EXTENDED HÜCKEL THEORY

ICON (Ver. 8)

USER'S GUIDE Release for IBM compatible personal computers by Luis A. Montero, Universidad de La Habana, 1984-1990. I- Introduction 2 II- Input Descriptions 2 III- Print and Punch Options 10 IV- Charge Iteration Procedure 11 V- Madelung correction 13 VI- Weighted Hij Formula 14 VII- Description of Output 16 VIII- Hardware and Storage Requirements 17 IX- ICON Errors 18 X- Appendix 19

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I.- INTRODUCTION ICON perform extended Hückel calculations on molecules containing a hundred or less atoms bearing s, s and p, and s, p and d electrons. Four different calculational methods are available: (0) Extended Hückel (1) Extended Hückel calculation with charge iteration according to Hii = Hoii + (sense) * (charge). (2) Extended Hückel calculation with charge iteration according to Hii = - VSIE(Q). See section IV. (3) Extended Hückel calculation as in method 2 with inclusion of Madelung potential correction term. See section V. The present version of ICON has been prepared to use the facilities of DOS in IBM PC compatible computers. Input cards are referred to text lines in input files. The main input file is <fn>[.ICN], where <fn> is any user defined DOS file name, and .ICN is a default DOS extension. The main output file is [<fn>.[EHT]], following the same rules. The file name is asked to user by the computer during the program run. Two special points should be recognized when using methods (2) and (3): a) all atoms must be user defined, and, b) if NCON = 3 (See section II) the program will only accept parameters for five or less atoms having d orbitals and any such atoms must be among the first five defined. II.- INPUT DESCRIPTIONS The following input information must be written in the <fn>.ICN file by any text processing program in ASCII code. Be careful to avoid special symbols introduced in document texts in certain modes of professional MS-DOS editor programs. Certain cards of the below described can be avoided if a <fn1>.CAR file (where <fn> could be equal to <fn1>) is used to input atomic Cartesian coordinates, titles, and number of atoms. This is properly signaled in this manual. However, in the simplest case, at least an empty card must exist in the <fn>.ICN main input file. The deck setups for the various methods are indicated below. N indicates that a particular card or set of cards is necessary, if lowercase n is used, indicates necessary if CAR files are not used to input Cartesian coordinates; O indicates that it is optional. The card(s) are described below.

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Methods 0 1 2 3 Title card n N N N Parameter card N N N N Coordinate cards n N N N Heavy atom card n N N N Atom definition cards O O N N Charge iteration parameters card N N N Iterated atoms card O VSIE cards N N Overlap population orbital specification card O O O O Energy matrix orbital specification card O O O O Overlap integrals deletion card O O O O Orbital occupation cards O O O O Non-integral orbital occupation cards O O O O

It is possible to perform more than one ICON calculation in the same job step. However, it is important to note that the following cards: Atom definition cards Charge iteration parameters card Iterated atoms card VSIE cards can only be used in the first calculation. In other words, only atoms defined in the first calculation can be used in later calculation within the same job step. Whenever in doubt, it is safest to use separate job steps. Descriptions of inputs card(s): ** 1. Title card (only if CAR file is not used) Two cards with up to 80 columns with any character you want. ** 2. Parameter card NH,NA,CHARGE,METH,IPRINT,IPUNCH,L1,L2,L3,L4,L5,CON,PEEP, COULH,(PRT(I),I=1,20),(PUN(I),I=1,20) format: (6I3 , 5L1, F5.2, 2F6.3, 40L1) cols. 1 to 18 (3 cols. per value without decimal point) NH Number of hydrogen atoms (maximum 50). If CAR file is used, it can be left in blank. NA Number of heavy atoms (maximum 40, maximum value of NH + NA is 100. Note that hydrogens may be treated as heavy atoms if desired. If CAR file is used it can be left in blank. CHARGE Molecular charge; positive implies cation, negative implies anion. METH Calculational method desired (see section I).

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= 0 for the first method.

= 1 for the second, etc...

IPRINT See section III. IPUNCH See section III. cols. 19 to 23 (1 col. per value) L1 If T (.TRUE.), molecular orbital occupations are read in from the orbital occupation cards; if F or blank (.FALSE.), molecular orbital occupations default to ground state. L2 If T (.TRUE.), certain overlap integrals, specified by the overlap integrals deletion card, will be set equal to zero. L3 If T (.TRUE.), individual overlap population analysis will be printed for the molecular orbitals specified in the energy matrix orbital specification card. L4 If T (.TRUE.), individual energy matrices will be printed for the molecular orbitals specified on the energy matrix orbital specification card. L5 If T (.TRUE.), the weighted Hij formula is used. See section VI. cols. 24 to 28 (5 cols. with decimal point) CON Constant used in Hij formula. See section VI (default value 1.75). cols. 29 to 40 (6 cols. per value with decimal point) PEEP Hydrogen orbital exponent (default value: 1.30). COULH Hydrogen H(I,I) (default value: -13.6). cols. 41 to 80 (1 col. per value) PRT(I) See section III. PUN(I) See section III. ** 3.- Coordinate cards (only if CAR file is not used) x, y, z format: (3F10.0) Coordinates of atoms in Angstrom units, one card for each atom. Hydrogens first, then heavy atoms. When NH.NE.0, otherwise, they can be entered in the order you want, bust you must define hydrogen as a heavy atom. ** 4.- Heavy atom card (only if CAR file is not used)

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Chemical symbols of all heavy atoms in the same order as used in specifying coordinates. format: (40A2) , are right justified. Atomic parameters for 15 kinds of atoms (hydrogen through chlorine, helium excluded) are stored internally. In addition, the program will accept user defined parameters for up to 20 of the atoms in the molecule. If an atom is to be defined by the user, an asterisk should be used in the place of the chemical symbol. In this case, an atom definition card (see point 5, below) must be present following the heavy atom card for every asterisk on it, in the same order. Once a chemical symbol (atom) is defined by an atom definition card, the chemical symbol may be used in the normal fashion (e.g. b*TH is a valid heavy atom card provided this card is followed by an atom definition card which defines TH). If a ** is entered for the symbol in the heavy atom card, the last defined atom is redefined. ** 5.- Atom definition card If a CAR file is used to enter Cartesian coordinates of the polyatomic system, a self explained question appears in the computer screen asking to enter the atomic numbers of atoms 1 to 17 (excluding 10) which parameters are wanted to be changed. In this case, an atom definition card must be entered in the ICN file for each one of the desired to be changed elements, in the same order as they appear in the CAR file, and only once if the appearance is repeated. Also, if an atomic number in the Cartesian coordinate CAR file is larger than 17, a corresponding atom definition card must be included for it. Atom definition cards, due to rules for entering Cartesian coordinates in the ICN main input file are explained in point 4, above. The data to be entered is the following: SYMB,VELEC,NS,EXPS,COULS,NP,EXPP,COULP,ND,EXPD1,COULD,C1,EXPD2,C2 format: (A2, I3, 3(I3, 2F6.3), F6.4, F6.3, F6.4) cols. 1 to 2 (right justified) SYMB Symbol of atom. cols. 3 to 5 (3 cols. without decimal point) VELEC Number of valence electrons for neutral atom. cols. 6 to 20 (3 cols. without decimal point, and 6 cols. per value with decimal point) NS s electron principal quantum number. EXPS s electron exponent

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COULS s electron H(I,I).* cols. 21 to 35 (3 cols. without decimal point, and 6 cols. per value with decimal point) NP p electron principal quantum number. EXPP p electron exponent COULP p electron H(I,I).* cols. 36 to 50 (3 cols. without decimal point, and 6 cols. per value with decimal point) ND d electron principal quantum number. EXPD1 d electron first exponent. COULD d electron H(I,I).*

The following need only be entered if contracted d orbitals of the form, X = N(ND - 1)(C1 * e- EXPD1 * r + C2 * e- EXPD2 * r) will be invoked. cols. 51 to 68 (6 cols. per value with decimal point) C1 coefficient of EXPD1. EXPD2 d electron exponent 2. C2 coefficient of EXPD2. ** 6.- Charge iteration parameters card DAMP1,DAMP2,DAMP3,LAMPRI,DELTAC,SENSE,MAXCYC,PRTCYC,NCON,PARTIT format: (6F10.5, 3I5, 4X, L1) cols. 1 to 40 (10 cols. per value with decimal point) DAMP1, DAMP2, DAMP3, LAMPRI Control the damping procedure when using methods 2 or 3 (see section IV). Default values depend on the method being used.

Method 2 3 DAMP1 0.1 0.1 DAMP2 0.25 0.75DAMP3 0.0 0.0 LAMPRI 0.25 0.75

* When using charge iteration , COULS, COULP and COULD serve as initial guesses for the H(I,I).

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cols. 41 to 50 (value with decimal point) DELTAC Calculation is assumed converged when DENOM is less than DELTAC (see section IV) (default value: 10-4). cols. 51 to 60 (value with decimal point) SENSE See description of method 1 in section I. cols. 61 to 75 (5 cols. per value without decimal point) MAXCYC Execution will be terminated if convergence has not been reached after MAXCYC cycles (default value: 25) PRTCYC Full charge iteration output will be printed for all cycles which are integral multiples of PRTCYC (default value: MAXCYC). NCON May have value of 1 o 3 ; number of configurations considered for transition metal atoms when using methods 2 and 3 (see section IV) (default value: 3). col. 80 PARTIT If F (false or blank), all atoms are iterated upon; if T (.TRUE.) (method 2 only), only those atoms are specified on the iterated atoms card are iterated upon. ** 7.- Iterated atoms card (only if PARTIT = .TRUE.) Chemical symbols of those atoms upon which charge iteration is to be performed, in same order as on heavy atom card. format: ( 20A2 ) ** 8.- VSIE cards (only if METH > 2) One, two or more cards for each atom upon which charge iteration is to be performed, in the same order as on the heavy atom card. format: (4F10.8) Setup of VSIE cards for various types of atoms:

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Type Cards Contents s orbitals only 1 A,B,C,MADS s, p orbitals only 2 A,B,C,MADS for s A,B,C,MADS for p s, p, d orbitals; NCON=1 3 A,B,C,MADS for s A,B,C,MADP for p A,B,C,MADD for d s, p, d orbitals; NCON=3 9 A,B,C,MADS for dn-1s A,B,C dn-2s2 A,B,C dn-2sp A,B,C,MADP for dn-1p A,B,C for dn-2p2 A,B,C for dn-2sp A,B,C,MADD for dn A,B,C for dn-1s A,B,C for dn-1p

Note that the MADS, MADP and MADD values are only needed if using method 3 . For further details see section IV and V. ** 9.- Overlap population orbital specification card (only if L3 = .TRUE.) Pairs of numbers indicating molecular orbitals for which overlap population analysis are to be printed. format: (24I3) This option allows the user to request the printing of overlap population matrices for individual molecular orbitals. For each pair of numbers the printout is given for the first molecular orbital specified through the last molecular orbital specified. For example, the card, bb3bb6b13b13bb8b10 will cause overlap population matrices to be printed out for molecular orbitals 3, 4, 5, 6, 13, 8, 9, and 10. Note that the second number of the pair should not be smaller than the first. ** 10.- Energy matrix orbital specification card (only if L4 = .TRUE.) Pairs of numbers indicating molecular orbitals for which energy matrices are to be printed. format: (24I3) This options allows the user to request the printing of energy matrices for individual molecular orbitals. Use of the options is analogous to the use of the overlap population orbital specification option above. ** 11.- Overlap integrals deletion card (only if L2 = .TRUE.) Pairs of numbers indicating overlap integrals which are to be set to zero.

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format: (20I3) Program will read in pairs of numbers indicating atom-atom pairs, atom-orbital pairs, or orbital-orbital pairs whose overlap matrix elements are to be set to zero. If a number within a pair is positive, it refers to an atom; if negative, it refers to an atomic orbital. bb1bb3bb4b-2-10b-7 indicates that the matrix elements between atom 1 and atom 3, atom 4 and orbital 2, orbital 10 and orbital 7, are to be set to zero. Remember that setting a given overlap matrix element to zero automatically sets the corresponding Hamiltonian matrix element to zero. Note: when using this option, the program looks for a zero to terminate the reading of input. A blank card should be read in if there is a multiple of 10 pairs of matrix elements to be dropped. ** 12.- Orbital occupation cards (only if L1 = .TRUE.) (IOCC(I), I=NDIM,I) (Note that loop runs NDIM -> 1) format: (80I1) IOCC(I) The number of electrons in molecular orbital I. This options allows the user to specify the occupation numbers of the molecular orbitals. The molecular orbital occupations are read in front the lowest to the highest molecular orbital in going from left to right on the cards. Each molecular orbital occupation must be specified, even though it may be zero. If there are more than 80 molecular orbitals in the molecule, an additional card will be necessary. Note: For non-integer occupation numbers see below. ** 13.- Non-integer orbital occupation cards (Only if L1 = .TRUE.) IOCC(I) format: (F15.8) The user can enter non-integer molecular orbital occupations by placing an asterisk in the appropriate column of the preceding card and following with this card. One additional card is needed for each asterisk. For example, consider a molecule with ten molecular orbitals, the set of cards, 22b*1bb*2b 1.66667 0.33333 would lead to the following occupation numbers:

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MO Occupation numbers 1 0 2 2 3 0.33333 4 0 5 0 6 1 7 1.66667 8 0 9 2 10 2 III.- PRINT AND PUNCH OPTIONS The method of controlling output has been set up to be both convenient for routine use and flexible for non routine use. The PRINT-PUNCH OPTION TABLE given on the table in page 13 gives the code numbers of the various matrices, etc. which can be printed and /or punched. 1. IPRINT option The PRINT PUNCH OPTION TABLE designates which matrices, etc. will be printed for various IPRINT values. 2. PRT(I) option Setting PRT(I) = T (.TRUE.) will suppress the printing of the matrix, etc. having code number I. Combining the IPRINT and PRT options allows complete flexibility in determining the printed output. 3. IPUNCH Option Punched output is sent to a file which name is asked to the user from the screen during program setup. Specifying a non-zero value for IPUNCH will cause the program to punch the complete input deck for another program according to the scheme: IPUNCH DECK PUNCHED 10 FMO molecule deck 11 FMO fragment deck Note that additional cards may be necessary in the ICON deck for various IPUNCH options. Refer to the program descriptions for the particular being punched. 4. PUN(I) option Setting PUN(I) = T (.TRUE.) will cause the particular matrix, etc. having code number I to be punched. Note that not all matrices, etc. which can be printed can be punched. Those which can be punched are punched in the following formats given in the PRINT-PUNCH OPTION TABLE.

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PRINT-PUNCH OPTION TABLE Code IPRINT PUNCH Number FORMAT 2 1 0 -1 -2 -3 -4 1 Coordinates, Parameters X X X X X X X 2 Overlap integrals deleted X X X X X X 3 Distance matrix X X X X X X 8F9.6 4 Overlap matrix X X X X X X 8F9.6 5 Madelung parameters X X X X X 8F9.6 6 Input hamiltonean matrix X 8F9.5 7 Hamiltonean matrix for next cycle* X 8F9.5 8 Energy levels X X X X X 8F9.5 9 Total energy X X X X X F20.8 10 Wavefunctions X X X X 8F9.6 11 Density matrix X 8F9.6 12 Overlap population matrix X X 8F9.6 13 Reduced overlap population matrix X X X 8F9.6 14 Complete charge matrix X X 8F9.6 15 Reduced charge matrix X X X 8F9.6 16 Net charges and populations X X X 17 Energy matrix X 8F9.5 18 Reduced energy matrix X X X 7F10.7 19 Energy partitioning X 8F9.5 20 Reduced energy partitioning X X 7F10.7 * Only printed for those cycles which are integral multiples of PRTCYC. IV.- CHARGE ITERATION PROCEDURE If METH = 2 is specified, the program will perform a self-consistent charge calculation of any molecule. The procedure can be used to iterate on the charges of all atoms in the molecule (PARTIT = .FALSE) or on only the charges of all atoms in the molecule (PARTIT = .TRUE.). The diagonal Hamiltonian matrix element are given by Hii = -VSIE(Q) where VSIE(Q) is the valence state ionization energy of orbital i when the atom has total charge Q. The off-diagonal Hamiltonian matrix elements are calculated in the normal manner (see section VI). The VSIE(Q) functions are assumed to be of the form, VSIE(Q) = AQ2 + BQ + C where A, B, and C are parameters which depend on the atom and the orbital. For atoms with d orbitals, one has two options. For the NCON = 1 option , three VSIE(Q) functions are read in, one for the s orbital, one for the p orbitals, and one for the d orbitals. For the other option, NCON = 3, nine VSIE(Q) functions are read in, three for each orbital, and the Hii's are then given by Gray's equations (C.J.Ballhausen and H.B.Gray, "Molecular Orbital Theory", W.A.Benjamin ,Inc. ,New York, 1965, p.125). -Hss = (2-s-p)(sVSIE:dn-1s)+(s-1)(sVSIE:dn-2s2)+p(sVSIE:dn-2sp) -Hpp = (2-s-p)(pVSIE:dn-1p)+(p-1)(pVSIE:dn-2p2)+s(pVSIE:dn-2sp)

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-Hdd = (1-s-p)(dVSIE:dn) + s(dVSIE:dn-1s) + p(dVSIE:dn-1p) where s, p, and d are the summed orbital occupations of the s, p, and d orbitals of the atom respectively. A damping scheme is employed during the charge iteration procedure. The orbital occupations are summed separately over the p and d orbitals on each atom. The resulting p and d occupation, along with the s occupations, are damped according to the equation, nrinputk+1 = nrinputk + l ( nroutputk - nrinputk) where nr is the summed orbital occupation of a given type, s, p, or d, indexed by r on the kth cycle, and l is a damping parameter. In previous work of self-consistent field charge calculations, l was always maintained at a fixed value. During the iterative process, the correction factor multiplying l can become very small. For a constant value of l this leads to slow convergence because of the necessity of having l small at the beginning of the iteration. In the iterative techniques used by ICON l is defined by the equation: l = ADJUST / DENOMk | outputk inputk| where DENOMk = max |nr - nr | r | | DENOMk is the maximum difference of the absolute value of the summed orbital occupation types, s, p, or d which are indexed by r. ADJUST is a constant which is decremented under certain conditions to be described below. DENOM will decrease as convergencies achieved and provides the variation in l. In order to insure stability in the iterative process, value for l are compared to a fixed constant, l' (LAMPRI). The value of l' represents an upper limit about which the procedure will usually diverge. l' depends significantly on the charge dependence. If the charge dependence is high, l' should be small ( l'¾ 0.10 ). For reduced charge dependencies a larger value of l' may be used. The following equations are used to determine values for ADJUST at various stages in the iterative calculations: 1. For the first cycle, ADJUST = DENOMk (i.e. l = 1.0). The first cycle is a normal extended Hückel calculation. Thus the initial guess for the orbital occupation is determined by the values of COULS, COULP, and COULD on the atom definition card. 2. For the second cycle, ADJUST = DAMP1 * DENOMk. 0 < DAMP1 ¾ l'. DAMP1 is usually set to 0.10, but can be increased, if the initial guess is known to be particularly good. 3. ADJUST = DAMP2 * DENOMk is used whenever l becomes equal to or greater than l'. 0 < DAMP2 ¾ l'. DAMP2 should be as nearly equal to l' as possible. 4. Whenever max [( nroutputk - nrinputk)] is of different r sign than max [(nroutputk-1 - nrinputk-1)], two options are r possible.

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a) DAMP3 <> 0. ADJUST = DAMP3*ADJUST where 0 < DAMP3 ¾ 1.0 . b) DAMP3 = 0. The program calculates a value for l using a linear interpolation between cycles k and k-1. The values of ADJUST is left unchanged. Convergence is assumed when DENOMk< DELTAC and the iteration procedure is terminated. V.- MADELUNG CORRECTIONS In general, Hii should contain, in addition to the -VSIE(Q) term discussed in section IV, a term representing the interaction of the electron in orbital i with the electrostatic field arising from the non-zero net charges on the other atoms in the molecule. This Madelung correction term can be included in the charge iterative calculation by specifying METH = 3. The formula for Hii used by ICON with this option is: Hii = -VSIE(Q) + SUM [ ( nsN- ZsN ) gisN + ( npN- ZpN) gipN + ( ndN- ZdN) gidN ] where N runs over all atoms in the molecule except the atom on which orbital i is located ; nsN, npN, ndN are the summed orbital occupations of the s, p, and d orbitals of atom N respectively; ZsN, ZpN, and ZdN are the corresponding summed orbitals occupations for the free atom N; and gis, gip, and gid are the average values of the coulomb integrals between orbital i and the s, p, and d orbitals of the atom N respectively. The average two-center coulomb integrals are evaluated using the formula: gii + gjj gij = [ rij2+ ( ------------- )2 ]-1/2 2 giigjj where rij is the interatomic distance and gii and gjj are the one-center coulomb integrals for orbitals i and j respectively. The gii values are read in as MADS, MADP, and MADD on the VSIE cards (see section II). For a molecule with not net charge the Hii's calculated from the above formula will be rather similar to those used in normal non-iterative extended Hückel calculation. In such cases the normal Hij formula, Hij= k/2 Sij ( Hii+ Hjj ) can be used. However, if the molecule has a non-zero net charge, QM, these will be a substantial shift ( magnitude approximately -QM gij ) of the Hii's from the normal values. This shift, which is similar in effect to a change in energy scale, makes it impossible to use the simple Hij formula above for calculations on molecular ions. The formula used by ICON in this situation is: Hij = k/2 Sij (Hii+ Hjj) + (1-k)/2 Sij (dGii+ dGjj) where QM dGii= - ----- SUM nk gik NELEC k

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NELEC is the total number of valence electrons and k runs over all valence orbitals. The program print out the average value of dGii for all valence orbitals. Subtracting this average value from Madelung corrected Hii's gives Hii values which can be roughly compared with normal extended Hückel values. Substracting the average value of dGii from the Madelung one-electron energies which can be compared with normal extended Hückel one-electron energies. Also printed out are two energy correction terms. These are defined... One-center: - SUMN SUMi [ 1/2 niN ( niN - 1 ) giiN + SUMj>i niN njN gijN ] Two center: - SUMN>M SUMi SUMj ( ZiN ZjM - niN njM ) gij where i and j run over s, p, d. The damping scheme used for METH = 3 is the same as that discussed for METH = 2 in the previous section. However, since the Madelung term tends to oppose the -VSIE(Q) term, the charge dependence is greatly reduced. METH = 3 calculations, in general, converge much faster than METH = 2 calculations and are therefore less expensive to run. VI.- WEIGHTED Hij FORMULA It seems reasonable to approximate the overlap density XiXj between orbitals i and j on different centers as a weighted average of the orbital densities XiXi and XjXj, i.e. XiXj = Sij ( a XiXi + b XjXj ) where a + b = 1 and Sij has been included to meet the normalization condition < Xi Xj > = Sij ( a < Xi | Xi > + b < Xj | Xj > ) = Sij If Xi and Xj have about the same degree of "diffuseness" a and b should be nearly equal and we can write Sij Xi Xj = ----- ( Xi Xi + Xj Xj ) 2 That is, the overlap population is essentially equally divided between atoms i and j. This is a simple way of rationalizing the Mulliken Population Analysis. Reasoning along the same lines, we might expect that the integral < Xi| H | Xj > would be given roughly by an expression of the form Hij = k Sij ( a Hii + b Hjj )

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where k is a constant. For Xi and Xj of similar "diffuseness" we again choose a = b and obtain Sij Hij = k ----- ( Hii + Hjj ) 2 the normal extended Hückel formula for Hij with k = CON. The assumption of similar "diffuseness" should hold fairly well in molecules where all of the basis orbitals have reasonably large occupation numbers and similar energies, e.g. organic molecules. However in molecules where this condition is not met - e.g. transition metal complexes containing unoccupied, high energy s and p basis functions - the simplification a = b is questionable. The obvious solution to this problem is to choose a =/ b such that Xi Xj is weighted in favor of the more contracted orbital. One way in which this can be done is to assume that Hii can be used as a measure of an orbital's "diffuseness" - a small Hii indicating an unstable, diffuse orbital; a large Hii indicating an stable, contracted orbital. Defining, Hii - Hjj DELTA = ------------- Hii + Hjj as a measure of the "relative diffuseness" of Xi and Xj, we can then write, Sij Hij = k ----- [ ( 1 + DELTA ) Hii + ( 1 - DELTA ) Hjj ] 2 where, in general, k is a function of DELTA which we choose so as to meet the following conditions, CON DELTA = 0 Hij = --- Sij(Hii + Hjj) 2 DELTA = 1 Hij = Sij Hii DELTA = -1 Hij = Sij Hjj The DELTA = 0 condition is of course, the normal Hückel formula. This leads to the weighted Hij formula Sij Hij = [CON-(CON-1)DELTA2] ----- [(1+DELTA) Hii + (1-DELTA) Hjj] 2 which can written in the more concise form,

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Sij Hij = k' ----- (Hii + Hjj) 2 where k' = CON + DELTA2 + DELTA4(1 - CON) Specifying L5 =.TRUE. will result in ICON using this weighted Hij formula rather than the normal extended Hückel formula with k' = CON. This is true for any value of METH. However, in the case of METH = 3, the Hii are replaced by H0ii = Hii - DGii when calculating DELTA (see section V). VII.- DESCRIPTION OF OUTPUT Given a set of empirical Hij's and a set of atomic basis functions, Xii, which can be used to calculate a set of overlap integrals Sij, ICON calculates a set of molecular orbitals, Φμ, defined by, Φμ = Σi Ciμ Xi with one-electron energies, eμ, and occupation numbers, nμ. In addition, ICON can provide a series of derived "matrices" which are useful in analyzing the calculational results. These are defined as follows: a) Density matrix Dij = Σμ nμ Ciμ Cjμ b) Overlap population matrix Pii = Σμ nμ C2iμ Pij = 2 Σμ nμ Ciμ Cjμ Sij c) Charge matrix Qiμ = 2 Ciμ Σi Cjμ Sij d) Energy matrix Eii = Σμ nμ Ciμ2 Hii Eij = 2 Σμ nμ Ciμ Cjμ Hij e) Energy partitioning eii = Σμ nμ Ciμ Σi Cjμ Sij Hii = ni Hii eij = 2 ΣμnμCiμCjμ [Hij-1/2 Sij(Hii+Hjj)]

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where ni is the population of orbital i. VIII.- HARDWARE AND STORAGE REQUIREMENTS ICON is compiled and linked to libraries of MS-FORTRAN v. 4.1 in the emulator mode. This allows to run programs in machines with or without i-8087/n87 coprocessors (n=2,3). If the coprocessor is installed, the program uses it to make more fast the number crunching. If not, the program runs, but about 7-10 times slower. The total storage requirements of ICON are given approximately by Total Storage = Basic program size + Storage for matrix allocation The basic program size is dependent only on the compiled structure and is constant once this structure is fixed. The storage for matrix allocation (in terms of 4 bytes words), however, varies with N, the number of orbitals in the molecule, roughly according to the following scheme: a) METH = 0, IPRINT < -1, IPUNCH = 0, PUN(I) = .FALSE. for I > 5 (i.e. no wavefunctions calculated) Storage = 12 N2 + 72 N b) METH = 0, 1, 2 Storage = 20 N2 + 72 N c) METH = 3 Storage = 21 N2 + 80 N The package ICONPACK contains two versions of ICON. The running program version advices the user the availability of storage and prevents failures in this aspect. ICON256.EXE can be renamed to simply ICON if it is used currently. It is the version 2.21 of this program. It requires a minimum of 412367 bytes of total RAM. The RAM requirements for matrix allocation is 262560 bytes, and it allows up to 65536 words in the storage for matrix allocation. ICON384.EXE can be renamed to simply ICON1 if it is used currently. It is the version 2.22 of this program. It requires a minimum of 543423 bytes of total RAM. The RAM requirements for matrix allocation is 393631 bytes, and it allows up to 98304 words in the storage for matrix allocation. The ICONPACK.EXE package directory is: ICON256 EXE 140485 3-01-89 ICON384 EXE 140751 3-01-89 ICONREAD ME 54784 3-01-89 TEST EHT 59251 3-01-89 TEST ICN 512 3-01-89

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TEST PTN 880 3-01-89 TEST1 CAR 512 3-01-89 TEST1 EHT 59250 3-01-89 TEST1 ICN 128 3-01-89 TEST1 PTN 880 3-01-89 - ICONREAD.ME is this file, which has been written with WordStar, v. 5.0. - TEST.EHT, TEST.ICN, and TEST.PTN are the main output, main input, and output potential curve files, respectively, of of a test compound run by ICON384. In this case the cartesian coordinates were in the main input file .ICN. - TEST1.CAR, TEST1.EHT, TEST1.ICN, and TEST.PTN are the cartesian coordinate input, main output, main input, and output potential curve files, respectively, of a test compound run by ICON384. In this case the cartesian coordinates were in the cartesian coordinate input file .CAR. It can be evolved to all the contained files calling it, or one of the contained files, in the following way: >iconpack [<fn>] [<destination path>] IX.- ICON ERRORS ICON is a very tested program which is expected to be free of simple programming mistakes. However, any trouble with the operation is kindly asked to be sent by mail to the following address: Prof. Luis A. Montero Laboratory of Computational and Theoretical Chemistry Facultad de Química Universidad de La Habana Habana 10400, Cuba e-mail: luis.montero@quimica.uh.cu Phones: (537) 878-1263, 870-3922, 879-4734, 879-6153 In any case, a quick answer will be delivered. If some true program mistake is found a new corrected copy will be sent to you.

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APPENDIX 1 ATOMIC PARAMETERS 1. First and Second Row Atoms ICON Default Values SYMB VELEC NS,NP,ND EXPS,EXPP EXPD COULS COULP COULD H 1 1 1.3 -13.6 Li 1 2 0.650 -5.4 -3.5 Be 2 2 0.975 -10.0 -6.0 B 3 2 1.300 -15.2 -8.5 C 4 2 1.625 -21.4 -11.4 N 5 2 1.950 -26.0 -13.4 O 6 2 2.275 -32.3 -14.8 F 7 2 2.425 -40.0 -18.1 Na 1 3 0.733 -5.1 -3.0 Mg 2 3 0.950 -9.0 -4.5 Al 3 3 1.167 -12.3 -6.5 Si 4 3 1.383 1.383 -17.3 -9.2 -6.0 P 5 3 1.600 1.400 -18.6 -14.0 -7.0 S 6 3 1.817 1.500 -20.0 -13.3 -8.0 Cl 7 3 2.033 2.033 -30.0 -15.0 -9.0 Note: COULS, COULP, and COULD in ev's Burns' Exponent SYMB VELEC NS,NP,ND EXPS EXPP EXPD H 1 1 Li 1 2 0.600 0.500

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Be 2 2 0.900 0.750 B 3 2 1.225 1.000 C 4 2 1.550 1.325 N 5 2 1.875 1.650 O 6 2 2.200 1.975 F 7 2 2.525 2.300 Na 1 3 0.900 0.533 Mg 2 3 1.100 0.700 Al 3 3 1.317 0.867 0.500 Si 4 3 1.533 1.083 0.667 P 5 3 1.750 1.300 0.833 S 6 3 1.967 1.517 1.000 Cl 7 3 2.183 1.733 1.167 Note: See reference 1 Charge Iteration Parameter A B C MAD H 13.618 27.18 13.60 12.8 Li 4.3 4.8 4.3 4.3 3.4 4.3 Be 7.2 9.6 7.2 7.2 5.6 7.2 B 9.8 14.8 9.8 9.8 8.1 9.8 C 11.9 20.4 11.9 11.9 10.6 11.9 N 13.7 26.4 13.7 13.7 13.4 13.7 O 15.2 33.0 15.2 15.2 16.4 15.2

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F 16.2 42.4 16.2 16.2 19.6 16.2 Na 4.85 4.55 4.8 4.85 2.43 4.8 Mg 6.0 8.26 6.0 6.0 4.38 6.0 Al 7.12 11.90 7.1 7.12 6.26 7.1 Si 8.09 15.49 8.1 8.09 8.16 8.1 P 8.95 19.02 9.0 8.95 10.04 9.0 S 9.70 22.50 9.7 9.70 11.94 9.7 Cl 10.66 25.93 10.7 10.66 13.82 10.7 Notes: a) First row gives parameters for s orbital. Second row gives parameters for p orbitals. b) All C values average of values for singly and doubly occupied orbitals. See reference 2, p.429. c) A, B, C for hydrogen from reference 2, p.424. d) MAD for hydrogen from reference 3. e) All values in ev's. SYMB VELEC EXPS EXPP EXP D1 C1 EXP D2 C2 Ti 4 1.075 0.675 4.55 0.4206 1.40 0.7839 1.175 0.800 4.55 0.4391 1.60 0.7397 V 5 1.200 0.750 4.75 0.456 1.50 0.752 1.300 0.875 4.75 0.476 1.70 0.706 Cr 6 1.325 0.825 4.95 0.4876 1.60 0.7205 1.425 0.950 4.95 0.5060 1.80 0.6750 Mn 7 1.450 0.900 5.15 0.514 1.70 0.693 1.550 1.025 5.15 0.532 1.90 0.649 Fe 8 1.575 0.975 5.35 0.5366 1.80 0.6678 1.675 1.100 5.35 0.5505 2.00 0.6260 Co 9 1.700 1.050 5.55 0.555 1.90 0.646 1.800 1.175 5.55 0.568 2.10 0.606 Ni 10 1.825 1.125 5.75 0.5683 2.00 0.6292 1.925 1.250 5.75 0.5817 2.20 0.5800 Cu 11 1.950 1.200 5.95 0.58 2.10 0.62

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2.050 1.325 5.95 0.5933 2.30 0.5744 ______________________________________________________________ Notes: a) For each metal the first row gives the parameters for the neutral atom, the second row the parameters for the +1 ion. b) NS, NP = 4 and ND = 3 for each metal. c) EXPS and EXPP from reference 1 assuming configurations dn-2 s and dn-2 sp for the neutral atom and dn-2 s and dn-2 p for the cation, where n = VELEC. d) d orbital parameters from reference 4. Charge Iteration Parameters ( NCON = 3 ) continued... Iron A B C MAD 0.911 7.916 7.10 6.3 0.911 9.056 8.47 0.911 8.350 10.1 0.91 6.30 3.71 4.5 0.91 7.16 4.92 0.91 7.16 5.00 1.71 10.7 5.19 10.7 1.71 12.58 8.68 1.71 12.63 10.1 Nickel A B C MAD 0.911 8.561 7.54 6.7 0.911 9.552 8.96 0.911 9.379 10.7 0.986 6.552 3.89 4.5 0.986 7.904 5.16 0.986 7.904 5.07 1.76 11.8 5.90 11.8 1.76 13.72 10.0 1.76 13.41 11.9 Cobalt A B C MAD 0.899 8.263 7.33 6.5 O.899 9.329 8.74 0.899 8.846 10.4 O.936 6.441 3.81 4.5 0.936 7.519 5.04 0.936 7.519 5.06 1.717 11.30 5.55 11.3 1.717 13.172 9.37 1.717 13.086 11.0

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Charge Iteration Parameters ( NCON = 3 ) continued... Copper A B C MAD 0.942 8.840 7.72 6.9 0.942 9.683 9.17 0.942 9.955 10.9 1.05 6.639 3.98 4.5 1.05 8.325 5.28 1.05 8.325 5.03 1.85 12.3 6.21 12.3 1.85 14.23 10.7 1.85 13.62 12.9 Titanium A B C MAD 1.2 6.25 6.02 5.4 1.2 7.25 7.09 1.2 6.82 8.18 0.97 4.41 3.33 3.1 0.97 6.06 4.45 0.97 6.06 4.26 2.126 7.544 3.40 7.5 2.287 9.652 5.53 2.287 9.515 6.87 Vanadium A B C MAD 1.06 6.713 6.32 5.6 1.06 7.804 7.49 1.06 7.135 8.75 0.924 5.635 3.43 4.2 0.924 6.304 4.56 0.924 6.304 4.51 1.96 8.43 3.89 8.4 1.74 10.8 6.37 1.74 10.8 7.61 Charge Iteration Parameters ( NCON = 3 ) End... Chromium A B C MAD

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0.998 7.135 6.59 5.8 0.998 8.288 7.85 0.998 7.494 9.26 0.899 5.895 3.52 4.3 0.899 6.552 4.69 0.899 6.552 4.72 1.829 9.267 4.35 9.3 1.21 11.90 7.18 1.21 12.02 8.39 Manganese A B C MAD 0.94 7.55 6.86 6.1 0.94 8.72 8.17 0.94 7.91 9.71 0.89 6.11 3.62 4.4 0.89 6.84 4.81 0.89 6.84 4.88 1.75 10.0 4.78 10.0 0.68 13.02 7.95 0.68 13.14 9.21 Charge Iteration Parameters ( NCON = 1 ) A B C MAD Ti 1.2 6.25 6.02 4.6 0.97 4.41 3.33 2.9 2.287 9.583 6.20 9.6 V 1.06 6.713 6.32 5.0 0.924 5.635 3.43 3.9 1.74 10.8 6.99 10.8 Cr 0.998 7.135 6.59 5.1 0.899 5.895 3.52 3.9 1.21 11.96 7.78 12.0 Mn 0.94 7.55 6.86 5.3 0.89 6.11 3.62 4.0 0.68 13.08 8.58 13.1 Fe 0.911 7.916 7.10 5.8 0.91 6.30 3.71 4.2 1.71 12.60 9.39 12.6 Co 0.899 8.263 7.33 6.0 0.936 6.441 3.81 4.3 1.717 13.129 10.18 13.1

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Ni 0.911 8.561 7.54 6.2 0.986 6.552 3.89 4.3 1.76 13.56 10.9 13.6 Cu 0.942 8.840 7.72 6.5 1.05 6.639 3.98 4.4 1.85 13.925 11.8 13.9 _____________________________________________________________ Notes: a) For NCON = 3 parameters are listed in order: 4s dn-1 s 4p dn-1 p 3d dn dn-2 s dn-2 p dn-1 s dn-2 sp dn-2 sp dn-1 p b) A, B, and C values for NCON = 3 are from reference 2 except for copper which is from reference 5. c) Configurations used for NCON = 1 are s: dn-1 s p: dn-1 p d: (dn-1 s + dn-1 p)/2 d) All values are in ev's 3. Platinum SYMB VELEC NS EXPS NP EXPP ND EXP D1 C1 Pt 10 6 2.554 6 2.535 5 6.013 0.633 EXP D2 C2 2.696 0.551 Charge iteration parameters ( NCON = 3 ) A B C MAD 1.05 5.112 8.728 3.6 1.05 6.112 9.721 1.05 7.112 12.156 0.95 3.892 5.209 2.5 0.95 2.892 7.053 0.95 2.892 6.168 1.05 9.050 8.773 9.0 0.919 11.524 10.768 3.743 5.520 13.237 Charge Iteration Parameters ( NCON = 1 ) A B C MAD 1.05 5.112 8.728 3.6 0.95 3.892 5.209 2.5 2.331 8.522 12.002 8.5

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Notes: a) Orbital exponents from reference 6. b) A, B, and C values from personal communication. See reference 7. c) NCON = 1 values as in section 2. d) Charge iteration parameters in ev's.

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