Computer-Assisted Drug Design - ACS Publications - American

Chemical Calculations on Large Drugs, Carcinogens,. Teratogens, and Biomolecules. JOYCE J. KAUFMAN, HERBERT Ε. ΡΟΡΚΙΕ, and P. C. HARIHARAN. Department...
1 downloads 8 Views 2MB Size
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.

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

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

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

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

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

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

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

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:

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

20.

is

KAUFMAN

less

than

represented

Quantum

some t h r e s h o l d T ] _ . by a

Chemical

The ρ s e u d o - f u n c t i o n φ . [ ΐ ) i s

single normalized s p h e r i c a l l y - a v e r a g e à is

itive

G a u s s i a n f u n c t i o n φ-[CO

i n the

φΐ(ΐ)φ^1) (h*?) ;

threshold

τ2 that

T 2 = 10"" )

c a n be

n

integrals

accurate.

reduced as

τ2 i s

have

of the

to

The

total

to

the

set

orbital

ab-initio

programs

τ

effect

agree to

treat

at

are

neglected. be n u m e r i ­

generate

the

We t e s t e d

inner

integrals

between the

10~6

atomic

isomers

calculations

shell

or

found

e x p l i c i t l y yet

are

(in

from

effect

of a m o d i f i e d model p o t e n t i a l

electrons

for molecules has t h e

a.u.)

completely

i n the is

total

0.009

a

«u.

computer

core model

permits

one

to

accurately.

is

carrying

valence

taken

(M0DP0T)

into

account

LCA0-M0-

(59-66). through

the

Hamiltonian.

composed o f

following

out

electrons

first

and second

form:

(1) 1

in

potential

a n d H u z i n a g a h a v e g i v e n a new f o r m u l a t i o n (M0DP0T) m e t h o d f o r

The

and h y d r o g e n i t

the

greater.]

The e r r o r

molecule

This

accur­

with

or

along a

d i p o l e moment

electrons.

use

a n example

core

a.u.

a.u.).

o p t i o n i n our l a r g e

considering only the

of the

integral

implies

fourth decimal place

and i n t h e

ref­

accuracy*

populations

(in

energy d i f f e r e n c e s

electrons

Recently Bonifacic

the

[*Where a c c u r a c y

and g r o s s

accur­

ρ s eudo-over l a p

hardly affects

i n t r o d u c t i o n of a b - i n i t i o e f f e c t i v e the

the

The i n t r o d u c t i o n o f

(the

2

t h r e s h o l d s Tj_

a good compromise

completely a b - i n i t i o

T h e maximum e r r o r

0.008

only the valence

As

2

substantially

yield

3 decimal places

about

of the model p o t e n t i a l

atoms

is

time.

10""^

all.

same r e l a t i v e

the for

than

of varying the that

running

=

energies

second d e s i r a b l e is

repul­ where

A l l two-electron

less

completely a b - i n i t i o calculations

calculations.

potentials

two-electron

η decimal places

input data.

retaining a l l

overlap population is The

our

A second

is

values

energy d i f f e r e n c e s the

into

CPU t i m e r e q u i r e d t o

and

accurate* to

energy curve

conserving.

programs-

of the

and n u m e r i c a l r e s u l t s .

threshold)

basis

valence

compared t o

SCF

at

computed p r o p e r t i e s

essentially the

accuracy

a large molecule

and computer

with respect

same a t o m i c

charge

computer

VRDDO a p p r o x i m a t i o n w i t h Tj_ = 1 0 ~

of the acy

for

function pair

u s e d by W i l h i t e and Euwema still

VRDDO m e t h o d by c o m p u t i n g t h e

prescreening

Our m e t h o d

basis

second a p p r o x i m a t i o n t o

the

arrive

erence c a l c u l a t i o n s the

·

Gaussian

diffuse prim-

increased.

investigated

T 2 i n order

the

accurate to

The computer for

o f t h e most

been i n t r o d u c e d 35.)

the are

show t h i s

integrals

between a c c u r a c y acy

is

s p e c i f i e d i n the

(Λ6-57)

two-electron

and

for

whose a b s o l u t e m a g n i t u d e

results

We

(3^,

controls

(integrals

that

from t h a t

a n d GIPSY

33)

integrals

cally

somewhat

o u r VRDDO p r o c e d u r e

VRDDO a p p r o x i m a t i o n has

MOLASYS (3£,

The

equal to

ρ s e u d o - o v e r l a p S*j

differs

however The

sion

contracted the

419

Calculations

f u n c t i o n whose e x p o n e n t calculating

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

Ab-initio

ET AL.

i>J

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

row

420

COMPUTER-ASSISTED DRUG DESIGN

hCi) = - |& - Z l / r k k -Γ Cz -N )(l

(2)

h

1

n

C/

k

c

+

A

l k

J^ik

e

2

k a

A

A

+

A

r

- 2k ik 2k

e

)

/

2

r

w

i k

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

η +

? k

{ B

lsl

l s

k

> < l s

kl

+ B

2

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

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

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

20.

KAUFMAN E T AL.

Ab-initio

Quantum

Chemical

Calculations

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

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

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

422

COMPUTER-ASSISTED DRUG

DESIGN

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

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

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

20.

KAUFMAN

Ab-initio

E TA L .

Quantum

Chemical

423

Calculations

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 -

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

424

COMPUTER-ASSISTED

DRUG DESIGN

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

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

+

+

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

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

20.

K A U F M A N E TA L .

Ab-initio

Quantum

Chemical

Calculations

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) .

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

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

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

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

426

COMPUTER-ASSISTED DRUG DESIGN

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

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

20.

KAUFMAN

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 .

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

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.

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

428

COMPUTER-ASSISTED DRUG DESIGN

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

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. +

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

20. KAUFMAN ET AL.

Ab-initio Quantum Chemical Calculations

Literature Cited 1.

2.

Giordano, W., Hamann, J . R., Harkins, J. J., and Kaufman, Joyce J., "Quantum Mechanically Derived Electronic Distribu­ tions in the Conformers of 2-PAM," in "Physico-chemical Aspects of Drug Action," Ed. Ariens on the Proceedings of the Third International Pharmacological Congress, Sao Paolo, Brazil, July 1966, Volume 7, 327-354, Pergamon Press, 1968. Giordano, W., Hamann, J . R., Harkins, J. J., and Kaufman, Joyce J., "Quantum Mechanical Calculations of Stability in 2-Formyl N-Methyl Pyridinium (Cation) Oxime (2-PAM) Conformers," Mol. Pharmacol. (1967), 3, 307-317. Wolfsberg, Μ., and Helmholz, L . , J . Chem. Phys. (1952), 29, 837. Eberhardt, W. Η., Crawford, B., J r . , and Lipscomb, W. Ν., J. Chem. Phys. (1954), 22, 989. Hoffman, R., J. Chem. Phys. (1963), 39, 1397. Burnelle, L . , and Kaufman, Joyce J., "Molecular Orbitals of Diborane in Terms of a Gaussian Basis," J . Chem. Phys. (1965), 43, 3540-3545. Sachs, L. Μ., and Geller, Μ., "MOSES, A Fortran IV System for Polyatomic Molecules," Int. J . Quantum Chem. (1967), 15, 445. Kaufman, Joyce J., "Semi-rigorous LCAO-MO-SCF Methods for Three-Dimensional Molecular Calculations Including Electron­ -Electron Repulsion," J. Chem. Phys. (1965) 43, S152-S156. Pople, J . Α., Santry, D. P., and Segal, G. Α., J . Chem. Phys. (1965), 43, S129. Pople, J. Α., and Segal, G. Α., J . Chem. Phys. (1965), 43, S136. Pople, J . Α., and Beveriage, D. Α., Approximate Molecular Orbital Theory, McGraw-Hill, New York, 1970. Diner, S., Malrieu, J. P., and Gilbert, Μ., Theor. Chim. Acta (1968), 15, 100 and references therein. Kaufman, Joyce J., and Kerman, Ellen, "Quantum Chemical Cal­ culations on Antipsychotic Drugs and Narcotic Agents," Int. J. Quantum Chem. (1972), 6S, 319-335. Kaufman, Joyce J., "Quantum Chemical and Theoretical Techni­ ques for the Understanding of Action of Psychoactive Drugs," Proceedings of the Symposia at the VIII Congress of the Collegium Internationale Neuro-Psychopharmacologicum on "Psychopharmacology, Sexual Disorders and Drug Abuse," 3142, North-Holland Publishing Co., Amsterdam-London, Avicenum, Czechoslovak Medical Press, Prague, 1973. Kaufman, Joyce J., and Kerman, Ellen, "Quantum Chemical and Other Theoretical Techniques for the Understanding of the Psychoactive Action of the Phenothiazines," International Conference on Phenothiazines and Related Drugs, Rockville, Maryland, June 25-28, 1973, in "Advances in Biochemical Pharmacology, Vol. 9: Phenothiazines and Structurally Related Drugs," 55-75, Eds. Irene S. Forrest, C. J . Carr, and E. Usdin, Raven Press, New York, 1974.

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

+

3. 4. 5. 6. 7· 8. 9. 10. 11. 12. 13. 14.

15.

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

429

430

COMPUTER-ASSISTED DRUG DESIGN

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

16. Kaufman, Joyce J., and Kerman, Ellen, "Quantum Chemical and Theoretical Techniques for the Understanding of Action of Drugs Which Affect the Central Nervous System: Antipsycho­ tics, Narcotics and Narcotic Antagonists," International Symposium on Chemical and Biochemical Reactivity, Jerusalem, Israel, April 9-13, 1973, in "The Jerusalem Symposia on Quantum Chemistry and Biochemistry, VI," 523-547, Jerusalem, Israel, 1974. 17. Kaufman, Joyce, and Kerman, Ellen, "The Structure of Psycho­ tropic Drugs (Including Theoretical Prediction of a New Class of Effective Neuroleptics)," Int. J . Quantum Chem.: Quantum Biology Symp. (1974), 1, 259-289. 18. Kaufman, Joyce J., and Koski, W. S., "Physiochemical, Quantum Chemical and Other Theoretical Techniques for the Understand­ ing of the Mechanism of Action of CNS Agents: Psychoactive Drugs, Narcotics and Narcotic Antagonists and Anesthetics," in "Drug Design," Vol. V., 251-340, Ed. E. J . Ariens, Academic Press, New York, 1975. 19· Kaufman, Joyce J., "Quantum Chemical and Theoretical Techni­ ques for the Understanding of Action of Psychoactive Drugs and Narcotic Agents," International Conference on Computers in Chemical Research and Education, Ljubljana, Yugoslavia, July 12-17, 1973, in Comput. Chem. Res. Educ. Proc. (1973), 3, 5/1-5/20. 20. Kaufman, Joyce J., and Koski, W. S., "Physiochemical, Quantum Chemical and Other Theoretical Studies of the Mechanism of Action of CNS Agents: Anesthetics, Narcotics and Narcotic Antagonists, and Psychotropic Drugs," Int. J. Quantum Chem.: Quantum Biology Symp. (1975), 2, 35-57. 21. Kaufman, Joyce J., Kerman, Ellen, and Koski, W. S., "Quantum Chemical, Other Theoretical and Physicochemical Studies on Narcotics and Narcotic Antagonists to Understand Their Mech­ anism of Action," Int. J . Quantum Chem.: Quantum Biology Symp. (1974), 1, 289-313. 22. Saethre, L. J., Carlson, Τ. Α., Kaufman, Joyce J., and Koski, W. S., "Nitrogen Electron Densities in Narcotics and Narcotic Antagonists by X-Ray Photoelectron Spectroscopy and Compari­ son with Quantum Chemical Calculations," Mol. Ρharm. (1975), 11, 492-500. 23. Kaufman, Joyce J., and Kerman, Ellen, "Conformational Profile of Nalorphine by PCILO Calculations," Int. J . Quantum Chem. (1977), 11, 181-184. 24. Janssen, P. A. J., CINP Meeting, Congress Internationale de Neuropsychopharmacologie, Paris, France, July, 1974. 25. Kaufman, Joyce J., and Predney, R., "Extensions of INDO Formalism to d Orbitals and Parameters for Second Row Atoms," Int. J. Quantum Chem. (1972), 6S, 231-242. 26. Kaufman, Joyce J., "A Suggested Procedure to Improve the Description of Lone Pairs in the PCILO or More General Ab­ -Initio Perturbative Configuration Interaction Schemes Based

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

20. KAUFMAN ET AL.

27. 28.

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

29. 30.

31. 32. 33. 34.

35.

36. 37. 38. 39· 40. 41. 42. 43. 44. 45.

Ab-initio Quantum Chemical Calculations

on Localized Orbitals," Workshop Letter, Int. J. Quantum Chem.: Quantum Biology Symp. (1974), 1, 197. Preston, H. J . T., and Kaufman, Joyce J., "Ab-initio SCF Calculations on Pyrrole and Pyrazole," Int. J . Quantum Chem. (1973), 7S, 207-215. Preston, H. J . T., Kerman, Ellen, Kaufman, Joyce J., and Cusachs, L. C., "Comparison for Pyrrole and Pyrazole of Orbital Energies and Population Analyses from Ab-initio SCF, CNDO/2, INDO, Extended Huckel and ARCANA Calculations," Int. J. Quantum Chem. (1973), 7S, 249-260. Popkie, Η, Ε., and Kaufman, Joyce J., "Ab-initio LCAO-MO-SCF Calculations of Chlorpromazine and Promazine," Int. J. Quantum Chem. (1976), 10, 569-580. Popkie, Η. E., Koski, W. S., and Kaufman, Joyce J., "Ab­ -initio LCAO-MO-SCF Calculations on Morphine and Nalorphine and Comparison with Their Measured Photoelectron Spectra," J. Am. Chem. Soc. (1976), 98, 1342-1345. Clementi, E . , and Popkie, H. E . , IBMOL, 6. Popkie, H. E., "MOLASYS: A Computer Program for Molecular Orbital Calculations on Large Systems," The Johns Hopkins University, 1974. Popkie, Η. E., "MOLASYS-MERGE," The Johns Hopkins University, 1978. Popkie, Η. E., "GIPSY (Gaussian Integral Program System): A System of Computer Programs for the Evaluation of One- and Two-Electron Integrals Involving s-, p- and d-type Contracted Cartesian Gaussian Functions," The Johns Hopkins University, 1975. Popkie, Η. E., "GIPSY (Gaussian Integral Program System): A System of Computer Programs for the Evaluation of One- and Two-Electron Integrals Involving s-, p- and d- and f-type Contracted Cartesian Gaussian Functions," The Johns Hopkins University, 1976. Raffenetti, R. C., J. Chem. Phys. (1973), 58, 4452. Raffenetti, R. C., Chem. Phys. Letts. (1973), 19, 335. Csizmadia, I. G., Harrison, M. C., Moskowitz, J . W., and Sutcliff, B. T., Theoret. Chim. Acta (1966), 6, 191. Hornbeck, C., New York University, private communication. Petrongolo, C., private communication, 1975. Hehre, W. J., Lathan, W. Α., Ditchfield, R., Newton, M. D., and Pople, J . Α., "Gaussian 70, Program 236, QCPE," Indiana University, Bloomington, Indiana. Pople, J. Α., and coworkers, "Gauss 76," National Resource for Computational Chemistry, Berkeley, California. Dupuis, M., Rys, J., and King, H. F . , J . Chem. Phys. (1976), 65, 111. Goutier, D., Macauley, R., and Duke, A. J., "PHANTOM: Pro­ gram 24l, QCPE," Indiana University, Bloomington, Indiana. Wilhite, D. L . , and Euwema, R. Ν., Chem. Phys. Letts. (1973), 20, 610.

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

431

432

COMPUTER-ASSISTED DRUG DESIGN

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

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

2

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

20. KAUFMAN ET AL.

Ab-initio Quantum Chemical Calculations

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.

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

+

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

433

434

COMPUTER-ASSISTED DRUG DESIGN

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

76.

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., +

2

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

20. KAUFMAN ET AL.

Ab-initio Quantum Chemical Calculations

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

"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

June 8, 1979.

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

435