600.043469-0.0660700.0728720.105900-0.1823900.2673550.179925-0.783835-0.0647630.0012920.1215910.0504420.016955-0.011560
0.0014240.0028560.002147-0.1588600.009540-0.001580-0.248711-0.145317-0.158331-0.070342-0.188252-0.002171-0.172792-0.0108480.0014500.000000
-0.003992-0.0044940.027600-0.2041510.002484-0.154308-0.204662-0.2107240.228701-0.1704270.038052-0.0162120.126272-0.012996-0.0021410.001517
0.0108490.016413-0.0435930.054442-0.000463-0.1257870.7599070.114181-0.200727-0.257056-0.0988400.0716830.1168640.041537-0.0024500.000000
-0.0064310.0174210.008897-0.0814640.101446-0.045363-0.2010920.707404-0.4311190.071731-0.1749630.062187-0.0169390.051112-0.006761-0.000000
0.0004650.029188-0.038080-0.0078310.214988-0.1792710.2461230.0621990.093311-0.1061730.166562-0.1178500.044455-0.0481070.0151540.000000
wave function 16
Supplementary Information
-15/2-13/2-11/2-9/2-7/2-5/2-3/2-1/21/23/25/27/29/211/213/215/2
-0.000000 0.007837 0.054451 0.020104 0.070532 0.186530 0.079208 0.436730 0.701069 0.218334-0.032304-0.085662-0.080686-0.011623 0.015269 0.006448
-0.000000 0.014627 0.044292 0.043116 0.113053 0.153498 0.100718 0.061947 -0.113101 0.230965 0.182078 0.221750 0.013691 -0.037339 -0.030369 0.000000
Supplementary Information
Table S4. SINGLE_ANISO computed composition of wave functions of the ground J=15/2 of Er(III) for complex 1a + 4 layers of point charges, @BS1 level of theory
wave function 1 wave function 2 wave function 3 wave function 4 wave function 5mJ real imag real imag real imag real imag real imag
-15/2-13/2-11/2-9/2-7/2-5/2-3/2-1/21/23/25/27/29/211/213/215/2
0.000067-0.000829 0.000028 0.002676 0.000580-0.001658-0.006112 0.002228-0.003989-0.026788-0.001893 0.020945 0.091985-0.025750-0.004468 0.994407
-0.000007 0.000608-0.000098 0.000088-0.000752 0.000490-0.001443 0.000980 0.000836-0.008628 0.007782-0.017634 0.017925 0.001866-0.002358 0.000000
0.989014 0.004198-0.025805-0.089622 0.022665 0.002692-0.025745 0.004054 0.002114 0.005929-0.001700-0.000655 0.002652-0.000038-0.000887-0.000068
-0.103423-0.002810 0.000823 0.027394 0.015361 0.007543 0.011367 0.000416-0.001206-0.002071-0.000315-0.000688-0.000366-0.000094-0.000519 0.000000
0.012647-0.659336 0.092556 0.067297 0.024623-0.011582 0.004229 0.029788-0.011531-0.005201-0.001573 0.004285-0.008883 0.003666 0.117396-0.000002
-0.000303 0.725667 0.004632 0.005605 0.026033-0.007654-0.009723-0.026757-0.002538 0.002323-0.000347-0.005919 0.004064 0.004904 0.089666 0.000000
-0.000002 -0.115212 0.003547 0.008977 0.004426 0.001564 -0.005255 0.011467 0.030421 -0.004461 -0.011395 -0.023991 0.067143 -0.092418 -0.676549 -0.012650
0.000000 0.092456-0.004990 0.003850 0.005814-0.000385-0.002197-0.002813 0.026035-0.009619 0.007929 0.026616-0.007218 0.006851-0.709646 0.000000
-0.013448 -0.064497 0.003147 -0.119850 -0.060320 -0.086914 -0.003066 0.009552 -0.013646 0.004272 0.004724 0.012360 0.004017 0.027187 -0.004027 0.000499
-0.019088-0.044892-0.966836 0.106372 0.051216-0.113392 0.026659 0.019165 0.058303-0.006139-0.012828 0.004107-0.006302-0.002739 0.012264 0.000000
wave function 6 wave function 7 wave function 8 wave function 9 wave function 10-15/2-13/2-11/2-9/2-7/2-5/2-3/2-1/21/23/25/27/29/211/213/215/2
-0.000288 0.007707-0.013419-0.002839-0.010476-0.007766 0.002558 0.039803-0.021168 0.020028 0.142754 0.007128-0.017933-0.788569 0.073845-0.023350
-0.000408-0.010356-0.023803 0.006913-0.007739 0.011250-0.007028-0.044734 0.003229-0.017860 0.005745-0.078809 0.159240 0.559411 0.026871-0.000000
-0.003405 0.002534 0.000570 0.014185 0.030934 -0.024517 -0.112606 0.026301 -0.048330 -0.171297 -0.063176 0.152089 0.914215 -0.066226 0.024804 -0.101172
-0.001385-0.003559 0.000457-0.012945-0.010807 0.006170-0.022713 0.028913 0.014764-0.133005 0.060029-0.139146 0.123070-0.114922 0.064088 0.000000
-0.093714-0.047126-0.104650-0.893198 0.088443 0.035898-0.208790 0.039204 0.035257 0.112864-0.020385-0.024582 0.008262-0.000700 0.001007 0.003676
-0.038125 0.050016 0.081495-0.230506 0.186200 0.079410 0.058650 0.031888-0.016870 0.021394-0.014954-0.021667 0.017336 0.000208 0.004251 0.000000
0.000979-0.030048-0.011732-0.133163-0.223411-0.294362 0.019847-0.136502-0.225355 0.075816 0.131140 0.555610-0.108489 0.083683-0.031537-0.003721
0.004317 0.011490 0.024185 0.006212-0.490042 0.196245 0.090371-0.086625 0.064460 0.057569 0.003628-0.345314-0.011162 0.009907-0.037131 0.000000
-0.000823 0.043188 0.028175 0.034887-0.213839-0.032550 0.072915-0.013008-0.114677-0.092523 0.126260 0.527325-0.023402-0.020990 0.004558-0.004427
-0.003629 0.022541 0.079418 0.103331 0.618237-0.127088 0.061202 0.234032-0.113955 0.000638-0.330484 0.109462-0.131238 0.016792-0.031845 0.000000
wave function 11 wave function 12 wave function 13 wave function 14 wave function 15-15/2-13/2-11/2-9/2-7/2-5/2-3/2-1/21/23/25/27/29/211/213/215/2
-0.001966-0.029122-0.089315 0.004162 0.237745 0.426724-0.161072-0.224587 0.010088-0.110761 0.322315-0.008244-0.028895-0.026176-0.016157 0.000661
0.003471 0.002421 -0.039298 -0.077287 -0.271660 -0.266712 -0.028891 -0.006011 -0.021980 -0.141242 -0.588141 -0.164408 -0.014788 -0.105406 0.002328 0.000000
-0.000326 -0.009989 -0.078813 -0.001374 -0.138989 0.670603 -0.068305 0.024097 0.105461 -0.054249 -0.442385 0.353549 -0.069299 -0.009827 0.016460 -0.003990
0.000575 0.012911 -0.074727 0.032431 -0.088204 0.009427 -0.165987 0.002056 -0.198377 0.154389 0.239842 -0.072971 -0.034471 0.097082 -0.024146 0.000000
0.009621 -0.011236 -0.016678 0.064538 0.025813 0.167456 0.402203 0.043554 0.052944 0.290896 -0.040392 -0.011996 0.132626 -0.005588 -0.000605 -0.000701
0.005438-0.010687-0.050041-0.198977 0.025113 0.033755 0.707726-0.217210-0.279804 0.092099-0.096964-0.049952 0.065980-0.032388-0.002544 0.000000
0.000610-0.001778 0.020803 0.147925 0.035024-0.082878-0.298558-0.091600 0.068973 0.698402-0.162388 0.034829 0.041732-0.039144 0.015041 0.011052
0.000345 0.001917 -0.025445 0.007826 -0.037582 0.064535 -0.062972 0.269635 -0.210523 -0.418184 -0.053019 -0.009159 -0.204977 0.035355 -0.003774 0.000000
-0.000000-0.014918 0.052232-0.042167 0.150824-0.211679 0.142108-0.400837 0.538578-0.290388 0.078884 0.013123-0.055179 0.011767 0.013617-0.005222
0.000000 0.006417-0.023562-0.008487-0.002446 0.028403 0.024376 0.318286-0.419236-0.023218 0.182910-0.213623 0.047012 0.034083-0.022945 0.000000
wave function 16
Supplementary Information
-15/2-13/2-11/2-9/2-7/2-5/2-3/2-1/21/23/25/27/29/211/213/215/2
-0.003761-0.025726-0.015174 0.072355 0.157668 0.070100-0.193012-0.678730-0.509495-0.085425-0.172145-0.110313-0.024478-0.053962-0.015195 0.000000
0.003623-0.007076-0.032709-0.004429 0.144733 0.186453 0.218198 0.071770 0.048899 0.116153 0.126414 0.102884 0.035368 0.019272 0.005730 0.000000
Supplementary Information
Table S5. CASSCF+RASSI computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex 1a with experimental geometry + 4 layers of point charges@BS1 level of theory.
J multiplet Energies of KDs gXX gyy gzz
4I15/2
0.0043.48987.625
140.706194.393286.802337.393374.963
0.0120940.1697970.1309570.74469
6.6633295.9906325.3007630.862937
0.0156220.1856780.2088020.8293856.1467185.8256274.0924234.759339
17.8315515.4705112.8733
10.172235.1344953.7816282.53549
13.62414
-3.85.15.8
107.67.4
29.287.3
Supplementary Information
Table S6. SINGLE_ANISO computed crystal field parameters of complex 1a and 1 along with experimental geometry + 4 layers of point charges on complex 1a@ BS1 level of theory.
It is important to note here that charges on complex 1a are computed in presence of all the solvent and counter ions.
Complex 1a@BS1level Complex 1@BS1level Complex 1a + 4 layers of point charges@ BS1level
k q 𝐵𝑘𝑞 𝐵𝑘
𝑞
2
-2 -1 0 1 2
0.1393E+00-0.6100E+
00-0.1861E+01-0.3198E+00 0.2322E+00
0.2548E+00-0.4451E+00-0.2025E+01-0.7480E+00 0.8028E-01
0.1662E+00 0.5757E+00-0.2086E+01 0.3969E+00 0.2434E+00
4
-4-3-2-1 0 1 2 3 4
0.2129E-02-0.3783E-01 0.2220E-02 0.4983E-02 0.2427E-02 0.1747E-02 0.8557E-03 0.2971E-01 0.1889E-02
0.1015E-02-0.5741E-02 0.2361E-02 0.2920E-02 0.2708E-02 0.4812E-02-0.1771E-02 0.4772E-01 0.3092E-03
0.2001E-02 0.2874E-01 0.2169E-02-0.4196E-02 0.2546E-02-0.2391E-02 0.5322E-04-0.3736E-01 0.6654E-03
6
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-0.1241E-03 0.9443E-04-0.3122E-04 0.2291E-03-0.4617E-04-0.1482E-04-0.5076E-05 0.5294E-05-0.1717E-04-0.2707E-03-0.4299E-04 0.9535E-04 0.1929E-03
0.2125E-03 -0.1424E-04 -0.4003E-04 -0.3595E-04 -0.2798E-04 0.2628E-05 -0.4135E-05 -0.3985E-05 0.4374E-04 -0.3550E-03 -0.2761E-04 -0.5276E-04 0.5941E-04
-0.2258E-05-0.8952E-04-0.3158E-04-0.1647E-03-0.4172E-04 0.4486E-05-0.4636E-05-0.1692E-05-0.5501E-06 0.3231E-03-0.2960E-04-0.7555E-05 0.2276E-03
Supplementary Information
Table S7. CASSCF+RASSI computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex 1a @BS2 level of theory.
Table S8. CASSCF computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex 2 @BS1 level of theory.
Table S9. CASSCF+RASSI computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex 1m@BS1 level of theory
J multiplet Energies of KDs gXX gyy gzz
4I15/2
0.00030.765.4113.0162.8254.7304.5339.7
0.024850.186460.079370.744066.869113.698932.144210.92027
0.030620.198760.311950.945976.098845.121693.577835.37676
17.7917515.4185412.8083810.197075.119136.916755.1974513.12406
-5.46.5
8.538114.49487.51865.41486.142
J multiplet Energies of KDs gXX gyy gzz
4I15/2
0.027.9 43.6 76.2 113.4 170.9 226.6268.6
0.023890.092060.252222.329954.248160.211880.727660.139209
0.068550.203780.577032.768254.990531.872511.202890.42886
17.6389716.8606913.178979.513938.68748
14.73415013.5682516.44025
-33.226.619.787.363.887.282.1
J multiplet Energies of KDs gXX gyy gzz
4I15/2
0161.426261.512350.14439.757557.428639.055693.349
0.001420.055810.0147650.3101124.1886735.0557012.7935240.971017
0.0016680.0581840.0868320.3814184.7911674.7090032.8614615.731619
17.8767915.4777113.0014810.424947.0864563.8710314.8081712.90281
-0.9660.132.0263.62291.90457.8989.765
Supplementary Information
Table S10. CASSCF computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex 1TP.
Table S11. CASSCF computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex 1TD.
Table S12. CASSCF computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex [Dy{N(SiMe3)2}3Cl]–
J multiplet Energies of KDs gXX gyy gzz
4I15/2
051.42385.907
135.075198.806285.643349.839388.713
0.00190.1990360.1573480.0661754.0546214.1081860.8388610.4111
0.002170.2000860.2155670.1263054.2184594.2238950.9552218.612665
17.870715.5108313.0471510.5707
7.3812265.0079523.5190311.130831
-1.45
1.1610.8381.5153.6133.3640.391
J multiplet Energies of KDs gXX gyy gzz
4I15/2
015.49235.82955.91562.078147.307161.036172.334
0.5210270.3836630.4712031.2275293.2481599.3757794.93665511.27383
0.6009910.6586840.6706061.5693725.8941586.4843333.078256.934004
15.0997312.1293211.6155714.539619.853561.4796790.2398510.950846
-4.6099.0815.40393.5616.81683.7793.106
J multiplet Energies of KDs gXX gyy gzz
6H15/2
054.226123.096233.874377.023544.323689.929773.974
0.6646313.2628790.5599391.6176580.1426170.0042360.0158240.00136
2.472766.1104363.0653251.8374470.179940.0318980.0186220.001667
17.569889.0453046.6031979.42195512.205114.6506117.2419619.78676
-65.44590.52190.16889.95690.16590.3287.518
Supplementary Information
Table S13. CASSCF computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex [Er{N(SiMe3)2}3F]–
Table S14. CASSCF computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex [Er{N(SiMe3)2}3Br]–
Table S15. CASSCF computed low-lying energies of eight KDs and associated g-tensors along with the deviation from the principal magnetization axes for complex [Er{N(SiMe3)2}3I]–
J multiplet Energies of KDs gXX gyy gzz
4I15/2
016.38345.28989.167112.052174.819210.499240.277
0.1211080.0804330.7998085.2326430.0676187.6646346.5555380.716746
0.5790420.4023551.2012715.7497
0.0832865.7096634.5943373.798668
15.983814.4376710.089057.72094117.621663.0234342.16594414.2454
-45.32831.79572.38334.53527.81428.55478.523
J multiplet Energies of KDs gXX gyy gzz
4I15/2
057.71199.813146.593195.211289.116339.438376.757
0.010220.188980.1035830.7507855.2522196.1808795.1297950.886134
0.0114430.2040220.2741520.8809736.0374086.0641813.946124.974724
17.8332515.4441412.8194810.115156.9229333.6569122.49378313.43618
-0.5832.094.29595.9194.82632.50588.43
J multiplet Energies of KDs gXX gyy gzz
4I15/2
075.558126.829178.584230.973326.11378.756417.494
0.0059960.153720.0780980.7126076.7281716.1366285.0320030.891076
0.0063110.1629510.2225110.8226986.1230335.8362043.9895195.005495
17.8514315.4616512.8500410.126195.203453.7530612.50210113.41989
-1.1961.4652.209
109.1786.12434.40688.808
Supplementary Information
Table S16. CASSCF+NEVPT2 computed low-lying spin-free states and spin-orbit states along with the ground state g-tensor for complex [Er{N(SiMe3)2}3F]–.
CASSCF computed spin-free states
NEVPT2 computed spin-free states
NEVPT2 computed energies of low-lying eight
KDs.00
15.649115.649142.645242.645283.157783.1577108.7098108.7098219.4431219.4431291.8797291.8797345.6315345.6315
Main value of g-tensor (NEVPT2)
0.832.737.872.9136139.5156.6186.8193.2229.5242255.513075.213095.213099.91312813132.713196.113199.713230.613239.913257.413257.922114.222138.822155.322226.822234.122287.522291.622321.822327.922596.322608.722662.52268022714.522715.722845.822922.1
24327.524410.124415.524460.124503.824511.429350.429353.129371.829445.229452.329467.429506.529513.335467.235475.535476.935644.235651.535717.735731.635744.635793.9416254162541799.841799.841925.641925.842040.842041.942144.54215142225.742245.142282.842321.842331.842398.942399.7
4345743473.743495.143501.547528.947531.247568.347582.547595.747615.847627.347634.847649.847665.547677.450852.750873.65088050890.550934.550944.950957.451349.451384.35143551503.351539.557943.257985.258262.858422.95850782098.282100.482169.982214.982298.182304.382347.582359.5
216.423.136.999.4104.2139.5226.7238332.1347.738112671.312693.812699.912765.51277012817.512818.312839.712847.8128841288421313.921349.521365.921459.92147121479.621490.821544.321564.421596.121637.321637.421646.821655.321784.221863.621923.5
23717.323874.523893.824066.82416824198.42800228010.728117.728135.928176.628183.328348.228370.833415.833432.633435.833662.233676.833728.233755.33381533904.739619.839619.839964.239964.240231.84023240492.740493.140735.340739.240966.440993.741002.941006.241008.241157.741162.8
42044.242067.542079.242098.445632.545633.745730.845738.345751.145796.345808.745810.145849.345868.745883.94793047946.24794747981.148063.148077.34808148928.44894149092.349103.949143.854651.354690.955510.555646.955657.578400.578400.878605.578660.578852.978862.778953.679009.3
gzz = 16.468435gyy = 0.597440gxx = 0.156503
Supplementary Information
24019.124019.52409824098.724129.724130.124210.32421224310.2
43162.743162.743325.943335.743341.243346.843371.243413.743416.1
82372.8111260.3111390.1111781.1111867.3111913.3112034.4112066.9
23109.323109.523210.723211.123231.723232.623482.923485.523693.5
41522.441522.541854.541870.241909.441926.341928.641974.541988.4
79010.4105840105983.1106882.8106915.9107085.5107217.8107285.5
Supplementary Information
Table S17. CASSCF+NEVPT2 computed low-lying spin-free states and spin-orbit states along with the ground state g-tensor for complex [Er{N(SiMe3)2}3Cl]–.
CASSCF computed spin-free states
NEVPT2 computed spin-free states
NEVPT2 computed energies of low-lying eight
KDs.00
55.448655.448674.73674.736
104.2855104.2855162.6404162.6404265.9998265.9998342.8371342.8371399.1787
Main value of g-tensor (NEVPT2)
144.645.189.293.5136.1205.5257.8261.4318.5336.8355.913084.513103.213108.913161.713168.813244.813252.713277.213277.613298.613299.222064.82210122120.422226.522232.72237622380.122490.622490.82260922613.422638.422666.722683.42275522979.823029.6
24487.524606.22461124671.924720.524731.129313.629325.629329.729439.729500.329508.429647.829653.935560.335561.8355743570335705.935737.835744.735769.935821.540995.740995.74142441424.141768.341768.542053.142053.64228442288.642457.242477.34257842610.342648.442727.942732.4
43614.94363243664.243666.84752847528.64761547618.647660.947700.847729.747732.747754.647771.447777.450733.650735.150847.650877.850967.650987.351056.651485.651505.851627.651661.95170157709.657734.658588.658659.958717.581941.881943.28216382211.682404.982406.482527.982560.9
3.659.460.462.466.177.3163.7245.5254.5359.6381.342012714.712728.812733.212778.312784.612855.112863.712884.412885.112906.41290721380.321413.621432.421532.12153721619.821638.321663.82167021673.121678.221683.421793.121793.321952.222008.122070.8
23812.523936.723943.424007.524056.824067.528174.328181.528255.628260.128319.128329.328543.628560.433686.233690.33374933872.833875.333938.333946.133972.734062.239678.639678.640069.240069.240400.340400.640676.140677.140903.140911.741072.841106.841205.641237.441277.341359.941363.7
42286.942298.542335.142339.245861.645862.745934.245937.345993.546031.346061.146064.146083.346098.646102.748165.948224.748253.148258.748338.5483514841049120.749136.349389.949411.249424.354929.654963.655837.255901.75590978794.278795.879020.879072.579249.379250.479375.279408.5
gzz = 17.884149gyy = 0.004298gxx = 0.002807
Supplementary Information
23741.823741.92390423904.524100.824100.924300.624302.724467.1
4307443074.243287.843287.943444.443445.943536.84355243596.8
82590.1110787.8110920.4111859.9111888.6112340112444.4112543.1
23097.523097.523226.823227.42341123411.223615.92361823790.9
41738.341738.341959.941960.14213342136.242210.242239.142262.3
79439.6106392.2106531.6107452.5107487.1107918.9108025.2108072.2
Supplementary Information
Table S18. CASSCF+NEVPT2 computed low-lying spin-free states and spin-orbit states along with the ground state g-tensor for complex [Er{N(SiMe3)2}3Br]–.
CASSCF computed spin-free states
NEVPT2 computed spin-free states
NEVPT2 computed energies of low-lying eight
KDs.00
93.471193.4711122.9477122.9477150.4914150.4914213.9123213.9123327.8859327.8859421.9603421.9603
Main value of g-tensor (NEVPT2)
167.367.6115.4119.8162.6235289.2292.7353.1371.9392.313105.213123.613129.213182.713189.913266.313273.713313.513313.913325.113325.822076.122114.222133.822245.722251.82240722410.522541.82254222619.222623.922651.822692.722707.122781.123019.523070.3
24534.624659.524664.32472824776.824788.129324.529339.929344.429459.429526.829534.629692.429698.435592.435593.735608.735727.435732.835770.735776.135798.335851.840913.240913.241382.441382.441763.341763.542074.142074.64232342327.842507.942529.342637.242668.44271042789.742794.8
43675.843702.943734.443738.847550.647551.14764347646.647699.147739.147770.847773.647794.847811.547816.450728.550729.550866.75089950989.751010.151097.951535.151554.151682.25171651755.157692.1577165864158712.158809.88193981940.482184.882234.782444.682446.182581.882615.6
3.1106.2106.3107.7112.7121.4192.6301.2313.6441.6467.2512.41255112564.112568.112614.612621.112692.812702.91274512745.612754.112754.820688.120728.820761.120771.520789.920944.820983.720994.321003.521115.821120.121176.621229.82128321287.721447.621447.9
23377.623526.32353423613.423672.223678.927041.527051.927111.727140.227190.827201.927476.227498.332193.132197.532265.732385.93239332465.532469.432517.832608.438172.538172.538594.238594.238977.838978.239298.739299.539566.339573.339768.839800.439936.639954.340009.240122.140128.5
40989.941015.341059.141061.744144.34414544235.844238.844324.444359.244397.944400.444419.444437.444438.946258.246311.946319.246324.646432.946448.146542.447247.447260.147517.347546.447555.35237452408.853452.753530.453580.875516.375517.675803.875855.976074.476074.67623676274.2
gzz = 17.883549gyy = 0.002194gxx = 0.001815
Supplementary Information
23704.123704.12389823898.524119.624119.824336.624338.624513.9
4308043080.143297.743297.843473.143474.143586.143598.543662
82650.9110734.3110868.4111892.9111918.7112436.4112538.2112650.5
22506.322506.42267322673.522899.522899.823145.923148.123354.7
40269.240269.240515.740515.940753.540755.440889.540906.140972.1
76313101847.8101984.7103059.7103091.1103711.9103825.5103871
Supplementary Information
Table S19. CASSCF+NEVPT2 computed low-lying spin-free states and spin-orbit states along with the ground state g-tensor for complex [Er{N(SiMe3)2}3I]–.
CASSCF computed spin-free states
NEVPT2 computed spin-free states
NEVPT2 computed energies of low-lying eight
KDs.00
122.3681122.3681158.3934158.3934187.8547187.8547254.1653254.1653373.1904373.1904472.1602472.1602543.3232543.3232
Main value of g-tensor (NEVPT2)
0.990.490.6147.1151.4198.3271.1328.5332395.5414.7436.213127.213145.713151.313206.213213.413291.513298.313353.113353.113361.313361.822085.222126.222146.122266.622272.522443.922446.822604.322604.422624.422636.422663.322719.722732.522810.623068.523118.8
24591.224725.624730.524798.924848.624860.929333.229352.229357.129480.929555.829563.329745.629751.63562835628.935644.13575735763.835807.235811.93583335887.340796.940796.941321.441321.441748.641748.842092.842093.24236542369.642565.24258742704.342734.842780.84286142866.8
43753.243794.8438264383447574.247574.647676.147679.647743.247782.847817.647820.347840.947857.647861.650712.850713.550885.550918.151012.251033.451143.751594.551612.551746.351782.351821.957659.957682.858704.658775.358921.881925.481926.782202.682253.582487.782489.28264382677.9
2.6139.9140.3141.3146.1154230.4342.5355.5489.9516.6564.312715.712727.912731.81277812784.212856.61286612918.71291912928.312928.521221.321235.921271.421277.321297.62130321322.521340.321417.221421.121534.421598.521603.621753.521791.621791.921810.6
23794.323951.523958.924042.124101.424109.127705.727710.527737.827795.627908.627919.428146.728162.933095.533099.633172.333277.333287.43336533367.533419.233510.538942.238942.239429.239429.239863.539863.940213.340214.240498.140505.340709.740743.640881.840902.24095941067.241073.4
41934.641970.64201342016.445235.545236.145330.645333.345435.2454724551645518.145536.445553.845554.747367.147397.847422.847549.447566.447678.248384.248396.748666.548706.54871253753.153789.254933.355010.955098.177398.677399.977713.977768.578012.178012.878197.178236.378285
gzz = 17.885379gyy = 0.001238gxx = 0.001132
Supplementary Information
23651.323651.323884.123884.624137.424137.524377.324379.324569.9
43080.243080.343306.443306.643505.743506.543644.843655.643743.1
82720.1110650.6110785.5111925.8111949.3112548112648.7112780.6
22808.722808.723018.423018.923278.123278.323547.523549.723771.2
41118.741118.74138241382.341654.441655.941820.941832.241921.1
104294.6104435.9105631.7105663.1106353.1106464.7106523.7
Supplementary Information
Table S20. Reduced LOEWDIN POPULATION ANALYSIS on model complexes [Er{N(SiMe3)2}3X]– (where X = F, Cl, Br and I). The Er is considered in +III oxidation state, while halide is considered as X– ion. The numbers provided here are net gain/loss of electron compared to reference (electronic structure of ions). The negative and positive sign here are the loss and gain of the electrons from reference electronic structure.
[Er{N(SiMe3)2}3F]– [Er{N(SiMe3)2}3Cl]– [Er{N(SiMe3)2}3Br]– [Er{N(SiMe3)2}3I]–
Er(III)(4f) 0.74 0.75 0.74 0.70Er(III)(5d) 0.76 0.93 0.99 1.08Er(III)(6s) 0.21 0.25 0.26 0.28Er(III)(6p) 0.61 0.73 0.77 0.84
X– (ns) -0.33 -0.47 -0.48 -0.48X– (np) -0.57 -0.81 -0.85 -0.93
Supplementary Information
Figure S3. Experimental and ab initio computed molar magnetic susceptibility plots for complex 1. The black hollow circle represents the experimental magnetic susceptibility extracted from the
[Er{N(SiMe3)2}3F]– [Er{N(SiMe3)2}3Cl]–
[Er{N(SiMe3)2}3Br]– [Er{N(SiMe3)2}3I]–
Supplementary Information
experimental data. The coloured lines represent computed magnetic susceptibility at BS1 level of theory.
Supplementary Information
Energy Decomposition Analysis (EDA)
Table S21. Energy decomposition analysis (in kcal mol-1) of complex 1a at the B3LYP/TZ2P level. The values in the parentheses give the percentage contribution to the total attractive interactions (ΔEelstat + ΔEorb)
Fragment Pair Complex 1aPauli
repulsion∆Epauli
Electrostatic interaction
∆Eelstat
Total steric interaction
Orbital interactions
∆Eorb
Total interaction
∆Eint
Total bonding energy
Fragment Pair A [Er{N(SiMe3)2}3
….Cl]– 1179.11 -214.51 (20.34) 964.59 -840.04
(79.65) 124.56 124.54
Fragment Pair B {Cl}….{Er….{(NSiMe)3} 397.58 -1250.70
(66.50) -853.12 -630.07(33.50) -1483.19 -
1483.19
Supplementary Information
Table S22. Structure of model complex 1TP generated from SHAPE code.
Er 8.845700000 4.215200000 12.419500000C 5.866944889 0.795726621 9.939975795H 5.569607889 1.278330621 9.166005795H 5.183693889 0.182646621 10.216070795H 6.666496889 0.308406621 9.724983795Si 7.653131715 3.872741035 9.377930198C 6.793668889 0.951354621 12.748447795H 6.080887889 0.364998621 13.015489795H 7.039202889 1.510986621 13.488471795H 7.551048889 0.429450621 12.476878795Cl 7.217900000 4.289600000 14.095500000C 4.582521889 2.765442621 11.793431795H 4.264204889 3.303066621 11.064722795H 4.689928889 3.312498621 12.574190795H 3.948905889 2.067474621 11.976739795Si 10.461818185 2.998557240 15.429178156C 6.009723715 4.488965035 8.700367198H 6.159171715 4.963709035 7.878872198H 5.600848715 5.078465035 9.338553198H 5.430011715 3.742265035 8.537426198Si 6.227484889 2.006638621 11.332669795C 8.290708715 2.608853035 8.145914198H 8.404631715 3.025433035 7.288210198H 7.658571715 1.888877035 8.068970198H 9.133621715 2.263013035 8.446903198Si 7.782688942 7.631468344 12.598593410C 8.877448715 5.274965035 9.238978198H 8.964546715 5.535917035 8.320171198H 9.731657715 4.988861035 9.571649198H 8.567274715 6.023237035 9.757221198Si 10.980073027 1.728771179 12.724484917Si 10.725344379 6.893955189 12.189232330N 7.284500000 3.293400000 10.944000000N 10.158100000 2.816900000 13.756200000N 9.094600000 6.535400000 12.558300000C 7.476981942 8.073200344 14.384157410H 6.669544942 8.587244344 14.454312410H 8.214183942 8.590388344 14.716828410H 7.390499942 7.269908344 14.902400410C 10.698567027 0.001143179 13.389148917H 9.756584027 -0.146624821 13.504565917H 11.142664027 -0.091604821 14.235537917H 11.051215027 -0.641804821 12.769066917C 11.870889379 5.424135189 12.121566330H 11.610424379 4.848783189 11.399646330
Supplementary Information
H 11.820590379 4.939959189 12.949850330H 12.771673379 5.725959189 11.981256330C 11.333631379 7.981779189 13.594825330H 12.222424379 8.288319189 13.400201330H 11.341419379 7.477167189 14.409531330H 10.749788379 8.737911189 13.689874330C 11.020943379 7.871739189 10.609834330H 11.963356379 7.903179189 10.424262330H 10.687019379 8.766207189 10.718462330H 10.565762379 7.447299189 9.878862330C 10.444214027 1.720911179 10.931452917H 10.522582027 2.605947179 10.569361917H 9.530438027 1.431663179 10.872612917H 11.001933027 1.120407179 10.433577917C 12.829972027 1.923699179 12.642334917H 13.173847027 1.415943179 11.904573917H 13.222406027 1.606155179 13.459303917H 13.048332027 2.851179179 12.524655917C 8.077520942 9.283640344 11.720522410H 8.481450942 9.123296344 10.865081410H 8.660807942 9.829124344 12.252344410H 7.239231942 9.734804344 11.598316410C 6.204957942 6.975944344 11.874411410H 6.320613942 6.826604344 10.932973410H 5.499404942 7.612604344 12.012458410H 5.975530942 6.147500344 12.304394410C 12.158379185 2.450243240 16.058538156H 12.380730185 1.596647240 15.678342156H 12.136987185 2.377931240 17.015817156H 12.819025185 3.096335240 15.802811156C 10.315425185 4.748507240 15.999698156H 11.060675185 5.256263240 15.669290156H 10.310449185 4.773659240 16.959240156H 9.497350185 5.125787240 15.667027156C 9.209799185 1.972355240 16.361790156H 8.326827185 2.308763240 16.185270156H 9.390103185 2.024231240 17.303227156H 9.268019185 1.059023240 16.072116156
Supplementary Information
Table S23. Structure of model complex 1TD generated from SHAPE code.
Er 8.520200000 4.230100000 12.754700000C 6.041298892 0.999597997 9.876194671H 5.743961892 1.482201997 9.102224671H 5.358047892 0.386517997 10.152289671H 6.840850892 0.512277997 9.661202671Si 7.682015382 3.926362636 9.232058331C 6.968022892 1.155225997 12.684666671H 6.255241892 0.568869997 12.951708671H 7.213556892 1.714857997 13.424690671H 7.725402892 0.633321997 12.413097671Cl 6.922400000 4.306600000 14.405100000C 4.756875892 2.969313997 11.729650671H 4.438558892 3.506937997 11.000941671H 4.864282892 3.516369997 12.510409671H 4.123259892 2.271345997 11.912958671Si 10.417088306 2.972791644 15.145536289C 6.038607382 4.542586636 8.554495331H 6.188055382 5.017330636 7.733000331H 5.629732382 5.132086636 9.192681331H 5.458895382 3.795886636 8.391554331Si 6.401838892 2.210509997 11.268888671C 8.319592382 2.662474636 8.000042331H 8.433515382 3.079054636 7.142338331H 7.687455382 1.942498636 7.923098331H 9.162505382 2.316634636 8.301031331Si 7.997394698 7.451110320 12.581368422C 8.906332382 5.328586636 9.093106331H 8.993430382 5.589538636 8.174299331H 9.760541382 5.042482636 9.425777331H 8.596158382 6.076858636 9.611349331Si 11.056169328 1.625344722 12.630911783Si 10.883986214 6.939963113 12.162555561N 7.602400000 3.350200000 10.840100000N 10.269900000 2.908400000 13.443100000N 9.285900000 6.355200000 12.330700000C 7.691687698 7.892842320 14.366932422H 6.884250698 8.406886320 14.437087422H 8.428889698 8.410030320 14.699603422H 7.605205698 7.089550320 14.885175422C 10.774663328 -0.102283278 13.295575783H 9.832680328 -0.250051278 13.410992783H 11.218760328 -0.195031278 14.141964783H 11.127311328 -0.745231278 12.675493783C 12.029531214 5.470143113 12.094889561H 11.769066214 4.894791113 11.372969561
Supplementary Information
H 11.979232214 4.985967113 12.923173561H 12.930315214 5.771967113 11.954579561C 11.492273214 8.027787113 13.568148561H 12.381066214 8.334327113 13.373524561H 11.500061214 7.523175113 14.382854561H 10.908430214 8.783919113 13.663197561C 11.179585214 7.917747113 10.583157561H 12.121998214 7.949187113 10.397585561H 10.845661214 8.812215113 10.691785561H 10.724404214 7.493307113 9.852185561C 10.520310328 1.617484722 10.837879783H 10.598678328 2.502520722 10.475788783H 9.606534328 1.328236722 10.779039783H 11.078029328 1.016980722 10.340004783C 12.906068328 1.820272722 12.548761783H 13.249943328 1.312516722 11.811000783H 13.298502328 1.502728722 13.365730783H 13.124428328 2.747752722 12.431082783C 8.292226698 9.103282320 11.703297422H 8.696156698 8.942938320 10.847856422H 8.875513698 9.648766320 12.235119422H 7.453937698 9.554446320 11.581091422C 6.419663698 6.795586320 11.857186422H 6.535319698 6.646246320 10.915748422H 5.714110698 7.432246320 11.995233422H 6.190236698 5.967142320 12.287169422C 12.113649306 2.424477644 15.774896289H 12.336000306 1.570881644 15.394700289H 12.092257306 2.352165644 16.732175289H 12.774295306 3.070569644 15.519169289C 10.270695306 4.722741644 15.716056289H 11.015945306 5.230497644 15.385648289H 10.265719306 4.747893644 16.675598289H 9.452620306 5.100021644 15.383385289C 9.165069306 1.946589644 16.078148289H 8.282097306 2.282997644 15.901628289H 9.345373306 1.998465644 17.019585289H 9.223289306 1.033257644 15.788474289
Table S24. Er-X bond lengths in the model [Er{N(SiMe3)2}3X]– model complexes.
Er-X bonds Bond lengths (Å)Er—F 2.053Er—Br 2.67Er—I 2.88
Supplementary Information
Figure S4. Ab initio blockade barrier for complex 1m. The thick black line indicates the Kramer’s doublets (KDs) as a function of magnetic moment. The green lines show the possible pathway of the Orbach process. The blue lines show the most probable relaxation pathways for magnetization reversal. The dotted red lines represent the presence of QTM/TA-QTM between the connecting pairs. The numbers provided on each arrow are the mean absolute values for the corresponding matrix elements of the transition magnetic moment.
-10 -8 -6 -4 -2 0 2 4 6 8 10-100
0
100
200
300
400
500
600
700En
ergy
(cm
-1)
M(B)
0.51E-03
1.54
2.10
0.19E-01
0.19E-01
0.11
1.54
2.50
2.75
-1
-2
-4
-5
-3
+1
+2
+4
+5
+3
Supplementary Information
Figure S5. Ab initio blockade barrier for complex 3. The thick black line indicates the Kramer’s doublets (KDs) as a function of magnetic moment. The green lines show the possible pathway of the Orbach process. The blue lines show the most probable relaxation pathways for magnetization reversal. The dotted red lines represent the presence of QTM/TA-QTM between the connecting pairs. The numbers provided on each arrow are the mean absolute values for the corresponding matrix elements of the transition magnetic moment.
-10 -8 -6 -4 -2 0 2 4 6 8 10-50
0
50
100
150
200
250
300
350
400En
ergy
(cm
-1)
M(B)
0.70E-02
1.53
-1
-2-3
-4
0.76E-01
0.41
0.76E-012.10
2.54
+1
+2
+3
+4
Supplementary Information
-out of plane shift parameter
Figure S6. CASSF+RASSI computed Ucal value plotted against parameter extracted from the experimental geometry of the complexes of 1-3.
Supplementary Information
Figure S7. SINGLE_ANISO computed principal magnetization orientation of each KDs of complex 1TD.
Figure S8. SINGLE_ANISO computed principal magnetization orientation of each KDs of complex 1TD.
123 6
47
8 5
1,2,3,4,5,6,7,8
Supplementary Information
Figure S9. Ab initio blockade barrier for complexes [Er{N(SiMe3)2}3X]– a) X=F, b) X=Cl, c) X=Br, d) X=I. The thick black line indicates the Kramer’s doublets (KDs) as a function of magnetic moment. The green lines show the possible pathway of the Orbach process. The blue lines show the most probable relaxation pathways for magnetization reversal. The dotted red lines represent the presence of QTM/TA-QTM between the connecting pairs. The numbers provided on each arrow are the mean absolute values for the corresponding matrix elements of the transition magnetic moment.
Supplementary Information
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Gisbergen, J. G. Snijders and T. Ziegler, J. Comput. Chem., 2001, 22, 931-967.9. K. Morokuma, J. Chem. Phys., 1971, 55, 1236-1244.10. T. Ziegler and A. Rauk, Theor. Chim. Acta., 1977, 46, 1-10.