New Optimal Strategies for Ab-Initio Quantum Chemical Calculations

20 New Optimal Strategies for Ab-initio Quantum Chemical Calculations on Large Drugs, Carcinogens, Teratogens, and Biomolecules

Downloaded by EAST CAROLINA UNIV on January 2, 2018 | http://pubs.acs.org Publication Date: November 28, 1979 | doi: 10.1021/bk-1979-0112.ch020

JOYCE J. KAUFMAN, HERBERT Ε. ΡΟΡΚΙΕ, and P. C. HARIHARAN Department of Anesthesiology, The Johns Hopkins University School of Medicine, Baltimore, MD 21205, and Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218 Our group has a long standing i n t e r e s t i n quantum chemical c a l c u l a t i o n s on l a r g e drug and biomolecules. The f i r s t a l l valence three-dimensional c a l c u l a t i o n s reported on any such mole c u l e s were extended Hiickel c a l c u l a t i o n s on p y r i d i n e aldoxime anta g o n i s t s t o organophosphorus i n t o x i c a n t s we presented at the I l l r d I n t e r n a t i o n a l Pharmacological Congress, Sao Paulo, B r a z i l , J u l y I966 ( l _ , 2) . These c a l c u l a t i o n s were c a r r i e d out w i t h a program we wrote o u r s e l v e s i n I963 from the o r i g i n a l papers o f Wolfsberg and Helmholz, 1952 (3.) , and Eberhardt, Crawford and Lipscomb, I956 (h) , t h e same papers from which the extended Hiickel method of Hoffman (5) was d e r i v e d and which he named "extended Hiickel". We even wrote i n I965-I966 an i t e r a t i v e scheme f o r charge c o n s i s tency i n the extended Hiickel method. I n s p i t e o f our e a r l y compu t a t i o n a l c a p a b i l i t y our study on the p y r i d i n e aldoxime antagonists was the one and o n l y time we ever used the extended Hiickel method f o r c a l c u l a t i o n s on drugs, biomolecules or any b i o l o g i c a l , m e d i c a l or pharmacological problem. The reason that we never used t h e extended Hiickel method a g a i n f o r drug and b i o l o g i c a l systems was that we were aware o f the d e f i c i e n c i e s o f the method. I t d i d not (and s t i l l t o t h i s day does not) always g i v e a c a l c u l a t e d energy minimum even f o r s t r e t c h i n g a bond and since the method does not i n c l u d e e l e c t r o n - e l e c t r o n r e p u l s i o n i t cannot d i s t i n g u i s h between s i n g l e t and t r i p l e t s t a t e s (or doublet and quartet s t a t e s , e t c . ) . I t i s i n c r e d i b l e t h a t i n t h i s day and age extended Hiickel c a l c u l a t i o n s ( i t e r a t i v e or not) a r e s t i l l being c a r r i e d out on drugs, biomolecules or carcinogens. I t i s a method whose time i s long since past. Instead, i n I963 we were already beginning t o c a r r y out abi n i t i o LCA0-M0-SCF c a l c u l a t i o n s on s i z a b l e rocket f u e l molecules, such as B2Hg with 56 Gaussian b a s i s f u n c t i o n s (6), using an e a r l y v e r s i o n of the P0LYAT0M program supplied t o us by the l a t e P r o f e s sor John C. S l a t e r , which we converted f o r use on an IBM 709^. A f t e r u s i n g that POLYATOM program f o r o n l y a few s i z a b l e molecules i t became obvious f o r l a r g e r systems i t would be advantageous t o w r i t e a newer more e f f i c i e n t Gaussian i n t e g r a l program. We wrote 0-8412-0521-3/79/47-112-415$05.25/0 © 1979 A m e r i c a n C h e m i c a l Society

Olson and Christoffersen; Computer-Assisted Drug Design ACS Symposium Series; American Chemical Society: Washington, DC, 1979.


416

COMPUTER-ASSISTED

DRUG DESIGN

the MOSES program (Molecular O r b i t a l s ) (£) p a r t l y so named because Moses was a prophet and such a program could p r e d i c t molecular p r o p e r t i e s . The MOSES program was e f f i c i e n t and went through sev e r a l v e r s i o n s up through c o n t r a c t e d d o r b i t a l s by 19&J. I t imple mented perhaps among t h e most e f f i c i e n t algorithms f o r c a l c u l a t i n g i n t e g r a l s over c o n t r a c t e d Gaussian b a s i s f u n c t i o n s and symmetry adapted c o n t r a c t e d b a s i s f u n c t i o n s a t that time and probably even today. When Clementi was w r i t i n g h i s f i r s t IBMOL program he asked us t o check t h e accuracy o f h i s i n t e g r a l s program against those we c a l c u l a t e d u s i n g our MOSES program. Subsequently t h e i n t e g r a l s s e c t i o n of t h e MOSES program was g i v e n t o H. Basch when he was a p o s t d o c t o r a l a t B e l l Labs and he incorporated i t i n t o a l a t e r v e r s i o n of t h e POLY ATOM program. Meanwhile, i n 196** we began u s i n g a CDC 6U00 computer and i n I965 a CDC 6600 computer with an o l d CHIPPEWA c o m p i l e r — b e f o r e a Scope compiler was even a v a i l a b l e . The MOSES program was converted immediately t o r u n on t h e CDC 6400 and CDC 6600 as soon as we got access t o them, and from t h a t day t o t h i s we remain devoted fans and great exponents o f t h e CDC 66ΟΟ s e r i e s and now o f t h e CDC 7000 serues and t h e CYBER s. We have always endeavored t o make optimal use o f t h e i r 60 b i t word l e n g t h . The MOSES program c o u l d handle 175 b a s i s f u n c t i o n s i n a CDC 6600 computer. However, CDC .6000 computer time was a v e r y l i m i t e d commodity t o us i n those y e a r s and we were i n t e r e s t e d s t i l l i n c a r r y i n g out quantum chemical c a l c u l a t i o n s on l a r g e mole cules. 1

Thus i n 196^ we d e r i v e d semi-rigorous LCA0-M0-SCF methods f o r three-dimensional molecular c a l c u l a t i o n s i n c l u d i n g e l e c t r o n - e l e c t r o n r e p u l s i o n (8). T h i s paper was presented a t t h e January I965 S a n i b e l I n t e r n a t i o n a l Symposium on Atomic, Molecular and S o l i d S t a t e Theory where Pople presented h i s CNDO method and our paper appears back t o back i n t h e same Symposium i s s u e o f t h e J o u r n a l o f Chemical P h y s i c s i n which P o p l e s f i r s t papers on CNDO and NDDO appeared (£, 10) . There were four degrees o f neglect o f i n t e g r a l s i n our paper. The f i r s t and simplest resembled CND0» t h e next INDO, t h e t h i r d NDDO and t h e r e was y e t another l e s s approximate scheme. We programmed up t h e method and t r i e d i t on a few com pounds. We were s t i l l convinced that a b - i n i t i o computations were the o n l y r e a l l y a p p r o p r i a t e method f o r quantum chemical c a l c u l a t i o n s on drugs and b i o l o g i c a l molecules. Having always o n l y a very small group we decided t o devote our major e f f o r t s t o abi n i t i o quantum chemical c a l c u l a t i o n s on l a r g e drug and biomolec u l e s and e s p e c i a l l y t o d e r i v i n g and implementing new and b e t t e r s t r a t e g i e s f o r a b - i n i t i o c a l c u l a t i o n s on such molecules. In t h e i n t e r v e n i n g years f o r computational t r a c t a b i l i t y we c a r r i e d out some c a l c u l a t i o n s w i t h l e s s r i g o r o u s quantum chemical techniques [CNDO (11)» INDO (11)» PCILO (12)] as w e l l as t o p o l o g i c a l * and t o p o g r a p h i c a l f analyses on a v a r i e t y o f l a r g e drugs t o understand and p r e d i c t t h e i r c o n f o r m a t i o n a l p r o f i l e s , e l e c t r o n i c s t r u c t u r e s and p r o p e r t i e s and t h e mechanism o f a c t i o n of t h e i r biological effects. [^Topological s i m i l a r i t y — i n d i c a t e s t h a t i n 1



20.

KAUFMAN E T AL.

Ab-initio

Quantum

Chemical

Calculations

417

d i f f e r e n t molecules the same kind o f atoms a r e connected i n e x a c t l y t h e same way. Oftentimes a common t o p o l o g i c a l p a t t e r n o f atoms i s buried w i t h i n a s e r i e s of much l a r g e r molecules. fTopog r a p h i c a l s i m i l a r i t y , — i n d i c a t e s that i n d i f f e r e n t molecules two p o r t i o n s of t h e molecule bear t h e same s p a t i a l r e l a t i o n s h i p t o one a n o t h e r — a l t h o u g h not n e c e s s a r i l y t o p o l o g i c a l l y r e l a t e d . ] These included LCA0-M0-SCF c a l c u l a t i o n s on n e u r o l e p t i c s Cthe major t r a n q u i l i z e r s ) (13-20), n a r c o t i c s and n a r c o t i c a n t a g o n i s t s (13» 16, 18-23)· We were able t o i d e n t i f y t h e topographical and e l e c t r o n i c r e q u i s i t e s f o r n e u r o l e p t i c a c t i o n and we c a r r i e d out quantum chemi c a l c a l c u l a t i o n s on a h y p o t h e t i c a l s e r i e s of new e f f e c t i v e neurol e p t i c s ( l U , 15» 16, 179 18). Two years a f t e r our o r i g i n a l p r e s e n t a t i o n , s i x such compounds were reported as synthesized and animal t e s t e d and they were a l l e f f e c t i v e n e u r o l e p t i c s (2U). We c a r r i e d out t h e f i r s t a l l - v a l e n c e e l e c t r o n c a l c u l a t i o n s on narcot i c s , CNDO/2 c a l c u l a t i o n s on morphine, which were presented a t the S a n i b e l I n t e r n a t i o n a l Symposium on Atomic, Molecular and S o l i d S t a t e Theory January 1972 and appeared i n that Symposium i s s u e o f the I n t . J . Quantum Chem. (13) and we followed t h a t s h o r t l y with CNDO/2, INDO and PCILO c a l c u l a t i o n s on a v a r i e t y o f n a r c o t i c s and n a r c o t i c a n t a g o n i s t s presented at t h e S a n i b e l I n t e r n a t i o n a l Symposium January 197^ and published i n that Symposium i s s u e of t h e I n t . J . Quantum Chem. (21). In connection with these e a r l i e r quantum chemical studies we had a l s o extended t h e d e r i v a t i o n s o f some of t h e semi-rigorous techniques [such as d e r i v i n g t h e necessary expressions f o r i n c l u ding d o r b i t a l s i n t h e INDO method (25)],suggested procedures t o improve other methods [how t o improve t h e d e s c r i p t i o n o f l o n e p a i r s i n t h e PCILO method (26)1 and performed c a l c u l a t i o n s by v a r ious techniques comparing t h e r e s u l t s o f l e s s r i g o r o u s c a l c u l a t i o n s with our l a r g e b a s i s set a b - i n i t i o c a l c u l a t i o n s (27 >28). We thus have an e x c e l l e n t grasp o f t h e l i m i t s o f v a l i d i t y of l e s s than a b - i n i t i o quantum chemical c a l c u l a t i o n s compared t o a b - i n i t i o c a l c u l a t i o n s and compared t o experiment. We a l s o c a r r i e d out a few completely a b - i n i t i o c a l c u l a t i o n s on t h e n e u r o l e p t i c chloropromazine and on promazine (29) and on the n a r c o t i c morphone and t h e n a r c o t i c agonist-antagonist nalorphine (30) using IBMOL 6 (31) · However, even though IBMOL 6 had been w r i t t e n e s p e c i a l l y t o c a r r y out a b - i n i t i o c a l c u l a t i o n s on l a r g e molecules, and we had improved i t s use by such techniques as repacking t h e i n t e g r a l tapes so that f o r t h e f i r s t s i x i t e r a t i o n s we read only i n t e g r a l s 10""^ a.u. or l a r g e r , f o r t h e next s i x i t e r a t i o n s a l l i n t e g r a l s 5 X 10~6 a.u. or l a r g e r , and f o r t h e f i n a l few i t e r a t i o n s a l l i n t e g r a l s 10~7 a.u. or l a r g e r , t h e c a l c u l a t i o n s mentioned above that we d i d with IBMOL 6 convinced us that we were going t o have t o develop something s t i l l b e t t e r t o make computat i o n a l l y t r a c t a b l e r o u t i n e a b - i n i t i o c a l c u l a t i o n s on l a r g e drug and biomolecules. Ab-initio

MODPOT/VRDDO/MERGE

Technique



418

COMPUTER-ASSISTED DRUG DESIGN

I t was i n 197*+ t h a t we began development o f our new s e r i e s o f Gaussian i n t e g r a l programs e s p e c i a l l y designed f o r l a r g e mole c u l e s : MOLASYS (Molecular O r b i t a l C a l c u l a t i o n s on Large Systems) (.32, 33) and GIPSY [Gaussian I n t e g r a l Program System) (3^, 35) . MOLASYS and GIPSY c a l c u l a t e s,p,d and f i n t e g r a l s i n b l o c k s , t a k i n g f u l l advantage of t h e information common t o members o f t h e same block. We a l s o use the f u l l 60 b i t CDC word t o store small two e l e c t r o n i n t e g r a l s indexing t h e i n t e g r a l a l s o i n the same word u s i n g t h e l e a s t s i g n i f i c a n t b i t s f o r indexing and converting t h e i n t e g r a l t o f l o a t i n g p o i n t when i t i s used. We have compared t h e timings d i r e c t l y with those o f other general s,p, and d i n t e g r a l packages i n current usage (and which we o u r s e l v e s had used p r e v i o u s l y ) . Our new i n t e g r a l program, GIPSY, f o r s,p and d i n t e g r a l s i s o f t h e order o f four times f a s t e r than R a f f e n e t t i ' s BIGGMOLI (36, 37) program and twice as f a s t as BIGGMOLI f o r s and ρ i n t e g r a l s only. Our GIPSY program i s o f t h e order o f eight times f a s t e r f o r s,p and d i n t e g r a l s than POLYATOM Ç38) [improved CDC 6600 v e r s i o n (39)] and four times f a s t e r than POLYATOM (3£) f o r s and ρ i n t e g r a l s only. I n d i r e c t timing comparisons {ho) i n d i c a t e that our GIPSY program i s twice as f a s t as GAUSSIAN 70 (kl) f o r general s and ρ i n t e g r a l s with d i f f e r e n t exponents and of t h e same speed as GAUSSIAN 70 when t h e same exponents a r e used i n GAUSSIAN 70 f o r s and ρ f u n c t i o n s . The same algorithm i s used i n GAUSSIAN 76 jh2) . Recently there has been introduced a new method e s p e c i a l l y e f f i c i e n t f o r e v a l u a t i o n of Gaussian i n t e g r a l s f o r b a s i s f u n c t i o n s of higher angular momentum (J+3) and t h e authors i n c o r porated i t i n t o a new program c a l l e d HONDO (j+3.) · I n d i r e c t timing comparisons f o r s,p and d i n t e g r a l s reported (k3) f o r HONDO com pared t o PHANTOM (hh) (a QCPE CDC 6600 v e r s i o n of POLYATOM) and t o BIGGMOLI (36, 37.) i n d i c a t e that our GIPSY s,p and d i n t e g r a l p r o gram i s probably a f a c t o r o f 1.3 f a s t e r than HONDO- An algorithm f o r d o r b i t a l s s i m i l a r t o that of HONDO i s used i n the newer v e r s i o n of GAUSSIAN 76 (h2). We p l a n t o check t h e timing comparison f o r f o r b i t a l s between GIPSY and HONDO as soon as f e a s i b l e . But even more importantly, our programs incorporate s e v e r a l v e r y d e s i r a b l e f e a t u r e s as time-saving options t o our a b - i n i t i o computer programs: a charge conserving i n t e g r a l prescreening approximation (VRDDO) e s p e c i a l l y e f f e c t i v e f o r s p a t i a l l y extended molecules; a b - i n i t i o e f f e c t i v e core, model p o t e n t i a l s (M0DP0T) which enable one t o t r e a t only the valence e l e c t r o n s e x p l i c i t l y yet a c c u r a t e l y ; and a MERGE technique which enables us t o r e t a i n a l l the i n t e g r a l s f o r a s k e l e t a l fragment which remains unchanged and j u s t r e c a l c u l a t e t h e new i n t e g r a l s f o r added atoms or t h e i r geometry variâtions,both f o r i n t r a - and i n t e r m o l e c u l a r c a l c u l a t i o n s . Our VRDDO approximation ( v a r i a b l e r e t e n t i o n o f diatomic d i f f e r e n t i a l overlap) was i n s p i r e d i n part by a suggestion from s o l i d s t a t e p h y s i c s by W i l h i t e and Euwema {k5) . The approximation cons i s t s o f n e g l e c t i n g a l l o n e - e l e c t r o n i n t e g r a l s (both energy and overlap) and two-electron i n t e g r a l s that i n v o l v e b a s i s f u n c t i o n p a i r s φ.(1)φ.(ΐ) whose pseudo-overlap:


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Calculations

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2 s

l V
, |2s^> and |2p > a r e inner s h e l l atomic o r b i t a l s for t h e k-th core. B o n i f a c i c and Huzinaga (58, 59) have introduced Gaussian terms i n t o t h e one-electron p a r t o f t h e Hamiltonian t o account f o r the screening o f t h e n u c l e i by t h e core e l e c t r o n s and pseudopotent i a l terms t o prevent t h e buildup o f t h e valence molecular o r b i t a l s i n t h e core r e g i o n s . B o n i f a c i c and Huzinaga d e r i v e d model p o t e n t i a l expressions f o r inner s,p and d o r b i t a l s . We extended the d e r i v a t i o n a l s o t o inner f o r b i t a l s . T h i s MODPOT procedure of B o n i f a c i c and Huzinaga has been introduced as an o p t i o n i n t o our MOLASYS and GIPSY computer programs. With t h e GIPSY computer program we can c a l c u l a t e t h e u s u a l o n e - e l e c t r o n o v e r l a p , k i n e t i c energy, nuclear a t t r a c t i o n and two-electron r e p u l s i o n i n t e g r a l s between s-, ρ-, d- and f - c o n t r a c t e d Gaussian f u n c t i o n s . I n a d d i t i o n , t h e new type o f one-electron i n t e g r a l s r e s u l t i n g from t h e use o f t h e Bonifacic-Huzinaga Hamiltonian with s-, ρ-, d- and f type core atomic o r b i t a l s can be c a l c u l a t e d . We v e r i f i e d t h e accuracy o f t h e MODPOT method f o r a v a r i e t y of molecules by c a r r y i n g out t h e r e f e r e n c e c a l c u l a t i o n s with twoe l e c t r o n i n t e g r a l s accurate t o 6 decimal p l a c e s . Then t h e MODPOT c a l c u l a t i o n s were c a r r i e d out with t h e valence s h e l l two-electron i n t e g r a l s accurate t o 6 decimal p l a c e s and t h e MODPOT m o d i f i e d one-electron i n t e g r a l s . The same r e f e r e n c e atomic b a s i s set was used f o r both c a l c u l a t i o n s . Comparison o f t h e MODPOT r e s u l t s t o the completely a b - i n i t i o ones ( i n c l u d i n g inner s h e l l e l e c t r o n s ) showed t h a t t h e valence o r b i t a l energies and gross atomic popula t i o n s a r e a c c u r a t e * [see footnote page Ul9] t o more than 2 decimal p l a c e s (the average error i s 0.005 a.u.). The maximum e r r o r i n c

k

k



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421

the o r b i t a l energies f o r t h e l a r g e s t molecule studied t o date i s o n l y 0.11 a.u. and i n t h e gross atomic p o p u l a t i o n s i s o n l y 0.010 a.u. I t should be emphasized that t h e accuracy obtained with t h e MODPOT approximation i s more than acceptable i f one wants t o reproduce a b - i n i t i o r e s u l t s f o r l a r g e molecules. Moreover, f o r molecules composed even o f two second row atoms, such as 01^» "the savings i n time between t h e MODPOT method compared t o t h e comp l e t e l y a b - i n i t i o i s a f a c t o r o f t e n . The savings i n time a l s o i n c r e a s e d r a m a t i c a l l y as t h e s i z e o f t h e molecule goes up. I f both t h e MODPOT and VRDDO approximations are introduced, t h e accuracy* [*see footnote page Ul9] with respect t o t h e r e f e r ence c a l c u l a t i o n s i s about t h e same as t h a t obtained u s i n g o n l y the MODPOT approximation. The maximum e r r o r i n t h e o r b i t a l energ i e s i s 0.012 a.u., i n t h e gross atomic p o p u l a t i o n s i s 0.009» i n the t o t a l o v e r l a p populations i s 0.027 and i n t h e d i p o l e moment

i s 0.009 a.u.

Since one u s u a l l y i s i n t e r e s t e d i n energy d i f f e r e n c e s r a t h e r than t h e t o t a l energy of a s i n g l e system, i t i s u s e f u l t o compare isomer energy d i f f e r e n c e s computed with t h e v a r i o u s procedures. In t h e 6-3G r e f e r e n c e c a l c u l a t i o n s (I18-U9) imidazole i s more s t a b l e than p y r a z o l e by 0.0150 a.u., p y r i m i d i n e i s more s t a b l e than p y r i d a z i n e by O.02U7 a.u., and p y r a z i n e i s more s t a b l e than p y r i d a z i n e by 0.0222 a.u. With t h e VRDDO method t h e corresponding energy d i f f e r e n c e s are 0.0153, 0.0258 and 0.0219 a.u. r e s p e c t i v e l y . Use of t h e MODPOT method y i e l d s v a l u e s o f 0.0136, 0.0219 and O.OI89 r e s p e c t i v e l y . F i n a l l y , t h e M0DP0T/VRDD0 method g i v e s v a l u e s o f 0.0139, 0.0231 and 0.0188 a.u. r e s p e c t i v e l y . Thus, even f o r t h e M0DP0T/VRDD0 method, t h e agreement with a b - i n i t i o r e s u l t s i s e x c e l l e n t ; 0.0011 a.u. f o r i m i d a z o l e - p y r a z o l e , 0.0016 a.u. f o r p y r i m i d i n e - p y r i d a z i n e and 0.003^ a.u. f o r p y r a z i n e - p y r i d a z i n e . The r e l a t i v e accuracy of t h e MODPOT/VRDDO method along a p o t e n t i a l energy surface (such as f o r molecular conformational changes or i n t e r a c t i o n s between two s p e c i e s , 0.0001 - 0.0002 a.u.) i s even greater than i t s absolute accuracy. For one aromatic r i n g with one s u b s t i t u e n t (such as NO2) t h e VRDDO c a l c u l a t i o n i s 1.5 times f a s t e r than t h e r e f e r e n c e c a l c u l a t i o n (using our own f a s t a b - i n i t i o programs [32, 33, 3^» 35]> t h e MODPOT c a l c u l a t i o n i s t h r e e times f a s t e r and t h e M0DP0T/VRDD0 c a l c u l a t i o n i s f i v e times f a s t e r ) . Moreover, t h e r e l a t i v e i n c r e a s e i n speed goes up even more d r a m a t i c a l l y as t h e molecules get l a r g e r . We v e r i f i e d t h e accuracy o f t h e MODPOT method f o r a v a r i e t y of molecules (V7, k8, U9) by c a r r y i n g out t h e r e f e r e n c e c a l c u l a t i o n s with two-electron i n t e g r a l s accurate t o 6 decimal p l a c e s . Then t h e MODPOT c a l c u l a t i o n s were c a r r i e d out with t h e valence s h e l l two-electron i n t e g r a l s accurate t o 6 decimal p l a c e s and t h e MODPOT m o d i f i e d one-electron i n t e g r a l s . The same r e f e r e n c e atomic b a s i s set was used f o r both c a l c u l a t i o n s . Comparison o f MODPOT r e s u l t s t o t h e completely a b - i n i t i o ones ( i n c l u d i n g inner s h e l l e l e c t r o n s ) showed t h a t t h e valence o r b i t a l energies and gross



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atomic p o p u l a t i o n s are accurate t o more than 2 decimal p l a c e s ( t h e average e r r o r i s 0.005 a.u.). Moreover, t h e accuracy o f t h e MODPOT r e s u l t s compared t o a b - i n i t i o i s much greater (0.005 eV [50]) f o r c a l c u l a t i n g e x c i t a t i o n energies, e l e c t r o n a f f i n i t i e s , t o t a l energy d i f f e r e n c e s between isomers, p o t e n t i a l energy curves, e t c . , s i n c e these i n v o l v e o n l y energy d i f f e r e n c e s . Moreover, f o r molecules composed even o f two second row atoms, such as C ^ » "the savings i n time between t h e MODPOT method compared t o t h e com p l e t e l y a b - i n i t i o i s a f a c t o r o f t e n . The savings i n time a l s o i n c r e a s e s d r a m a t i c a l l y as t h e s i z e o f t h e molecule goes up. As a t e s t o f t h e e f f i c i e n c y o f t h e method, we r a n a b - i n i t i o M0DP0T/VRDD0 c a l c u l a t i o n s on t h e DNA bases ($k) : Molecule

No. Atoms

C,N,0 DNA C o n s t i t u e n t s

No. B a s i s Fns.

Time (minut es) Integrals*

H

Cytosine

8

5

37

Guanine

11

5

k

Thymine

9

6

38

Adenine

10

5

9

5.1 11.2

SCFt

2.0 k.3

ΊΛ

3.1

9.2

3-5

*CDC 6600 computer, FTN, 0PT=0. (The i n t e g r a l s run even ~75# f a s t e r under 0PT=2 on a CDC 6600 computer which supports a f u l l 0PT=2 compiler.) fCDC 6600 computer, FTN, 0PT=2. We have obtained t h e MODPOT parameters f o r t h e f o r m u l a t i o n we use by matching MODPOT c a l c u l a t i o n s t o t h e completely a b - i n i t i o c a l c u l a t i o n s f o r atoms or small molecules u s i n g t h e same atomic r e f e r e n c e b a s i s set. We a r e c u r r e n t l y working on matching these parameters f o r higher elements. There are a number o f methods f o r t r e a t i n g t h e e f f e c t i v e core p o t e n t i a l s , r e l a t i v i s t i c e f f e c t i v e core p o t e n t i a l s (and some comparisons and c r i t i q u e s ) . Space l i m i t a t i o n does not permit us t o l i s t a l l these r e f e r e n c e s . F o r a complete up-to-date b i b l i o g r a p h y on v a r i o u s model p o t e n t i a l methods see our recent NATO Advanced Study I n s t i t u t e l e c t u r e (6θ). However, i t appears t h a t t h e core p r o j e c t i o n model p o t e n t i a l s o f the B o n i f a c i c and Huzinaga type we use which y i e l d valence o r b i t a l s with t h e u s u a l o s c i l l a t o r y behavior i n t h e core r e g i o n may have advantages f o r c a l c u l a t i o n o f c o r r e l a t i o n energies over t h e pseudopotentials g i v i n g valence p s e u d o o r b i t a l s which a r e smooth i n t h e core r e g i o n . We have j u s t f i n i s h e d w r i t i n g a new MERGE technique which allows us t o r e t a i n t h e i n t e g r a l s f o r a s k e l e t a l fragment which remains unchanged. T h i s i s e s p e c i a l l y u s e f u l i n s t u d i e s o f l a r g e c l o s e l y r e l a t e d molecules and t h e i r complexes since only an atom or a few atoms are changed and except f o r t h e r i n g which i s being



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attacked, t h e s t r u c t u r e o f t h e r e s t o f t h e molecule remains i n v a r i a n t . I t was not s t r a i g h t f o r w a r d t o i n c o r p o r a t e a MERGE t e c h n i que i n t o our program s i n c e we c a l c u l a t e i n t e g r a l s v e r y e f f i c i e n t l y by blocks r a t h e r than one by one. We are now u s i n g t h i s MERGE o p t i o n f o r a l l our c a l c u l a t i o n s since t h e systems we are i n v e s t i g a t i n g at present are q u i t e l a r g e . The MERGE o p t i o n i s u s e f u l for l a r g e molecules (even one and two r i n g systems], and excep t i o n a l l y v a l u a b l e f o r l a r g e r molecules and where t h e part t o be v a r i e d i s small compared t o a l a r g e i n v a r i a n t s t r u c t u r a l fragment. As an example, while t h e s k e l e t a l i n t e g r a l s f o r b e n z o p y r e n e - 7 , 8 d i h y d r o d i o l (a 5 - r i n g aromatic proximate carcinogen) took 3 0 0 5 seconds (CDC 6 6 0 0 , 0 P T = 1 ) t o form t h e u l t i m a t e carcinogen benzo p y r e n e - 7 , 8 - d i h y d r o d i o l - 9 , 1 0 - e p o x i d e , t h e extra MERGE i n t e g r a l s for t h e oxygen with the r e s t o f t h e skeleton took o n l y 5 6 0 seconds (CDC 6 6 0 0 , 0 P T = 1 ) (57_) . Thus i t was computationally extremely t r a c t a b l e f o r us t o vary t h e stereochemistry o f t h e epoxide r i n g and i t s opening t o form an a t t a c k i n g agent. We have r e c e n t l y run a b - i n i t i o MODPOT/VRDDO/MERGE c a l c u l a t i o n s on t h e a t t a c k of CH3 , t h e simplest u l t i m a t e carcinogen, on guanine f o r a t t a c k on t h e 0 ° and N7 p o s i t i o n s ( 5 8 ) using s e v e r a l d i f f e r e n t types o f CDC computers (CDC 6 6 0 0 and CYBER 1 7 5 ) with a v a r i e t y o f d i f f e r e n t operating systems (which d i d or d i d not support, f u l l 0 P T = 1 and 0 P T = 2 compilers at v a r i o u s t i m e s ) . Some idea o f comparative timings can be seen below. +

Times (minutes) necessary t o c a r r y out a b - i n i t i o M 0 D P 0 T / V R D D 0 and a b - i n i t i o MODPOT/VRDDO/MERGE c a l c u l a t i o n s Species

No. Atoms

No. B a s i s Fns.

Time (minutes) Integrals or S k e l e t a l Integrals

C,N,0

H

Guanine

11

5

1+9

Guanine + CH

12

8

56

MERGE Integrals

11.2

SCF

^ . 3

6.8

Δ

T

2.3*

5·0

0.9

1 · /

+

+

3

2.9

V

V

* CDC 6600 computer, FTN, 0 P T = 0 (The i n t e g r a l s run even ~75# f a s t e r under 0 P T = 1 or 0 P T = 2 on a CDC 6600 computer t h a t supports a f u l l 0 P T = 1 or 0 P T = 2 compiler.) t CDC 6600 computer, FTN, 0 P T = 2 Δ CDC 66ΟΟ computer, FTN, 0PT=1 V CYBER 1 7 5 , FTN, 0 P T = 1 # CYBER 1 7 5 , FTN, 0 P T = 2 An unusual behavior occurred i n t h e system CH-^"** + guanine (G). As t h e i n t e r n u c l e a r 0 or Ν t o Me d i s t a n c e approached 5 bohrs, there was a mixing o f e l e c t r o n i c c o n f i g u r a t i o n s . When we saw t h e e l e c t r o n i c c o n f i g u r a t i o n mixing, our experience with t h e theory and p r e v i o u s l a r g e s c a l e a b - i n i t i o c o n f i g u r a t i o n i n t e r -


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a c t i o n c a l c u l a t i o n s on ion-molecule r e a c t i o n s i n d i c a t e d t h e p h y s i c a l b a s i s had t o be due to the f a c t that while the r e a c t a n t s were CH^ " + G, at the d i s s o c i a t i o n asymptote t h e r e was a lower energy set of fragments C H 3 + G . When we i n i t i a t e d our c a l c u l a t i o n s the experimental IP o f guanine had never been r e p o r t e d . However, we knew t h e p h o t o e l e c t r o n s p e c t r a of DNA bases was being i n v e s t i g a t e d by Le Breton. We c a l l e d him and indeed the i o n i z a t i o n p o t e n t i a l of guanine, 8.3 eV (68), i s c o n s i d e r a b l y lower than that of C H 3 , 9.8 eV (69). Using our e f f i c i e n t MERGE technique the time consuming p a r t of computing a s e r i e s of higher s u b s t i t u t e d m a t a b o l i t e s o f a common skeleton or p o t e n t i a l energy surfaces as a f u n c t i o n of nuclear geometry now becomes t h e SCF r a t h e r than the i n t e g r a l s . S i n c e t h e Fock matrix elements corresponding t o t h e i n v a r i a n t s k e l e t a l i n t e g r a l s remain v i r t u a l l y unchanged (except f o r a s l i g h t dependence on o r t h o g o n a l i t y ) e i t h e r f o r a f a m i l y of s u b s t i t u t e d molecules or f o r a l a r g e molecule being attacked by a smaller s p e c i e s , we have d e r i v e d a new s t r a t e g y based on p a s s i n g through f o r t h e SCF, e i t h e r i n t r a - or i n t e r m o l e c u l a r , the Fock matrix c o n t r i b u t i o n s from t h e i n v a r i a n t s k e l e t a l i n t e g r a l s making up o n l y the a d d i t i o n a l c o n t r i b u t i o n s t o the Fock matrix elements from t h e new i n t e g r a l s , a l l o w i n g o n l y t h e c o n t r i b u t i o n s from t h e new i n t e g r a l s t o the Fock m a t r i x elements t o change u n t i l the SCF c a l c u l a t i o n i s about converged, then r e l a x i n g and making up new Fock matrix elements from a l l of t h e i n t e g r a l s f o r each c y c l e u n t i l convergence. C o n s i d e r a b l e numerical t e s t i n g must now be done w i t h t h i s procedure.* I t i s expected t h a t t h i s technique w i l l work most e f f e c t i v e l y f o r systems where no convergence problems would otherwise be expected. I f the scheme works w e l l , we p l a n t o extend a s i m i l a r scheme t o do t r a n s f o r m a t i o n s o f i n t e g r a l s f o r CI c a l c u l a t i o n s f o r s e r i e s o f congeners or f o r c l o s e l y spaced p o i n t s along a p o t e n t i a l energy s u r f a c e . I n order t o o b t a i n convergence and compute at l e a s t the d i a b a t i c c o n t i n u a t i o n past 5 bohrs of t h e curve d e s c r i b i n g t h e c l o s e approach of CH3 t o guanine, we wrote new more e f f i c i e n t e x t r a p o l a t i o n and damping r o u t i n e s (70)» Both c l o s e d and o p e n - s h e l l systems can be c a l c u l a t e d . The programs can handle s e v e r a l hundred b a s i s f u n c t i o n s i n a CDC 6600 computer and more i n a CDC 7600. I n a d d i t i o n , we p l a n t o explore f u r t h e r new and n o v e l methods f o r subsequent c a l c u l a t i o n on l a r g e molecules the s i z e of block regions of DNA and f o r i n t e r a c t i o n of reagents with h e l i c a l DNA by molecular p a r t i t i o n i n g . 4


+

+

Configuration Interaction Calculations The M0DP0T/VRDD0 LCA0-M0-SCF programs have been meshed i n with t h e c o n f i g u r a t i o n i n t e r a c t i o n programs we use. In t h i s CI (71) program each c o n f i g u r a t i o n i s a s p i n - and symmetry-adapted l i n e a r combination of S l a t e r determinants i n the terms of t h e spin-bonded f u n c t i o n s of Boys and Reeves (72, 73 Jh) as formu?

9


20.

K A U F M A N E TA L .

Ab-initio

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425

l a t e d o r i g i n a l l y by S h a v i t t , Pipano and co-workers Ç75, 76, 77) and subsequently m o d i f i e d and extended i n our l a b o r a t o r y (78, 79,

80).

The determinants can be obtained from s i n g l e determinant or MC-SCF wave f u n c t i o n s . We have a l s o added a method o f c a l c u l a t i n g improved v i r t u a l o r b i t a l s . Our use o f t h i s procedure f o r N - e l e c t r o n e x c i t e d s t a t e v i r t u a l o r b i t a l s Ç81) i n the framework o f the SCF c a l c u l a t i o n o f the N - l e l e c t r o n problem c l o s e l y resembles those proposed by Huzinaga (82). We have a l s o i n v e s t i g a t e d Huzinaga s recent method f o r improved v i r t u a l o r b i t a l s i n the extended b a s i s f u n c t i o n space Ç83). T h i s i s a l s o a u s e f u l procedure where t h e r e a r e convergence problems f o r the Hartree-Fock c a l c u l a t i o n s f o r t h e N - e l e c t r o n occupied space o f t h e e x c i t e d s t a t e s . T h i s should a l s o be h e l p f u l i n o p t i m i z i n g v i r t u a l o r b i t a l s t o use them i n p e r t u r b a t i o n theory expressions. The most time and space consuming part and t h e l i m i t i n g f a c t o r o f a CI c a l c u l a t i o n i s the t r a n s f o r m a t i o n o f i n t e g r a l s from i n t e g r a l s over atomic b a s i s f u n c t i o n s t o i n t e g r a l s over molecular o r b i t a l s . We have implemented a technique which i n c o r p o r a t e s i n t o an e f f e c t i v e CI Hamiltonian operator t h e e f f e c t o f a l l molec u l a r o r b i t a l s from and t o which no e x c i t a t i o n s are made (Ok) .


1

P e r t u r b a t i o n Procedures f o r Molecular I n t e r a c t i o n s I t would be d e s i r a b l e t o be a b l e t o c a l c u l a t e the m a j o r i t y o f the molecular i n t e r a c t i o n surface between l a r g e molecules by a p e r t u r b a t i o n technique r a t h e r than by the supermolecule technique. P r e v i o u s l y we had shown by comparison with accurate a b - i n i t i o c a l c u l a t i o n s t h e n o n - a p p l i c a b i l i t y o f the customary approximate m o n o p o l e - t r a n s i t i o n moment long range f o r c e expressions Ç86, 87) as w e l l as t h e n o n - a p p l i c a b i l i t y o f CNDO and INDO supermolecule p o t e n t i a l energy surfaces themselves f o r molecular i n t e r a c t i o n s even when the i n t e r a c t i n g supermolecule system i s c o r r e c t l y e x p r e s s i b l e by a s i n g l e determinant wave f u n c t i o n . The same a p p l i e s t o NDDO,MIND0 (88) , MNDO (8£, 20) and a l l other ZDO methods. Even worse, i n recent work presented on c a r c i n o g e n e s i s by others t h e MIND0/3 method (which was d e r i v e d t o d e s c r i b e s t a t i c thermochemistry) was used t o d e s c r i b e the r e a c t i o n pathway o f i n s e r t i o n o f s i n g l e t oxygen i n t o an R-H bond. F i r s t l y , no ZDO s i n g l e determinant method i s a p p r o p r i a t e even when the lowest energy surface o f the system separates c o r r e c t l y t o c l o s e d s h e l l ground s t a t e s p e c i e s . Secondly, the use of any s i n g l e determinant wave f u n c t i o n i s not c o r r e c t t o d e s c r i b e p o t e n t i a l energy surfaces f o r r e a c t i o n s o f t h i s 0 i n s e r t i o n t y p e , since there i s no way t h e lowest energy curve can d i s s o c i a t e c o r r e c t l y i n a s i n g l e determinant. T h i r d l y , t h e r e are f i v e s i n g l e t p o t e n t i a l energy surfaces a r i s i n g from 0 ^Dg + R-H which l i e lower i n energy a t the d i s s o c i a t i o n asymptote than the s i n g l e t p o t e n t i a l energy surface a r i s i n g from 0 -^S^ + R-H and a l l f i v e w i l l mix at some p o i n t s i n the p o t e n t i a l



426


energy surfaces f o r t h e r e a c t i o n with t h e s i n g l e t surface a r i s i n g from 0 "^Sg + R-H. There i s no way t o d e s c r i b e such processes c o r r e c t l y except by a b - i n i t i o CI (or a b - i n i t i o MODPOT/VRDDO/CI or a b - i n i t i o M O D P O T / V R D D O / M E R G E / C I c a l c u l a t i o n s ) . A great prob lem (perhaps t h e g r e a t e s t ) i n e s t a b l i s h i n g and keeping t h e c r e d i b i l i t y o f quantum chemical c a l c u l a t i o n s i n b i o l o g y and medicine i s t h e poor q u a l i t y of much o f t h e quantum chemical c a l c u l a t i o n s c a r r i e d out i n b i o l o g i c a l , pharmacological and medical a r e a s — and what i s even worse, i n c o r r e c t use o f quantum chemistry i n these areas. We are examining t h e question o f v a r i o u s r i g o r o u s p e r t u r b a t i o n expressions ( 9 1 ) f o r i n t e r m o l e c u l a r i n t e r a c t i o n s and a r e c u r r e n t l y doing t h e a n a l y s i s and w r i t i n g a program t o c a l c u l a t e these (j?2) . We s h a l l t e s t t h e v a l i d i t y o f t h i s l a t t e r procedure by comparison with accurate a b - i n i t i o supermolecule c a l c u l a t i o n s for smaller t e s t systems. The e l e c t r o s t a t i c , exchange, charge-induced m u l t i p o l e , m u l t i pole-induced m u l t i p o l e , and c h a r g e - t r a n s f e r c o n t r i b u t i o n s can a l s o be c a l c u l a t e d by p a r t i t i o n i n g o f t h e SCF c a l c u l a t i o n . The d i s p e r s i o n energy must be c a l c u l a t e d or estimated s e p a r a t e l y . We s h a l l a l s o g i v e c o n s i d e r a t i o n t o an a l t e r n a t i v e f o r m u l a t i o n f o r molecular i n t e r a c t i o n s f o r both s i n g l e determinant and m u l t i d e t e r minant wave f u n c t i o n s and t e s t these against a b - i n i t i o c a l c u l a tions . In a d d i t i o n there a r e c o r r e l a t i o n energy terms ( A E r r ) "both i n t r a - and i n t e r - m o l e c u l a r . The l a r g e s t change i n i n t e r a c t i o n o f two non-polar molecules i s i n the i n t e r - m o l e c u l a r d i s p e r s i o n energy term r e s u l t i n g from the instantaneous p o l a r i z a t i o n o f A and B . Over t h e years v a r i o u s approximate formulas f o r i n t e r a c t i o n s between l a r g e molecules have been d e r i v e d from p e r t u r b a t i o n theory (91). The b e t t e r o f such p e r t u r b a t i o n theory expansions custom a r i l y i n c l u d e a short-range f i r s t order "exchange" term and long range terms ( e l e c t r o s t a t i c , p o l a r i z a t i o n and d i s p e r s i o n ) . Various approximations (such as the m u l t i - c e n t e r e d m u l t i p o l e expansion, r e p r e s e n t a t i o n o f t r a n s i t i o n d e n s i t i e s by bond d i p o l e and t h e decomposition o f molecular p o l a r i z a b i l i t y i n t o bond p o l a r i z a b i l i t i e s , t h e use o f atomic p o l a r i z a b i l i t i e s , bond-bond i n t e r a c t i o n terms, etc.) have been introduced f o r t h e c a l c u l a t i o n o f c e r t a i n of t h e terms. A c a r e f u l a n a l y s i s o f t h e SCF energy decomposition f o r an i n t e r - m o l e c u l a r i n t e r a c t i o n o f A and Β o f v a r i o u s p e r t u r b a t i o n energy expressions i n d i c a t e that f o r c e r t a i n p e r t u r b a t i o n formula t i o n s there i s a one-to-one correspondence between c e r t a i n SCF energy decomposition terms and c e r t a i n terms i n t h e p e r t u r b a t i o n expressions. Thus one can c a l c u l a t e t h e values f o r t h e terms from energy decomposition o f a b - i n i t i o or a b - i n i t i o MODPOT/VRDDO SCF wave f u n c t i o n s and compare these t o t h e values f o r t h e same type term r e s u l t i n g from t h e p e r t u r b a t i o n theory expressions. Care must be taken t o c o r r e c t f o r p o s s i b l e b a s i s set incompleteness. C O


20.

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ET AL.

Ab-initio

Quantum

Chemical

Calculations

427

Once both t h e form o f t h e v a r i o u s p e r t u r b a t i o n theory terms and t h e approximations t h a t may be involved i n estimating these terms have been v a l i d a t e d by comparison with a b - i n i t i o MODPOT/ VRDDO c a l c u l a t i o n s , then the most a p p r o p r i a t e p e r t u r b a t i o n theory expressions can be used i n p r e l i m i n a r y c a l c u l a t i o n s o f i n t e r molecular i n t e r a c t i o n s f o r t h e v a r i o u s r e a c t a n t s . T h i s same p e r t u r b a t i o n theory approach i s capable o f d e s c r i b ing both i n t e r - and i n t r a - m o l e c u l a r i n t e r a c t i o n s .


E l e c t r o s t a t i c Molecular

P o t e n t i a l Contour Maps

For molecular i n t e r a c t i o n s i n v o l v i n g molecules having net charges or permanent d i p o l e s , u s e f u l i n f o r m a t i o n may be drawn by examination of t h e e l e c t r o s t a t i c p o t e n t i a l , a r i s i n g from one o f the p a r t n e r s , and by simple e l e c t r o s t a t i c c a l c u l a t i o n s , i n v o l v i n g a p o t e n t i a l and a s i m p l i f i e d d e s c r i p t i o n of t h e charge d i s t r i b u t i o n of t h e other molecule i n v o l v e d i n the i n t e r a c t i o n (£G, 9*0 · The e l e c t r o s t a t i c p o t e n t i a l V(r) g i v e s more d e t a i l e d and l e s s ambiguous information than a p o p u l a t i o n a n a l y s i s , being a f u n c t i o n computed i n t h e o v e r a l l molecular surrounding space. From t h e p o t e n t i a l d e f i n i t i o n , t h e f i r s t order i n t e r a c t i o n energy between the molecular charge d i s t r i b u t i o n and a p o i n t charge distribution i s W ( {r.} ) =

Zq(r.) V ( r . )

Such an expression has p r e v i o u s l y been used f o r comparative purposes, f o r t h e study o f i n t e r a c t i o n between two molecular s p e c i e s , by computing t h e e l e c t r o s t a t i c p o t e n t i a l of t h e f i r s t partner and by assuming some point charge model as r e p r e s e n t a t i v e of t h e charge d i s t r i b u t i o n of t h e second p a r t n e r . We a l s o p l a n t o extend t h i s concept i n a more s u b t l e way by using an e l e c t r o n d e n s i t y contour map t o d e s c r i b e the charge d i s t r i b u t i o n o f t h e second p a r t n e r as a f u n c t i o n o f t h e space surrounding t h i s second partner. We were a b l e t o show t h a t a b - i n i t i o l a r g e b a s i s set and abi n i t i o optimized small b a s i s set wave f u n c t i o n s generate e l e c t r o s t a t i c molecular p o t e n t i a l contour maps almost i d e n t i c a l i n shape and magnitude (95). We a l s o confirmed t h e e a r l i e r f i n d i n g s by other r e s e a r c h e r s t h a t CNDO/2 and INDO wave f u n c t i o n s , e i t h e r orthogonal or deorthogonalized, d i d not generate maps which compared c o r r e c t l y with those generated from a b - i n i t i o wave f u n c t i o n s (95, 96, 97)* Those CNDO/2 and INDO maps a r e e s p e c i a l l y i n a c c u r a t e for aromatic compounds and even f o r i s o l a t e d double bonds (jté, 9 7 ) · Such maps a r e r e f l e c t i v e of dynamic r e a c t i o n i n d i c e s and prove more accurate i n d i c a t o r s o f t h e p o s i t i o n s favored f o r e l e c t r o p h i l i c a t t a c k than do such s t a t i c i n d i c e s as charges on t h e atoms.


428



Abstract The optimal strategy for ab-initio quantum chemical calculations on large molecules (drugs, carcinogens, teratogens and biomolecules) is somewhat different than for smaller molecules. It is possible to take advantage of certain computational properties of large molecules and of series of closely related congeners of large molecules. We have implemented several desirable options into our fast ab-initio Gaussian integral programs (SCF, MC-SCF and CI): the use of ab-initio effective core model potentials (MODPOT) which enable one to calculate only the valence electrons explicitly yet accurately, a charge conserving integral prescreening evaluation (VRDDO) especially effective for spatially extended molecules and a new MERGE technique which enables reuse of integrals from a common skeletal fragment and only recalculation of integrals involving new positions of certain atoms or new atoms. We have also recently derived a new SCF strategy which passes through Fock matrix elements as a starting Fock matrix, reutilizes the Fock matrix elements from the common skeletal integrals, takes advantage of the fact that the common Fock matrix elements change little during the preliminary iterations. We have also derived new MC-SCF and CI integral transformation strategies which take advantage of behavior similar to that utilized above. Examples are given from our recent research. Supported in part by NCI Contract NO1-CP-75929 and by NINCDS Contract NO1-NS-5-2320.

Ac kno wledgment T h i s r e s e a r c h was supported i n p a r t by NCI under Contract NOl-CP-75929. We thank our NCI contract monitor, Dr. Kenneth Chu, f o r h i s perceptiveness i n a p p r e c i a t i n g t h e c o n t r i b u t i o n s quantum chemical s t u d i e s could make t o t h e f i e l d o f chemical carcinogenesis. T h i s r e s e a r c h was supported i n p a r t by NINCDS under c o n t r a c t N01-NS-5-2320. We thank our NINCDS contract monitor, Dr. E r n s t Freese, f o r h i s a p p r e c i a t i o n o f t h e fundamental i n s i g h t quantum chemical c a l c u l a t i o n s , both i n t r a - and i n t e r - m o l e c u l a r , could make t o t h e processes l e a d i n g t o t e r a t o g e n e s i s and t o t h e general problems of membrane t r a n s p o r t and biomolecular i n t e r actions. We a l s o thank CDC f o r a grant o f CYBER 175 computer time. The timings f o r a b - i n i t i o MODPOT/VRDDO/MERGE c a l c u l a t i o n s on CH3 + guanine u s i n g t h e CYBER 175 a r e v e r y encouraging f o r t h e f u t u r e o f a b - i n i t i o c a l c u l a t i o n s on l a r g e drugs and biomolecules as w e l l as on carcinogens and teratogens. +


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Ab-initio Quantum Chemical Calculations

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46.

Popkie, Η. Ε., and Kaufman, Joyce J., "Test of Charge Con serving Integral Approximations for a Variable Retention of Diatomic Differential Overlap (VRDDO) Procedure for Semi Ab -Initio Molecular Orbital Calculations on Large Molecules," Int. J . Quantum Chem.: Quantum Biology Symp. (1975), 2, 279-288. 47. Kaufman, Joyce J., "Quantum Chemical Calculations on Small, Medium and Large Molecules," Presented at the Summer Conf. in Theoretical Chemistry, Boulder, Colorado, June 1975. 48. Popkie, Η. Ε., and Kaufman, Joyce J., "Molecular Calculations with the VRDDO, MODPOT and MODPOT/VRDDO Procedures. I. HF, F , HC1, Cl , Formamide, Pyrrole, Pyridine and Nitrobenzene," Int. J. Quantum Chem. Symp. Issue (1976), 10, 47-57. 49. Popkie, H. E., and Kaufman, Joyce J., "Molecular Calculations with the VRDDO, MODPOT and MODPOT/VRDDO Procedures. II. Cyclopentadiene, Benzene, Diazoles, Diazines and Benzonitrile," J. Chem. Phys. (1977), 66, 4827-4831. 50. Popkie, H. E., and Kaufman, Joyce J., "Molecular Calculations with the MODPOT, VRDDO and MODPOT/VRDDO Procedures. III. M0DPOT/SCF + CI Calculations to Determine Electron Affinities of Alkali Metal Atoms," Chem. Phys. Letts. (1977), 47, 55-58. 51. Kaufman, Joyce J., Popkie, H. E . , and Preston, H. J . T., "Ab-initio and Approximately Rigorous Calculations on Small, Medium and Large Molecules," Int. J. Quantum Chem. (1977), 11, 1005-1015. 52. Popkie, H. E., and Kaufman, Joyce J., "Molecular Calculations with the MODPOT, VRDDO and MODPOT/VRDDO Procedures. IV. Boron Hydrides and Carboranes," Int. J. Quantum Chem. (1977), 12, 937-961. 53. Popkie, Η. Ε., and Kaufman, Joyce J., "Molecular Calculations with the MODPOT, VRDDO and MODPOT/VRDDO Procedures. V. Ab-initio and MODPOT LCAO-MO-SCF Calculations on the Chlorofluoromethanes," Int. J . Quantum Chem. (1977), S11, 433-443. 54. Kaufman, Joyce J., and Popkie, H. E., "Molecular Calculations with Non-Empirical Ab-initio MODPOT, VRDDO and MODPOT/VRDDO Procedures. VI. Nucleic Acid Constituents: A, G, C, T," Presented at the Sixth Canadian Conference on Theoretical Chemistry, Fredericton, Ν. Β., Canada, June 1977. Manuscript in preparation for publication. 55. Kaufman, Joyce J., Popkie, H. E., and Preston, H. J . T., "Molecular Calculations with the Non-Empirical Ab-initio MODPOT, VRDDO and MODPOT/VRDDO procedures. VII. Prototype Normal Neurotransmitters and Their Metabolites," Presented at the Sixth Canadian Conference on Theoretical Chemistry, Fredericton, Ν. Β., Canada, June 1977. 56. Kaufman, Joyce J., Popkie, H. E., and Preston, H. J . T., "Molecular Calculations with the Ab-initio Non-Empirical MODPOT, VRDDO and MODPOT/VRDDO Procedures. VIII. Charge Derealization in the Anions of Aromatic Carboxylic Acids and Phenolic Compounds," Int. J . Quantum Chem. (1978), S12, 283291. 2

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57. Kaufman, Joyce J., Popkie, H. E., Palalikit, S., and Hariharan, P. C., "Molecular Calculations with the Ab-initio Non -Empirical MODPOT, VRDDO and MODPOT/VRDDO Procedures. IX. Carcinogenic Benzo(a)pyrene and Its Metabolites Using a MERGE Technique," Int. J . Quantum Chem. (1978), 14, 793-800. 58. Hariharan, P. C., Popkie, H. E., and Kaufman, Joyce J., "Molecular Calculations with the Ab-initio Non-Empirical MODPOT, VRDDO, and MODPOT/VRDDO Procedures. X. The Attack of the Simplest Ultimate Carcinogen, CH3 , on Guanine by a MERGE Technique and the Fundamental Difference Between Methylating versus Ethylating Carcinogens," Presented at the Sanibel International Symposium on Quantum Biology and Quan tum Chemistry, Palm Coast, Florida, March 1979. In press Int. J. Quantum Chem.: Quantum Biology Symp. Issue. 59. Bonifacic, V., and Huzinaga, S., J . Chem. Phys. (1974), 60, 2779. 60. Ibid., J . Chem. Phys. (1975), 62, 1507. 61. Ibid., J . Chem. Phys. (1975), 62, 1509. 62. McWilliams, D., and Huzinaga, S., J . Chem. Phys. (1975), 63, 4678. 63. Huzinaga, S., personal discussion, August 1975. 64. Huzinaga, S., "Atomic and Molecular Calculations with Model Potential Method," Presented at the Quantum Chemistry Symposium, first North American Chemical Congress, Mexico City, December 1975. 65. Bonifacic, V., and Huzinaga, S., J . Chem. Phys. (1976), 64, 956. 66. Huzinaga, S., private communication, July 1977. 67. Kaufman, Joyce J., "potential Energy Surfaces for Ion-Mole cule Reactions," Presented at the NATO Advanced Study Insti tute on Ion-Molecule Reactions, La Baule, France, September 1978. In press in the Proceedings of the Meeting. 68. Le Breton, P. R., private communication, November 1978. 69. Rosenstock, Η. Μ., Draxl, K., Steiner, B. W., and Herron, J . T., J . Phys. Chem. Ref. Data (1977), 6, Supplement 1, 1-87. 70. Hariharan, P. C., The Johns Hopkins University, 1979. 71. Shavitt, I., "The Method of Configuration Interaction," in "Modern Theoretical Chemistry, Vol. II, Electronic Structure Ab-initio Methods," Ed. H. F. Schaefer, Plenum Press, New York, 1976. 72. Reeves, C. Μ., Ph.D. Thesis, Cambridge University, 1957. 73. Reeves, C . M . , Commun. ACM (Assoc. Comput. Mach.) (1966), 9, 276. 74. Cooper, I. L . , and McWeeny, R., J . Chem. Phys. (1966), 45, 226. 75. The basic CI programs described below are those written ori ginally by I. Shavitt and A. Pipano and continued by A. Pipano while he was a postdoctoral in our group at The Johns Hopkins University 1970-1971. In addition we have subse quently written a number of additional features to these CI programs 1971-present.


+


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Gershgorn, Z., and Shavitt, I., Int. J. Quantum Chem. (1967), 1S, 403. 77. Pipano, Α., and Shavitt, I., Int. J . Quantum Chem. (1968), 2, 741. 78. Pipano, A., and Kaufman, Joyce J., The Johns Hopkins Univer sity, unpublished, 1971. 79. Preston, H. J . T., and Kaufman, Joyce J., The Johns Hopkins University, 1972-present. 80. Raffenetti, R. C., Preston, H. J . T., and Kaufman, Joyce J., The Johns Hopkins University, 1973. 81. Hunt, W. J., and Goddard, W. A., III, Chem. Phys. Letts. (1969), 3, 4l3. 82a. Huzinaga, S., and Arnau, C., Phys. Rev. (1970), A1, 1285. b. Huzinaga, S., and Arnau, C., J . Chem. Phys. (1971),54,1948. c. Hirao, Κ., and Huzinaga, S., Chem. Phys. Letts. (1977), 45, 55. 83. Huzinaga, S., and Hirao, K., J . Chem. Phys. (1977), 66, 2157. 84a. Raffenetti, R, C., The Johns Hopkins University, 1973. b. Raffenetti, R. C., ICASE, 1974-1976. 85. Kaufman, Joyce J., and Predney, R., "Non-Applicability for the Li - H Ion Molecule System of an INDO Potential Surface or of the Approximate Monopole-Transition Moment Long Range Force Expressions," Int. J . Quantum Chem. 5, 235. 86a. Rein, R., and Pollak, M., J. Chem. Phys. (1967), 47, 2039. b. Pollak, M., and Rein, R., J . Chem. Phys. (1967), 47, 2045. c. Rein, R., Claverie, P., and Pollak, Μ., Int. J . Quantum Chem. (1968), 2, 129. d. Claverie, P., and Rein, R., Int. J . Quantum Chem. (1969), 3, 537. 87. Pullman, Β., Claverie, P., and Caillet, J., Proc. Natl. Acad. Sci. USA (1966), 55, 911. 88. Dewar, M. J. S., and Dougherty, R. C., "The PMO Theory of Organic Chemistry," Plenum Publishing Corp., New York, 1975. 89. Dewar, M. J . S., and Thiel, W., J . Am. Chem. Soc. (1977), 99, 4899. 90. Ibid., (1977), 99, 4970. 91. Claverie, P., "Elaboration of Approximate Formulas for the Interactions Between Large Molecules: Applications in Organic Chemistry," in "Intermolecular Interactions: From Diatomic to Biopolymers," 69-305, Ed. B. Pullman, John Wiley and Sons, New York, 1978. (This review is extensive and contains several hundred references covering both rigor ous and approximate treatments.) 92. Sokalski, W. Α., Hariharan, P. C., and Kaufman, Joyce J., The Johns Hopkins University, research in progress, 1979. 93. Scrocco, E . , and Tomasi, J., Top. Curr. Chem. (1973), 21, 97, and references therein. 94. Petrongolo, C., Gazz. Chim. Ital. (1978), 108,445,and references therein. 95. Petrongolo, C., Preston, H. J . T., and Kaufman, Joyce J., +

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"Ab-initio LCAO-MO-SCF Calculations of the Electrostatic Molecular Potential of Chlorpromazine and Promazine," Int. J. Quantum Chem. (1978), 13, 457-468. 96, Kaufman, Joyce J., "Recent Physicochemical and Quantum Chemical Studies on Drugs of Abuse and Relevant Biomolecules," in "Quantitative Structure Activity Relationships of Analgesics, Narcotic Antagonists and Hallucinogens," 250-277, Eds. G. Barnett, M. Trsic and R. E. Willette, NIDA Research Monograph 22, DHEW, NIDA, 1978. 97. Petrongolo, C., Preston, H. J. T., Popkie, H. E . , and Kaufman, Joyce J., The Johns Hopkins University, 1975-1978. RECEIVED

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New Optimal Strategies for Ab-Initio Quantum Chemical Calculations

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