Correct Orthogonalization of the Basis Set in a Semiempirical SCF-LCAO-MO Calculation

Indian Journal of Chemistry Vol. 17A,March 1979,pp. 211·217

Correct Orthogonalization of the Basis Set in a Semiempirical SCF-LCAO-MO Calculationt

S. MOLDOVEANU

l.P.B., Institute of Chemistry, Chemical Faculty; Bucharest, Romania and

S. GRIGORAS, ILEANA RUSU & ANCA MEDESAN

Department of Experimental Pathology, Fundeni Clinical Hospital, Bucharest, Romania

Received 24 April 1978

Using the correct orthogonallzatton of the basis set ofatomic orbitals and some appropriate approximations, an important reduction in the volume of computation has been obtained in a new scheme of semiempirical SCF-LCAO-MO type. The method is better than other semi- empirical methods of comparable complexity and can be applied to a large range of molecules with essentially better results on ionization potentials, dipole moments, molecular geometry, as well as with fairly acceptable results for heats of formation. The method yields accurate values concerning different physical quantities, though a balance exists between the accuracy of the results and the range of molecules with the same parametrization. The main usefulness of the method consists in its ability to be trustworthy in computations on large molecules, thus providing a reliable tool for calculations in a field insufficiently provided for presently. Unlike the existing simple semiempirical methods, the proposed scheme is also reliable in computa- tions on large molecules e.g. adrenaline and [adrenaline H+].

T

^{HE full overlap} semiempirical methodsv-, though superior to the semiempirical methods in which the initial orthogonality of the basis set is assumed, however, usually require greater volume of computations and that is an important impediment in their development and applicability.

A detailed study of the approximations used in the semiempirical SCF-LCAO-MO methods shows that a major simplification of the computation is not possible only by neglecting the overlap.

This paper presents a new semiempirical full overlap method with the approximations :in the evaluation of Fock's matrix elements thus chosen so that the volume of computation is small, even when compared to the simplest ZDO type methods.

This method is hereafter referred to as SMCO (semi- empirical method with correct orthogonalization).

•

Theory

The approximate solutions ofthe Roothaan equa- tion are obtained by solving th egeneralised algebraic pseudo eigenvalue problem,

FC=SC€ ...⁽¹⁾

the elements of the overlap matrix S being computed and those of Fock's matrix F estimated.

The S"v elements have been .comput ed by standard procedures using Slater type orbitals" or atomic orbitals as given by Clementi and Roetti-.

tCorrespondence may be made with Dr. E. Pausescu,v

Department of Experimental Pathology, Fundeni Clinical Hospital, Bucharest, Romania.

\

Using generally accepted symbols, the

F""

ele- ments of the Roothaan equation were:

F~"= U~J-L- ~ ZB ([J./B/[J.) + (~ +~) P~~ [([J.[J./~~)

B#A ~.!....A ~€A

2rc

-t([J.~/ [J.~)J + ~~ p~..•[([J.[J./~'r)- t([J.~1[J.'r)] ... (2)

1;#..•

(~€A indicates that the X~ orbital belongs to the A core).

When using the approximation (3),which does not imply the orthogonality of the basis set:

~ P~~ [([J.[J./~~)-t([J.~/[J.~)J

= ~

(~P1;i;) ([J./B/[J.)

. ..(3) we assume that the charge density created by an electron in the orbital belonging to the atom B is unity, and centred on the atom B.

Using the well known expression- for the

U~J-L term, which is defined by Eq. (4)

U~"=-1~-(ZA-1) ([J.[L/[L[J.) ... (4) where 1~is the valence state ionization potential for the XI' orbital, the FJ-LJ-L elements become:

F1J-L=-11-

1::

QB([J./B/[L)-(ZA-l) ([L[L/[J.[J.)

. B#A

+ ~

P1;i;[([J.[J./~~)-t([L~/[L~)]+ ~ ~ P~..•[([J.[L/~'r)

~EA ;#..•

-H[J.~/fL'r)J ." (5)

211

INDIAN ]. CHEM., VOL. 17A, MARCH 1979

In expression (5) the first' three terms alone can be easily evaluated: ionization potentials from experimental data5,6, (!1-/B/!1-) integrals computed using Roothaari's formulae? and (!1-!1-/!1-!1-)integrals calculated without difficulty.

To avoid the calculation of the remaining integrals, an empirical evaluation of all the uncomputed terms in Eq. (5) has peen performed so that the results be in good agreement with the experiment. In order to obtain this evaluation by means of a single parameter without dimensions for each orbital, Eq. (5) is rewritten as:

FA =_IA_ ~ QH(!1-/B/!1-)-I-P",,(!1-!1-/!1-!1-).K: ... ⁽⁶⁾

"" "B""A

where:

~ P~~[(!1-!1-/;~) - !(!1-;/ !1-;)]

KA

= _

ZA-1 -I-~.:..€_A_---,:=---:---:--:- _

"P"" P",,(!1-!1-/!1-!1-)

~ ~ P~~[(!1-!1-/;T)-H!1-;/w')]

+ ~""~

^•.•(7)

P",,(!1-!1-/!1-!1-)

The value of KA is obviously dependent on a

" . .

number of factors. However, takmg 1I1toaccount that the integrals in expression (7) which may take high values are the rnonocentric ones (centre A)8 and P"", P~~, ;€A vary in the same manner but not too much for different molecular environments, one mJ.Y assume that K~ is primarily determined

1.0

0.9

0·8

0.7

0.&

0.5

by the X" orbital, !1-€A, and by the type of the bond in which it is implied; for a class of mole- cules, K~ remaining almost constant and, therefore, transferable.

A detailed analysis on various molecules where J(~ is adju ited in such a way as to reproduce computation ally some molecular properties, shows that the above suppositions are correct. Fig. 1 illustrates the· K~~,r2tpnvalues (for single bonds) optimized for ionization potentials, net charges and geometries on different molecules.

One observes that K~ becomes almost constant for bigger molecules. This suggests the possibility of utilizing the proposed method to relatively big molecules for which the J(~ parameter remains practically constant.

In order to evaluate the F"v elements the Mulliken approximation has been used":

A B S"v (A A-I- B B)

X"Xv =

2:

X" X" Xv'Xv ••.(8) In this approximation the core Hamiltonian elements are10:

5 '

~1!= i:!

^{{-11-(Z A}-1)(!1-!1-/!1-!1-)-I!J - (ZB-1)(w/w) -tZA[(!1-/A/!1-)-I- (v/A/v)] -tZB[(!1-/B/!1-)

+

(v/B/v)]

-~ Zc(!1-/C/!1-)-~

z:

^{(v/Cfv)} ...(9)}

C""A,B C""A,B

It it It it

•• ...

I.CH, LCH)CH3 5. C.H3CH2CH3 7.CH3(CH2)2CH3 12. C6H,2(Chair.)

...

_*

.•. ...

3. CH3 NH2 &.C H3 CH2NH28.CH (CH3)J 13.CH3(CH2)4CH3

...

.,.

4. CH3 OH 14.CH3CH2C (CH3

h

I·

9.CH3(CH

••

2»)CH3

.,.

10•.CH3CH2CH (CH3)2

lLC(CH3

••

)4

t4 6 8· _.11

2·- ^___5·^e_

-.

₇ 10·

.

.14 Kcsrbon

9 12. ·,3 2p

5 •• 6 7· 9 .13 KCarbon

;0

,--~l!....:---8:-.:----:,I:--!O'----'i ·14 2s

I •

0.4+0---.,O---2rO~--~30r----4~O---5TO---6rb----~70~---.8~O~--~9~O--

Moi'ecular weight

Optimum values 10r. K: parameters in som••e carbon (optimization has been made for C )

compunds

Fig. 1,

MOLDOVEANU et al.: CORRECT ORTHOGONALIZATION IN SCF-LCAo-MO CALCULATION

are, nevertheless, computed in order to obtain re- sonance integrals.

From the mathematical point of view, in this approximation the problem (1) is well posed= and invariant under a unitary transformation of the orbitals of an individual atom. It can be solved after multiplication by

5-

^1/2 using the well known iterative procedure.

.. (10) On the basis of the method described above a FORTRAN programme was elaborated in such a side in (10) is manner that it could be run even on low perfor-

mance computers (an IBM 360/30 and/or a FELIX C:-256). The convergence of the iterative proce- dure in solving Eq. (1) is extremely good in this approximation, so that after 4-5 iterations a difference of no more than 0·005 eV is observed in the orbital energy for two consecutive iterations.

The better convergence and the reduced number of the integrals actually computed make the method - suitable for studies on large molecules. as well.

The remaining terms in the expression of

F,1V

are written in the form:

~ ~ P~ .•[(v-v/;'t')-i(v-;/v't')]

= ~~~

~l

P~ .• {[(V-V-/;'t')

~ .• . 2 ~ .•

-t([l;/V-'t')] + [(w/;'t') -t(v;/v-r)J}+ :E ^~Il p~.•~v5

~ .• 4

[(fLC:/IJ.'t')+(vC:/v-r)]-

i~

^~lll

P~"(V-C:/v't')

~

..

The first double sum in the right split as:

1:

~l

=

~l

+

^~l+~l

+~

^~l

~ .• ~2~A,b

~= .•

Using the obtain:

~I

=:?'t ~ Pcc [(v-/c/v-) +

^(v/C/v)]

~~ A CftA,B 271:

~EA c,EB c,# .•

c,=.• ~=.•

approximation

... (11) introduced by (3) we

... (12)

The third double sum in the right side of (10) is written in the form:

~ ~lll

=

P"v[(p.V-/w)-t(v-v/v-v)] +3/2P"v(V-v/v-v) + c, .•

~ ~IVPc,.•(V-;/v't') ... (13)

c, .•

(except;

=

V-' 't'='.1, ; = », 't'= V-) Considering

V-EA

and vEB, we can write:

[(V-V-/w)-t(v-v/v-v)] ~

U(v-/B/v-)

+ (v/A/v)]

(V-/A/V-) ~ (V-V-/V-V-),

(v/B/v) ~ (w/w)

Using all the above mentioned relations, we get after a slight rearrangement, the term:

F~: ⁼ 5;v {-I~-I~-tZA[(I'.V-/V-V-)-(v!A/v)]

,

- iZB[(W/W) - (V-/B/V-)] -~ Q A

(vIA/v) -~

QB(V-'B/V-)}

A#B B#A

-!Pv,,[(v-/B/v-H- (v/A/v)]+R ... (16) ... (14) ... (15)

where:

R=~

^{~Il_t~ ~IV}

-iP"v(V-v/v-'J) + ~1_(ZA -1)(V-V-/V-V-)

c, .• c,..

c,EA

+~l

-(ZB-l)(w/w) ... (17)

c,EB

The value of

R

is very small in the case V-EA,vEB, either due to the smallness of the integrals involved or due to the vanishing of different terms with opposite signs and similar magnitudes, such as ~l

. c,EA

and

(ZA-1) (V-V-/V-V-)

(ref. 11). For these reasons we consider R

=

0 in expression (16).

For V-' '.IEA we have considered

F:!v

^{A ~} 0 because of its smallness and for reasons of economy of com- putational volume.

The F v elements were then evaluated using the computed values for the same integrals as in the case of Full-' Thus, the number of the actually computed integrals is small, even when <:ampared to the simplest semiempirical methods us~ng zero overlap approximation, in which overlap integrals

Choice of the Parameters in the Proposed Method

The high flexibility of the SMCO due to the parameters

KA

permits us to use the atomic data given in the literature directly. Thus, Slater atomic orbitals with unmodified Slater exponents- have been used for each atom (atomic wave functions as given by Clementi and Roetti+ have also been employed).

The ionization potentials are taken dependent on the net atomic charge:

IA = A(V-).Q~+B(V-).QA+C(V-) ... (18)

where

A(V-), B(V-)

and

C(V-)

were obtained from the ionization potentials for the negative and positive ions and for the neutral atoms, as given by Hinze and Jaffe5,6 employing Slater orbitals. Ionization potentials as given by Clementi and Roetti+ have been used when atomic wave functions are double

?:

type.

Unlike other methods, special care is not required in selecting the atomic data, since

KA

can be also

TABLE 1 - VALUES OF THE PAR~METERS K~ FOR VALENCE TYPE SLATER ORBITALS OF H, C, N, AND 0 Ele- Type of bond, compound K:' K~

ment

H Any (K~= 0'68)

C Single bonded 0·60 0'84

C Double bonded C atoms -0'50 1'00

C In C= 0 group -0'50 0·40

C In COOH group -0,50 0·10

C Triple bonded C atoms -0,64 0'90

C In C

==

N group -0·24 -0'46

C In aromatic (and heterocyclic) -0·90 0·75 compounds

N In amino group 3·00 0·18

N In C

==

N group 1'6 -0,22

N In heterocyclic compounds 3·8 -0,06 0 In alcohols {phenols), ethers 1'87 0·155

0 In C= 0 group 2·40 0·10

0 fn-o 2·40 0·10

In COOH group in

=

^{OH 2'80 -0,30}

0 In heterocyclic compounds 2·80 -0'40

213

INDIAN j. CHEM., VOL. 17A, MARCH 1979

employed as adjustable parameters, their usefulness being not restricted only to the evaluation of the uncomputed integrals. Thus, there are three possi- bilities to determine the parameters KA and, con- sequently, to apply the method: (i) The first possi- bility was previously described, and namely the choice of the K~ values for big molecules for which the values remain almost constant.

(ii) Since the variation in the KA values are re- latively small even for small molecules, one may choose an intermediate value between the extremes in a series of molecules. Table 1gives the st andard parametrization performed according to this alter- native.

(iii) For charged molecules for which the above described procedures are not valid, the following recipe has been applied: standard

Ki

values are used everywhere, excepting the molecular frag- ments on which the charge is mainly localized. For these fragments particular Ki:'s are obtained if with these fragments small molecules are built by ad- justing the K~ values until the agreement between calculated and experimental molecular properties is satisfactorily reached. (In this paper the special case of the ionic adrenaline molecule is treated as an example).

In adjusting the parameters Ki:, several mole- cular properties have been considered: vertical ionization potentials-correlated with the molecular orbital energies (Kcopmans' theoremw ) (both in the highest and different other occupied molecular orbitals), heats of formation-correlated with the

total energies of the molecules, dipole moments, charge distributions and molecular geometries.

The standard parametrization .is determined by adjusting the Kf; for different types of molecules containing H, C, Nand 0 atoms, the values thus obtained for the parameters being given in Table 1 (Slater exponents'', atomic ionization poten- tials+").

Several compounds containing silicon have also been investigated.

Results and Discussion

Obviously, the main advantage of SMCO is that it can be employed in the study of large molecules, though this possibility is justified only by the transferability of the parameters K~, i.e. only on account of the reliability of the standard parametrization on the largest possible range of molecules.

The results obtained for different series of com- pounds are presented below, the calculation implied being performed with the standard parametrization (Table 1).

The best results were obtained for the molecular ionization potentials both in the highest occupied levels (the average error being less than 0·2-0·3%) and in other occupied levels, for the net charges on the centres and the dipole moments (Tables 2-4). The results obtained in this study are by far more correct than those calculated by standard semiempirical methods such as EHT14, IEHT15, CND016,17, INDO (closed shell)18, and at least as

TABLE 2- COMPUTED ORBITAL ENERGIES FOR HOMO AND EXPERIMENTAL IONIZATION POTENTIALS FOR SOME MOLECULES21-24

Molecule Computed Vertical Molecule Computed Vertical

energy IP energy IP

(eV) (eV) (eV) (eV)

CH. -13·41 12·99 CH3(CH2)2NH² -9·23 9·17

C2Ha(stagg.) -11·56 11·56 CH³NHC²H⁵ -8·47 8·44

C,H. -11·05 11·06 CH³(CH2⁾³NH² -9·15 9·19

n-C⁴H^1O -10·50 10·50 CHa(CH²).NH² -9·09

iSJ-C.H,o -10·82 10·78 NH2(CH2)2NH² -9·27

n-C5H" -10·06 10·37 (CH³hN -8·41 8·32

CH3CH2CH(CH3)2 -10·47 10·32 Aniline -7·67 7·70

CH.C(CH3ls -10·12 10·42 _Pyridine -9·14 9·23

n-CaH14 -9·96 10·18 Quinoline -8·46 8·62

CH.CH2C(CH3ls -10·19 10·08 CH3CN -12·19 12·22

C6H" (chair) -9·68 9·79 Benzonitrile -9·08 9·20

CH2CH2 -10·73 10·48 H2O -14·80 12·61

CH3CHCH² -9·64 9·69 CH30H -10·83 10·83

CH3CHCHCH3 (trans) -9·01 9·12 C2H⁵OH -10·32 10·46

CH3CHCHCH3 (cis) -8·98 9·12 CH3CCH')20H -10·31 10·25

s-cis-C.H6 -8·61 8·59 CH3CHOHCH3 -10·20 10·18

s-trans-C.H6 -8·89 9·07 CH3(CH2lsOH -10·28 10·37

C,H2 -11·42 11·40 CH3(CH2)40H -9·97

CHaCCH -10·41 10·36 CH3OCH3 -10·02 9·94

Benzene -9·41 9·25 Phenol -8·41 8·52

Toluene -8·67 8·80 C⁶H⁵CCH3 -8·06 8·21

a-CaH.CCH3)2 -8·20 8·45 HCHO -10·94 10·89

m-CaH.(CH3)2 -8·22 8·50 CH3CHO -10·00 10·20

P-C.H.CCH3)2 -8·11, 8·37 Benzaldehyde -9·38 9·59

C.H⁵CHCH. -8·29 8·43 HCOOH -12·25 11·51

Naphthalene -7-80 8·10 CH3COOH -10·66 10·66

NH3 -11·80 10·35 Benzoic acid -9·51

CH3NH2 -9·39 9·41 Furan -8·80 8·88

CH3CH2NH2 -9·29 9·19 Furaldehyde -9·08 9·22

CH3NHCH3 -8·45 8·93

MOLDOVEANU et al.: CORRECT ORTHOGONALIZATION IN SCF-LC~O-MO CALCULATION

correct as those calculated by the much more para- metrized method MINDO/3 (refs. 19. 20).

On account of the correlation between the ioni- zation potentials and the chemical reactivity in patterns of HOMO-LUMO interaction'" and between the values of the net charges on the centres and different chemical effects26•27 their correct values are parjicularly important. Also. the fact that the symmetry of the computed wave functions is the correct one is equally important.

Molecule

TABLE 4- COMPUTED CHARGE DENSITIES AND/OR DIPOLE MOMENTS FOR SOME MOLECULES

C.Ho C.H.

n-C.H,o iso-C.H,o n-CsH,o CH3C(CH')3 C.H, CH3CHCH.

Benzene Toluene C,H, NH3 CH3NH.

C,H.NH, C3H,NH2 CH.NHCH3

NH2C2H.NH2 Aniline Pyridine HCN CH3CN H²0 CH30H C,H.OH Phenol CH30CHa CHaCHO Furan HCOOH Benzoic acid

C

Cprim Cprim Cprim Ccentr Cprim C C C TABLE 3- SOME EXAMPLES OF COMPUTED ORBITAL

ENERGIES AND CRBITAL SYMMETRIES FOR MOLECULES GIVEN IN TABLE 2

Molecule and symmetry

MO type

C6H12 (D3d)

(chair) eu

eg

«e eu eu

Computed energy

(eV)

-11·04785 -11-05678 -11'14060 -12·91200 -13'01157 -14·75902 -15·38378 -17'21654 -20·29071 -24·95941 -9·68437 -9·68486 -11'23831 -11'23911 -12'33165 -12-33930 -11·804435 -12·77376 -13'62526 -14·45243 -14'51008 -16'05545 -16'30067 -18·19513 -18'20677 -23·07007 -23'11893 -27,32373 -9·41495 -9·41505 -10'21247 -10'21737 -12'74630 -13·05015 -13·06110 -14'17438 -16'03461 -23'54721 -26·054721 -26·05644 -29'67761 -29·68430 -32·33638 -12'17359 -12'17362 -13-24313 -15-68512

~18'08624 -18'08637 -23·06822, -29·22247 .

IP (eV)23, ••

11·06

13·17 15'17 18'57

9·79 11·33 12'22

14'37

9'25 11'49 12-19 -13'67 14'44 16·73 18'75

12'18 13'11 15'15 17'4

Atom and net charge computed=

-0·082 -0'107 -0,107 -0'115 -0'051 -0,126 -0·222 -0'187 -0·252

Inductive charge as given in

referen- ces^20-2•

Com- puted dipole moment

(in D)

Exp.

dipole mo- mentw .a,

0'08 0·13

0'35 0'43 1'47 1·29 1'11

1'56 2'20 2·95 3·97 1'82 1·71 1'55 1·30 2-68 0'69 1'53

*Negative values indicate an excess of electrons.

-0'071 -0'065 -0-066 -0,059 -0'080 -0'054

0013 0'021 0'030

TABLE 5 - COMPUTED AND EXPERIMENTAL HEATS OF ATOMIZATION FOR SOME MOLECULES

Calc. heat of formation kcal/mol

281'1 611'4 608'9 918·95 1233·94 1242'51 1538'95 1561'06 1845'77 1784'44 1925·24 1580'13 2669'00 564'70 1060'74 1058'16 394'83 657'36 983'09 1301'00 1619'24 1936'19 1322'00 1638-70 1994'7 2493'58 2206'6 1291'9 1655'13 1972'58 2290'9 3179'3 1593'7 Molecule

CH4

c.n,

(stagg.) C,Ho (eclip.) C³Ha n-C.HlO

iso-C.H,o n-C.H12 neo-C^SH'2 n-COH14

is:J-CoH14

CoH,.

C.Ho C,oHa

c.a,

s-trans-C.Ho s-cis-C.Ho

c,a,

NHa CH3NH, C,H.NH.

C3H,NH.

C,H9NH.

(CH3}.NH CH3NHC,H.

NH.CH,CH2NH.

CoHsNH, CoHsN

H20

CH.OH C.H.OH C,H,OH CoH.OH HCHO

-0,173 0'38 0'58 1'41 1·29 1·26 1'281-14 2'171-43 2·65 3·21 5·41 1'98 1·71 1'64 1'67 1'28 3'26 0·35 1'22 3'17

Experi- mental"

674-6 671'7 954'3 1234'7 1236'8 1514'7

1680'2 1318'1 537'7 1103'0 1102'0 391'8

215

n

E - (a): -7.'52311 eV

HOIofO.

INDIAN J. CHEM., VOL. 17A, MARCH 1979

E_HOHO (aH): -IO.590!l8eV_•

(O.I67)H

o I

(-O.IBI)

I //J.'60}

(out! <,

^(d.fU),

/PO.,'6}

C C

(-Or) (OJ7)

(-o~E"-....

^/f-aSSIJ

W"".. t: ^<,H

(0.2'S)

(O'or

^(Ool70)

(OUo . --O--H

\ ro.JiJ

^{f-O.207) (0.I66)}

H-C/ \

(O(}UJ (-0.0")

I'

^(0.D07)H

(ooti,

^N

\ (-0'9')'-...

H-C/ H

(0056) (-0. ",) (0.'00)

H

I

(0.056)

,.

i'''''

Some results on adrenaline {gJ and [fldrenaline 1ij+(aHJ

However, as far as the calculation of the energy of formations,

n 1. ~ ZAZB

E

= },;

E'i+ 2 },;},;P,"V~I'V+"" },;--

i~l '"v A",B rAB

the present form of the SMCO has a few shortcomings, resulting probably from the rather simplified evalua- tion of the intercore energy which has 'been cal- culated as pure electrostatic repulsion. N evert he- less, the values obtained for the molecular heats of atomization are in proportional satisfactory accord with the experimental values and, using a scale factor of 0·36, relatively good results-can be obtained (Table 5)

The molecular geometries also compare well with the experiment (Table 6). when the total energy is calculated according to expression (19)_ The in- vestigation is restricted to a few, though significant, cases, due to the great volume of work required.

By adopting a more sophisticated procedure in the calculation of the core repulsion or by a different evaluation of the parameters K~, better results for the energy of atomization could be obtained,

In order to test the possibility of applying SMCO to molecules containing third row elements, several calculations have been performed on several silicon hydrides to which the method was found to be equally applicable (Table 7).

...(19) Fig. 2

TABLE 6 - CALCULATED ANDOBSERVED MOLECULAR GEOMETRIES

[Values in parentheses are experimental values.'J

Molecule Geometry

C.H.

C~H.

NH.

CH3NH2 H20

CC 1-35 (1-532), CH 1-10 (1'107), CCH 111·0 (111-1)

CC 1·30 (1-397), CH 1-00 (1-084), CCC 120-0 (120-0)

NH 1-20 (1-012). HNH 103-9 (106'7)

CH 1-15 (1-093). NH 1-20 (1-014). CN 1-30 (1-474), CNH 110-0 (108-11)

HO 1-1 (0-957), HOH 104'0 (104-5)

TABLE 7 - SOME COMPUTED RESULTS ON Si-H COMPOUNDS

[KgSSi= 0-6,- KSi_gp = -0 9-; KH^Is = -0 26J

Molecule IP Atom and net charge

12,81 (12-82)34

10-76 10-38 9-51

Si, 0-046

Si, 0-032

Siprim0'060; Sisec 0'011 Siprim 0'063; Sisec 0·008

n

The findings presented above, thus, prove the efficacy of SMCO to the study of various molecules.

To exemplify the calculation procedure in the case of larger molecules, adrenaline and [adrenaline H]+

have been studied.

In the calculations on adrenaline the standard parametrization has been used, the results being summarized in Fig. 2. Due to lack of experimental data on molecular ionization potentials and dipole moment a direct comparison with the experiment could not be made; nevertheless, the computed values have been compared with other theoretical results's ,36 and the molecular geometry (in the in- vestigated range) correctly predicteds".

For [adrenaline H]+ a new parametrization has been done, as pointed out under the section, choice of parameters. Thus, Kr. and K~pare first adjusted to obtain the accord with the experiments" for the molecular fragments (CHaNH3)+ and [(CH3)2NH2]+' Using the standard parametrization for the rest of the molecule and Kr.

=

-1'00, K~p= 1'00, the results presented in Fig. 2 are obtained.

The relatively low absolute value of the ionization potential of [adrenaline H]+ [as compared with [CH3NH2]+, IP = -20'47 eV] and the values of the net charges on the centres could be easily ex- plained in terms of, conjugative-hyperconjugative stabilization of the arylalkvl substituted cations.

This stabilization and the values calculated for the net charges on the centres of [adrenaline HJ+

compare very well both with the experiments" and with other theoretical studies performed on alkyl- ammonium ions39.

MOLDOVEANU etol.: CoRRECT ORrHOGONALIZATlON IN SCF-LCAO-MO CALCULATION

Acknowledgement

The authors thank Dr C. 1. Lepadatu of Centre of Chemical Physics (Bucharest) and Dr E. P~usescu of Clinical Hospital, Fundeni for helpful discussions.

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