Rational Drug Design - American Chemical Society

Chapter 8

New Tools for Rational Drug Design 1

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Gregory D . Hawkins, Jiabo Li, Tianhai (Tony) Zhu, Candee C . Chambers, D a v i d J. Giesen, Daniel A. L i o t a r d , Christopher J . C r a m e r , and Donald G . T r u h l a r 1,3

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Downloaded by GEORGETOWN UNIV on August 16, 2015 | http://pubs.acs.org Publication Date: July 7, 1999 | doi: 10.1021/bk-1999-0719.ch008

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Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, MN 55455 Laboratoire de Physico-Chimie Theorique, U n i v e r s i t é de Bordeaux, 351 Cours de la Liberation, 33405 Talence Cedex, France

We have developed two new tools for molecular m o d e l i n g that can be very useful for c o m p u t e r - a i d e d drug design, n a m e l y class IV charges and the SMx series of solvation models. This c o n t r i b u t i o n overviews the current status of our efforts i n these areas, i n c l u d i n g the C M 2 charge m o d e l a n d the S M 5 series of solvation models. The solvation models may be used to estimate partition coefficients for phase transfer e q u i l i b r i a of organic solutes between water a n d 1-octanol, the m o s t w i d e l y u s e d m i m i c of cellular biophases, a n d also between water and other solvents that have been used for this purpose, e.g., hexadecane and chloroform.

1. Introduction T h e p a r t i t i o n i n g o f a n o r g a n i c s o l u t e b e t w e e n a n a q u e o u s p h a s e {aq) a n d a n o n p o l a r m e d i u m (np) is c r i t i c a l f o r m a n y p h e n o m e n a i n b i o l o g i c a l a n d m e d i c i n a l c h e m i s t r y . I n p a r t i c u l a r this p a r t i t i o n i n g c a n be c r i t i c a l for drug delivery, binding, and clearance. P r e d i c t i o n s o f t h e r e l a t i v e free energy of organic molecules i n aqueous a n d n o n p o l a r m e d i a c a n be very useful for p r e d i c t i n g the b i o a v a i l a b i l i t y o f p o t e n t i a l drugs. Lipid-like n o n p o l a r m e d i a are e s p e c i a l l y i m p o r t a n t b e c a u s e t h e y m i m i c c e l l m e m b r a n e s , a n d t h e l i p o p h i l i c c h a r a c t e r o f o r g a n i c c o m p o u n d s is o n e o f the m o s t w i d e l y u s e d predictors o f their bioactivity. T h e l i p i d s o l u b i l i t y of a m o l e c u l e c o r r e l a t e s w i t h its a b i l i t y to e n t e r t h e b r a i n (i.e., p a s s t h e b l o o d b r a i n b a r r i e r ) o r o t h e r p a r t s o f t h e c e n t r a l n e r v o u s s y s t e m a n d is g e n e r a l l y b e l i e v e d to have a large influence o n p h a r m a c o l o g i c a l properties.

3 4

Current address: Departments of Physics and Chemistry, Mercyhurst College, Erie, PA 16504 Current address: Eastman Kodak Company, Rochester, NY 14650

© 1999 American Chemical Society

In Rational Drug Design; Parrill, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1999.

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122

T h e l i p o p h i l i c character of a m o l e c u l e is typically m e a s u r e d quantitatively by its partitioning between an organic phase a n d water. 1Octanol is the most widely used solvent for m i m i c k i n g biophases i n this respect, and H a n s c h and D u n n have attempted to rationalize the success of correlations based o n 1-octanol by noting that proteins (with their amide groups) a n d lipid phases (with their ester a n d phosphate functionalities) b o t h present accessible h y d r o g e n - b o n d i n g o p p o r t u n i t i e s to d r u g molecules, and the O H functional group of octanol can serve as a hydrogen b o n d acceptor or donor to m i m i c such effects, while the molecule is large enough to remain overall hydrophobic. T h e partitioning coefficient P of organic solutes between water and 1-octanol is widely used i n propertyactivity relationships i n rational drug design, a n d a very large amount of work concerned with the measurement a n d / o r prediction of such partition coefficients has been reported. T h e reader is referred to representative articles for further references. " Hexadecane is another important example of a n o n p o l a r solvent because solute-hexadecane interactions, like solute-1-octanol interactions, are recognized as a surrogate for hydrophobic interactions of molecules with l i p i d bilayers or other cellular m a t e r i a l " or with the nonpolar active site of a n enzyme or receptor. In such models, the partition coefficient of a solute between an alkane solvent a n d water provides some indication of how likely it is to penetrate the bilayer, skin, brain, central nervous system, or other biophase or to b i n d to the nonpolar site i n (or on) the protein. The difference between log P for an amphiphilic solvent like 1octanol or 1-hexanol and apolar, aprotic inert solvents like straight-chain alkanes or cyclohexane is generally interpreted as a measure of the hydrogen-bond donor capacity of s o l u t e s . Furthermore this difference has b e e n u s e d i n r a t i o n a l d r u g design because it correlates with b r a i n / b l o o d a n d cerebrospinal/blood partitioning e q u i l i b r i a . Another solvent that has been used for similar purposes as 1-octanol a n d hexadecane is chloroform. R e y n o l d s has discussed the utility of w a t e r / c h l o r o f o r m p a r t i t i o n coefficients for c o r r e l a t i n g m e m b r a n e permeability and bioactivity properties that depend o n such permeability. T h e ability to u n d e r s t a n d the solvation of organic solutes i n nonpolar media is also important for conformational analysis of bioactive c o m p o u n d s . A recent example of the importance of solvent effects o n conformation is the interpretation of octanol/water a n d heptane/water partition coefficients for the immunosuppressant cyclosporin A i n terms of solvent-dependent conformational changes and of the relationship of these changes to solvent-dependent inhibitory activity. Historically, most attempts to develop predictive models for solvation free energies or p a r t i t i o n i n g coefficients have i n v o l v e d multivariate quantitative structure-property relationships ( Q S P R s ) . M o r e recently, methods for i n c l u d i n g solvent electrostatic effects self consistently i n q u a n t u m mechanical solute descriptions have advanced vigorously, and such models are preferred for making predictions o n molecules outside the QSPR training sets or for transition states. Accurate quantitative predictions must include nonelectrostatic effects as well, and we have developed successful models for q u a n t u m m e c h a n i c a l self-


1

1

-15

1 6

21

2 0

24

25

2 6

24

2 7 - 3 3

3 4 - 4 5


123

4 6

5


5 9

consistent electrostatics i n b o t h aqueous s o l u t i o n s " a n d organic solvents A n especially important aspect of the framework of our m o d e l is that only solute atoms are treated explicitly; the solvent is treated as a continuous fluid. There are three kinds of terms i n the solvation free energy: long-range electrostatic contributions (labeled E N P , to denote that they include self-consistent solute electronic and n u c l e a r contributions and solute-solvent electric rjolarization effects), intermediate-range cavitystructural (CS) contributions, a n d short-range cavity-dispersion (CD) effects. Hydrogen bonding affects all three terms, E N P , C D , a n d CS. T h e functional forms and parameters of the electrostatic m o d e l for organic solvents are identical to those for water except that the dielectric constant, e, of the organic solvent replaces the dielectric constant of water. The electrostatic treatment involves a three-dimensional integration over the free energy density due to electric polarization of the solvent i n the regions of space not occupied by the s o l u t e , ' ' ' ' a n d therefore it reflects the solute shape realistically. The solute electronic wave functions and solute internal energies are calculated with semiempirical molecular orbital t h e o r y , ab initio Hartree-Fock t h e o r y , or density functional theory. T h e c o m p e t i t i o n between solvent p o l a r i z a t i o n a n d solute distortion is accounted for by placing solvation terms inside the effective one-electron Hamiltonians for the molecular o r b i t a l s . ' T h e atomic partial charges needed for the electrostatic solvation terms may be calculated by conventional M u l l i k e n analysis or by class IV ' ' charge models. The latter capability is a particular strength of our solvation m o d e l since these charges, according to previous v a l i d a t i o n , ' yield remarkably accurate electrostatic properties, and i n addition they are very inexpensive to calculate. Accurate atomic partial charges are of great interest for molecular modeling i n general a n d their usefulness extends beyond solvation m o d e l i n g . Thus we shall review our recent progress i n this area as a separate topic. In addition to electrostatics, our solvation models also include n o n electrostatic effects i n the first solvation shell. These effects are modeled in terms of solvent-accessible surface a r e a s ' a n d semiempirical atomic surface t e n s i o n s . The solvent dependence of our predicted free energies of solvation comes from two sources: (i) The electrostatic term contains the factor (1 - e ) , where e is the dielectric constant of the solvent, (ii) The atomic surface tensions are determined separately for water a n d organic solvents, and i n the latter case they depend o n one or more of the following solvent descriptors: n, the index of refraction; a a n d P, A b r a h a m ' s hydrogen b o n d acidity and basicity parameters (converting our notation to H H his, a is £ a and P is £ P ) ; y, the macroscopic surface tension of the solvent; and two descriptors which depend u p o n the fraction of non-hydrogenic atoms within the solvent w h i c h are aromatic c a r b o n or electronegative halogen atoms (we define "electronegative halogen atoms" as F, CI, a n d Br since these are the halogen atoms that are more electronegative than c a r b o n ) . A major advantage of using these parameters is that they are 5

-

6

5

3 8

6 8

4 2

5 1

6 6

6 7

69

7 0

4 2

5 0

7 4

7 1 - 7 3

7 5

7 4

7 5

76

7 7

7 8

79

-1

8 0 - 8 3

2

2

8 4


124

available for almost all possible solvents. Should one desire to treat an unusual solvent for which a and b are not known, three possibilities present themselves. First, they c o u l d be determined by generating the k i n d of partition coefficient data and fits used originally by A b r a h a m . Second, they c o u l d be determined by correlating them against other acidity or basicity s c a l e s ' that are known for the solvent of interest. Third, Murray and P o l i t z e r have shown that A b r a h a m ' s single-site h y d r o g e n - b o n d H H acidity and basicity parameters (cc and P ) correlate well with maxima and 8 0 - 8 3

8 5

8 6

8 6


2

2

m i n i m a of calculated electrostatic potentials o n the molecular surface, and H H these single-site parameters can be used to estimate £cc and £ p i n most 2

2

cases. Section 2 summarizes the current status of class IV charges. Section 3 presents a level chart of S M 5 models. Section 4 s u m m a r i z e s the performance of several SM5 models for free energies of solvation i n water, 1octanol, hexadecane, and chloroform. 2. Class IV charges Partial atomic charges may be classified as follows: Class I: n o n - q u a n t u m - m e c h a n i c a l charges, for example, the empirical charges in a molecular mechanics force field; Class II: charges obtained directly from wave functions without calculating p h y s i c a l observables, for example, charges o b t a i n e d by M u l l i k e n or L o w d i n population analysis; Class III: charges obtained by fitting to electrostatic potentials or m u l t i p o l e m o m e n t s c o m p u t e d f r o m wave functions, for example, C h E l P G charges; Class IV: charges m a p p e d from class II or class III charges with semiempirical parameters designed to make the m a p p e d charges better r e p r o d u c e experimental m u l t i p o l e m o m e n t s or c o n v e r g e d q u a n t u m mechanical electrostatic potentials or multipole m o m e n t s . ' ' We have presented two models for class IV charges: Charge M o d e l 150,74 (CMl) and Charge M o d e l 2 (CM2). In the C M l model, we c o m p u t e d zero-order charges by M u l l i k e n analysis a n d m a p p e d t h e m as nonlinear functions of calculated b o n d orders with 15-19 parameters based o n data (experimental dipole moments and calculated electrostatic potentials) for compounds containing H , C , N , O, F , Si, S, CI, Br, a n d I. Parameters were determined for A M I and PM3 semiempirical molecular orbital wave functions. We achieved rootmean-square errors i n the dipole moments of 0.27 D for maps based o n A M I wave functions and 0.20 D for maps based o n P M 3 wave f u n c t i o n s . In the C M 2 m o d e l we c o m p u t e d zero-order charges by L o w d i n analysis a n d m a p p e d them as quadratic functions of calculated b o n d orders with 20 parameters based o n 198 experimental dipole m o m e n t s for compounds containing H , C , N , O, F, Si, P, S, CI, Br, a n d I. Parameters were determined for A M I , for four different basis sets for ab initio Hartree-Fock wave functions ( M I D I ! , MIDI!(6D), 6 - 3 1 G * , and 6-31+G* ), a n d for four combinations of basis set (MIDI!, MIDI!(6D), or 6-31G*) with density 74

8 7

8 8

8 9

5 0

7 4

7 5

7 5

9 1 - 9 3

9 4

74

95

69

69


125 Table 1. Partial atomic charges and dipole moments for P-propiolactone^


HF/MIDI!

partial charges: 0-1 C-2 0 (carbonyl on C-2) C-3 H-1,2 on C-3 C-4 H-3,4 on C-4 dipole moment (D)

BPW91/MIDI!

Mulliken

Lowdin

CM2

Mulliken

Lowdin

CM2

-0.82 1.09 -0.69 0.09 0.20 -0.58 0.25

-0.46 0.58 -0.41 0.10 0.09 -0.25 0.13

-0.36 0.56 -0.44 0.10 0.07 -0.20 0.10

-0.57 0.76 -0.50 -0.00 0.22 -0.51 0.19

-0.33 0.41 -0.31 0.04 0.10 -0.26 0.13

-0.31 0.51 -0.41 0.02 0.10 -0.26 0.13

7.69

4.71

4.31

6.02

3.81

4.21

fl

dipole moment from H F / M I D I ! density: 4.18 D ; from B P W 9 1 density: 3.41 D ; from experiment: 4.18 D

9 6

9 7

9 8 - 1 0 0

functional (BPW91 > or B 3 L Y P ) . We achieved root-mean-square errors i n d i p o l e m o m e n t s i n the range 0.17-0.19 D for H F / 6 - 3 1 G * , B 3 L Y P / M I D I ! , B P W 9 1 / 6 - 3 1 G * , H F / M I D I ! , a n d B P W 9 1 / M I D I ! , 0.20-0.21 D for t w o cases w i t h t h e M I D I ! ( 6 D ) b a s i s , 0.25 D w i t h A M I , a n d 0.41 D w i t h H F / 6 31+G*, t h e l a t t e r v a l u e r e f l e c t i n g t h e d i f f i c u l t y o f o b t a i n i n g a c c u r a t e c h a r g e s f r o m w a v e f u n c t i o n s w i t h diffuse b a s i s f u n c t i o n s . O n t h e average, e r r o r s i n t h e d i p o l e s c o m p u t e d as e x p e c t a t i o n v a l u e s f r o m t h e f u l l w a v e f u n c t i o n s w e r e a b o u t 1.8 t i m e s l a r g e r t h a n t h o s e c o m p u t e d f r o m t h e C M 2 c h a r g e s . A s a n e x a m p l e o f the p r e d i c t i o n s o f the C M 2 charge m o d e l , c o n s i d e r P - p r o p i o l a c t o n e . T h e e x p e r i m e n t a l d i p o l e m o m e n t is 4.18 D , a n d t h e u s e o f B P W 9 1 / M I D I ! w a v e f u n c t i o n s y i e l d s 3.41 D , w h e r e a s t h e C M 2 m o d e l b a s e d o n t h i s s a m e B P W 9 1 / M I D I ! w a v e f u n c t i o n for P - p r o p i o l a c t o n e y i e l d s 4.21 D . T h e p a r t i a l c h a r g e s o n t h e o x y g e n a t o m s d i f f e r b y as m u c h as 0.25 w h e n obtained by M u l l i k e n analysis of H F / M I D I ! a n d B P W 9 1 / M I D I ! wave f u n c t i o n s a n d b y as m u c h as 0.13 for L o w d i n a n a l y s i s . B u t t h e m a p p e d c h a r g e s f r o m t h e s e t w o q u i t e d i f f e r e n t w a v e f u n c t i o n s a g r e e w i t h i n 0.05. F u l l r e s u l t s are g i v e n i n T a b l e 1. 7 5

3. S u m m a r y of SM5 models A q u e o u s / n o n p o l a r p a r t i t i o n i n g is u s u a l l y q u a n t i f i e d b y t h e p a r t i t i o n c o e f f i c i e n t P o r its, l o g a r i t h m ("log P " ) , w h e r e

Jsolute]

p

np

[solute]^ A n o t h e r ( e q u i v a l e n t ) d e f i n i t i o n o f P is


( 1 )

126

log P = AAG^/(-2.303A7)

(2)

where A A G ° = Acf (np)

- AcP (aq),

s

(3)

s

(? {solv) is t h e s t a n d a r d - s t a t e free e n e r g y o f s o l v a t i o n o f t h e s o l u t e i n s o l v e n t s


solv, R is t h e gas c o n s t a n t , a n d T is t e m p e r a t u r e . T h e s t a n d a r d - s t a t e free e n e r g y o f s o l v a t i o n i n w a t e r i s w r i t t e n as AG° = A G

E

N

p+£ a

G ,a

(«

CDS

w h e r e a denotes o n e o f the atoms o f the solute a n d G DS,a = ^ a E C

faW°ai

®

i

w h e r e f i i s a f u n c t i o n o f t h e g e o m e t r y R o f t h e s o l u t e ( a c t u a l l y it d e p e n d s o n l y o n s e l e c t e d b o n d d i s t a n c e s , a n d it h a s n o d e p e n d e n c e o n b o n d a n g l e s o r d i h e d r a l angles) a n d a is a s u r f a c e t e n s i o n c o e f f i c i e n t . T h e s t a n d a r d state free e n e r g y o f s o l v a t i o n i n a n o r g a n i c s o l v e n t h a s t h e s a m e f o r m as for water except that a is n o t a c o n s t a n t b u t r a t h e r d e p e n d s o n s o l v e n t a

a i

a i

d e s c r i p t o r s . T h e s o l v e n t d e s c r i p t o r s are g e n e r a l l y n, a , P, a n d y. I n s o m e cases ( S M 5 . 4 p a r a m e t e r i z a t i o n s ) s p e c i a l p a r a m e t e r s are u s e d for c h l o r o f o r m , b e n z e n e , a n d toluene; i n other cases (SM5.42R, S M 5 . 2 R , a n d S M 5 . 0 R p a r a m e t e r i z a t i o n s ) t w o s p e c i a l solvent d e s c r i p t o r s are a d d e d to the four m e n t i o n e d i n the previous sentence, i n particular descriptors c o m p u t e d f r o m the f r a c t i o n o f n o n h y d r o g e n i c solvent a t o m s that are a r o m a t i c carbons or electronegative halogens. Some a v a l u e s are i n d e p e n d e n t o f a a n d h a v e f t = 1; t h e s e are s o m e t i m e s c a l l e d t h e C S t e r m s . T h e o t h e r t e r m s are s o m e t i m e s c a l l e d C D terms; h o w e v e r , o n e s h o u l d b e c a u t i o u s a b o u t p h y s i c a l interpretations of the i n d i v i d u a l terms. T h e a c t u a l p a r a m e t e r i z a i t o n i s c a r r i e d o u t as f o l l o w s : First the n o n l i n e a r p a r a m e t e r s are fixed b a s e d o n a v a r i e t y o f c o n s i d e r a t i o n s , i n c l u d i n g t r e n d s o v e r s o l u t e s a n d s o l v e n t s f o r s o l v a t i o n free e n e r g i e s o f n e u t r a l s a n d i o n s . T h e n the surface t e n s i o n c o e f f i c i e n t s are fit to a l a r g e set a i

a

1 0 1

o f d a t a t a k e n c h i e f l y f r o m t h e t a b u l a t i o n o f C a b a n i et a l for A G f o f neutrals i n w a t e r a n d m o s t l y c o m p u t e d f r o m l o g P values f r o m the M e d C h e m data b a s e for o r g a n i c s o l v e n t s . I n t h e p r e s e n t p a p e r w e c o n s i d e r s o l u t e s c o n t a i n i n g H , C , N , O , F , S, CI, B r , a n d I. ( S o m e , b u t n o t a l l , m o d e l s are a l s o p a r a m e t e r i z e d f o r s o l u t e s c o n t a i n i n g P , b u t P - c o n t a i n i n g s o l u t e s are n o t d i s c u s s e d i n t h i s c h a p t e r . ) A s a n e x a m p l e o f t h e s i z e o f t h e t r a i n i n g set, w e c o n s i d e r t h e t r a i n i n g set u s e d for s o l u t e s w i t h H , C , N , O , F , S, CI, B r , a n d I i n t h e S M 5 . 2 R m o d e l . T h i s t r a i n i n g set h a s d a t a for 43 i o n s a n d 248 n e u t r a l s i n w a t e r . It a l s o h a s 1836 d a t a p o i n t s f o r 2 2 7 n e u t r a l s i n 90 o r g a n i c s o l v e n t s . The SM5.2R p a r a m e t e r i z a t i o n s h a v e 46 s u r f a c e t e n s i o n c o e f f i c i e n t s f o r o r g a n i c s o l v e n t s a n d 25 f o r w a t e r . 1 0 2



Unbranched Alkanes Branched Alkanes Cycloalkanes Alkenes Alkynes Arenes Alcohols Ethers Aldehydes Ketones Carboxylic Acids Esters Bifunctional CHO Water, Dihydrogen Aliphatic Amines Aromatic Amines Nitriles Nitrohydrocarbons Amides & Ureas Bifunctional HCN and HCNO Ammonia & Hydrazine Thiols Sulfides Disulfides Fluorinated Hydrocarbons Chloroalkanes Chloroalkenes Chloroarenes Brominated Hydrocarbons Iodinated Hydrocarbons Other Halo Compounds A l l solutes:

Solute Class

8 5 5 9 5 8 16 12 6 12 5 13 5 2 15 10 4 6 4 5 2 4 6 2 6 13 5 8 14 8 25 248

Data Points 0.6 0.7 0.2 0.5 0.2 0.2 0.5 0.8 0.3 0.4 0.8 0.5 0.4 1.6 0.8 0.7 0.5 0.5 2.6 0.9 2.8 0.3 0.6 0.2 0.6 0.3 0.7 0.2 0.3 0.3 0.6 0.6

0.6 0.7 0.1 0.3 0.2 0.2 0.4 0.9 0.4 0.4 0.8 0.5 0.4 1.2 0.8 0.7 0.5 0.1 1.2 1.1 3.1 0.2 0.5 0.2 0.4 0.3 0.5 0.3 0.2 0.2 0.8 0.5

SM5.4/ PM3 AMI 0.7 0.5 0.4 0.3 0.1 0.2 0.2 0.6 0.3 0.5 0.4 0.3 0.5 0.0 0.5 0.8 0.5 0.1 1.4 0.9 0.2 0.6 1.2 0.1 0.7 0.3 0.6 0.8 0.2 0.3 0.7 0.5 0.7 0.5 0.4 0.3 0.1 0.2 0.2 0.6 0.3 0.5 0.4 0.3 0.5 0.0 0.5 0.8 0.5 0.1 1.4 0.9 0.2 0.6 1.0 0.1 0.7 0.4 0.4 0.9 0.2 0.3 0.7 0.5 0.6 0.5 0.4 0.2 0.2 0.2 0.2 0.5 0.3 0.3 0.4 0.3 0.4 0.0 0.6 0.6 0.4 0.5 1.1 0.8 0.4 0.5 1.1 0.0 0.4 0.3 0.7 0.3 0.4 0.3 0.6 0.4

SM5.2R/ MNDO(d) MNDO AMI 0.6 0.4 0.4 0.2 0.2 0.2 0.2 0.6 0.3 0.4 0.4 0.3 0.4 0.0 0.5 0.7 0.3 0.4 1.1 0.9 0.2 0.6 1.0 0.0 0.5 0.8 1.0 0.5 0.2 0.6 1.0 0.5

PM3 0.5 0.3 0.5 0.2 0.1 0.5 0.3 0.6 0.3 0.4 0.5 0.3 0.5 0.9 0.5 1.0 0.7 0.4 2.2 1.1 1.1 0.3 0.5 0.1 1.1 0.4 1.0 0.3 0.4 0.3 0.8 0.5

SM5.0R

Table 2. Mean Unsigned Error (kcal/mol) in the Aqueous Solvation Free Energies Predicted by Selected SMJC Solvation Models.



Unbranched Alkanes Branched Alkanes Cycloalkanes Alkenes Alkynes Arenes Alcohols Ethers Aldehydes Ketones Carboxylic Acids Esters Bifunctional CHO Water, Dihydrogen Aliphatic Amines Aromatic Amines Nitriles Nitrohydrocarbons Amides & Ureas Bifunctional HCN and HCNO Hydrazine Thiols Sulfides Disulfides Fluorinated Hydrocarbons Chloroalkanes Chloroalkenes Chloroarenes Brominated Hydrocarbons lodinated Hydrocarbons Other Halo Compounds All solutes:

Solute Class

8 2 4 6 4 8 16 11 4 10 5 9 4 2 9 7 4 6 1 3 1 2 3 1 2 7 3 6 12 5 15 180

Data Points 0.4 0.1 0.6 0.6 0.3 0.2 0.2 0.6 0.5 1.0 0.7 1.2 1.1 1.2 0.6 0.8 0.7 0.7 1.7 2.0 2.0 0.3 0.8 0.0 0.4 0.3 0.5 0.7 0.3 0.2 0.7 0.6 0.3 0.1 0.6 0.4 0.3 0.2 0.3 0.5 0.5 1.0 0.7 1.1 1.0 1.1 0.5 0.5 0.6 0.1 0.2 1.6 3.3 0.2 0.7 0.0 0.2 0.3 0.4 0.5 0.4 0.2 0.7 0.5

SM5.4/ AMI PM3 0.1 0.1 0.4 0.2 0.2 0.3 0.5 0.5 0.4 0.8 0.3 0.3 0.8 0.7 0.4 0.5 0.2 0.2 2.6 0.7 1.7 0.4 1.0 0.1 1.2 0.3 0.8 0.7 0.3 0.5 0.7 0.5

0.1 0.1 0.4 0.2 0.2 0.3 0.5 0.5 0.4 0.8 0.3 0.3 0.8 0.7 0.4 0.5 0.2 0.2 2.6 0.7 1.7 0.4 0.6 0.2 1.2 0.6 0.5 0.9 0.4 0.6 0.7 0.5

0.4 0.2 0.3 0.6 0.2 0.3 0.5 0.6 0.4 0.8 0.4 0.4 0.9 0.8 0.6 0.5 0.4 0.7 3.1 0.7 1.7 0.5 0.8 0.2 0.6 0.4 0.8 0.3 0.3 0.7 0.6 0.5

SM5.2R/ MNDO(d) M N D O AMI 0.3 0.2 0.3 0.4 0.2 0.3 0.5 0.5 0.4 0.8 0.4 0.3 0.8 0.7 0.5 0.5 0.2 0.4 2.1 0.6 1.7 0.4 0.6 0.3 0.3 0.5 1.1 0.3 0.3 0.5 0.9 0.5

PM3 0.1 0.1 0.4 0.2 0.1 0.3 0.4 0.5 0.5 0.9 0.1 0.6 0.6 0.5 0.4 0.6 0.5 0.1 2.5 0.9 1.8 0.3 0.3 0.3 0.5 0.5 1.0 0.3 0.2 0.6 0.8 0.5

SM5.0R

Table 3. Mean Unsigned Error (kcal/mol) in the 1-Octanol Solvation Free Energies Predicted by Selected SMx Solvation Models.



Unbranched Alkanes Branched Alkanes Cycloalkanes Alkenes Alkynes Arenes Alcohols Ethers Aldehydes Ketones Carboxylic Acids Esters Bifunctional CHO Water, Dihydrogen Aliphatic Amines Aromatic Amines Nitriles Nitrohydrocarbons Amides & Ureas Bifunctional H C N and HCNO Ammonia Thiols Sulfides Disulfides Fluorinated Hydrocarbons Chloroalkanes Chloroalkenes Chloroarenes Brominated Hydrocarbons Iodinated Hydrocarbons Other Halo Compounds A l l solutes:

Solute Class 9 5 4 6 5 9 17 9 7 12 5 13 1 2 8 9 4 6 1 0 1 3 5 2 4 7 4 3 12 8 8 189

Data Points

Table 4. Mean Unsigned Error (kcal/mol) in

0.4 0.6 0.4 0.2 0.1 0.4 0.2 0.3 0.3 0.2 0.4 0.3 0.1 0.1 0.1 0.2 0.2 0.2 0.1 0.4 0.5 0.6 0.3 0.4 0.2 0.5 0.2 0.2 0.3 0.7 0.3

0.4 0.6 0.4 0.2 0.1 0.4 0.2 0.3 0.3 0.2 0.4 0.3 0.1 0.1 0.1 0.2 0.2 0.2 0.1 0.4 0.5 0.8 0.3 0.4 0.2 0.6 0.2 0.2 0.3 0.6 0.3

0.5 0.5 1.2 0.2 0.1 0.3 0.2 0.3 0.2 0.3 0.2 0.4 0.3 0.5 0.3 0.3 0.1 0.2 1.0 0.5 0.5 0.2 0.1 0.6 0.1 0.3 0.2 0.1 0.2 0.4 0.3

0.7 0.5 0.2 0.1 0.7 0.2 0.4 0.3 0.1 0.1 0.4 0.3

0.3 0.5 0.3 0.3 0.2 0.5 0.3 0.3 0.3 0.2 0.4 0.3 0.0 0.1 0.1 0.2 0.1 0.3 0.2 0.3 0.4 0.6 0.3 0.4 0.2 0.7 0.2 0.2 0.2 0.4 0.3

0.5 0.4 0.7 0.3 0.4 0.3 0.7 0.4 0.2 0.3 0.6 0.3

PM3

0.2 0.4 0.2 0.4 0.1 0.5 0.2 0.3 0.2 0.2 3.5 0.3 0.2 0.1 0.1 0.2 0.2 0.6 0.0

SM5.2R/ MNDO(d) MNDO AMI

0.5 0.5 1.2 0.4 0.2 0.4 0.2 0.3 0.1 0.3 0.2 0.5 0.2 0.5 0.3 0.4 0.2 0.5 1.2

SM5.4/ PM3 AMI

0.4 0.4 0.5 0.3 0.6 0.2 0.5 0.3 0.4 0.2 0.3 0.3

0.4 0.7 0.5 0.2 0.1 0.5 0.3 0.2 0.4 0.3 0.5 0.3 0.4 0.1 0.1 0.2 0.2 0.1 0.4

SM5.0R

;ies Predicted by Selected S M * Solvation Models.



Unbranched Alkanes Branched Alkanes Cycloalkanes Alkenes Alkynes Arenes Alcohols Ethers Aldehydes Ketones Carboxylic Acids Esters Bifunctional CHO Water, Dihydrogen Aliphatic Amines Aromatic Amines Nitriles Nitrohydrocarbons Amides & Ureas Bifunctional H C N and HCNO Ammonia & Hydrazine Thiols Sulfides Disulfides Fluorinated Hydrocarbons Chloroalkanes Chloroalkenes Chloroarenes Brominated Hydrocarbons Iodinated Hydrocarbons Other Halo Compounds A l l solutes:

Solute Class

1 0 1 0 0 6 14 6 3 3 5 9 2 1 8 8 2 2 2 3 2 1 4 0 1 0 0 2 1 1 4 92

Data Points 0.3 1.2

0.2 0.3 0.4 0.5 0.2 0.2 0.2 0.8 1.2 0.2 0.4 0.2 0.2 0.5 2.8 2.9 0.7 1.0 0.1

0.2 0.2 0.2 0.5 0.5

0.2 1.1

0.1 0.4 0.4 0.6 0.2 0.2 0.2 0.8 1.5 0.4 0.3 0.2 0.1 1.5 3.0 2.4 0.7 1.0 0.3

0.2 0.0 0.1 0.6 0.5

SM5.4/ AMI PM3

Table 5. Mean Unsigned Error (kcal/mol) in the Chloroform

0.2 0.4 0.5 0.8 0.4 0.4 0.7 0.8 0.7 0.5 1.0 1.0 0.5 2.5 1.0 0.7 0.8 1.2 0.3

0.3 0.4 0.9 0.7 0.6

0.5 0.3 0.5 1.0 0.3 0.2 0.5 0.8 0.2 0.6 0.8 0.4 0.2 2.1 1.3 0.8 0.6 1.2 0.8

0.6 0.8 0.5 0.7 0.6

0.7 0.3 0.5 0.9 0.3 0.2 0.4 0.8 0.1 0.6 0.4 0.7 0.3 2.2 1.3 0.6 0.5 1.2 0.8

0.6 1.0 1.4 0.6 0.6

0.2 0.3 0.6 0.9 0.4 0.1 0.5 0.7 0.3 0.5 0.8 0.7 0.2 2.3 1.3 0.8 0.6 1.2 1.0

0.2 0.3 0.6 0.9 0.4 0.1 0.5 0.7 0.3 0.5 0.8 0.7 0.2 2.3 1.3 0.8 0.7 1.2

0^6 0.7 0.9 0.6 0.6

0.7 0.7 1.0 0.5 0.6

0.1

0.0

0.2

0.0

0.0

1.0

0.4

0.1

SM5.0R

0.1

PM3

0.2

0.2

SM5.2R/ MNDO(d) MNDO AMI

Free Energies Predicted by Selected S M * Solvation Models.


131

Table 6. Free Energy of Solvation and Partition Coefficient Results for 1,2 Ethanediol.

A G

Model

ENP

G

CDS

A

G

S

l o

8 ôrg/water

theory

experiment


water SM5.4/AM1 SM5.4/PM3 SM5.2R/MNDO(d) SM5.2R/MNDO SM5.2R/AM1 SM5.2R/PM3 SM5.0R

-6.5 -6.3 -1.9 -1.9 -2.8 -2.2

SM5.4/AM1 SM5.4/PM3 SM5.2R/MNDO(d) SM5.2R/MNDO SM5.2R/AM1 SM5.2R/PM3 SM5.0R

-5.9 -5.8 -1.7 -1.7 -2.5 -2.0

-2.3 -2.9 -7.0 -7.0 -6.4 -7.1

-8.8 -9.2 -8.9 -8.9 -9.2 -9.3 -8.7

-1.4 -1.9 -6.3 -6.3 -5.6 -6.3

-7.2 -7.7 -8.0 -8.0 -8.2 -8.2 -8.1

-1.1 -1.1 -0.7 -0.7 -0.7 -0.8 -0.4

-3.1 -3.4 -3.5 -3.5 -3.5 -3.7 -3.8

-4.2 -4.3 -4.0 -4.0 -4.2 -4.1 -3.6

-5.2 -5.5 -5.2 -5.2 -5.4 -5.4 -5.1

-2.6 -2.7 -2.7 -2.7 -2.8 -2.9 -2.6

1-octanol

SM5.4/AM1 SM5.4/PM3 SM5.2R/MNDO(d) SM5.2R/MNDO SM5.2R/AM1 SM5.2R/PM3 SM5.0R SM5.4/AM1 SM5.4/PM3 SM5.2R/MNDO(d) SM5.2R/MNDO SM5.2R/AM1 SM5.2R/PM3 SM5.0R

hexadecane -3.2 0.1 -3.2 -0.2 -0.9 -2.6 -0.9 -2.6 -1.3 -2.2 -1.1 -2.6 chloroform -5.0 -0.2 -5.0 -0.5 -1.5 -3.7 -1.5 -3.7 -2.1 -3.3 -1.7 -3.7

T a b l e s 2 - 5 s h o w t h e m e a n u n s i g n e d d e v i a t i o n s i n s t a n d a r d - s t a t e free e n e r g i e s o f s o l v a t i o n for v a r i o u s classes o f s o l u t e s i n w a t e r a n d t h e t h r e e o r g a n i c s o l v e n t s s i n g l e d o u t i n the i n t r o d u c t i o n . I n e a c h t a b l e w e s h o w t h e a p p l i c a t i o n o f s e v e r a l m o d e l s t o t h e s a m e set o f d a t a , n a m e l y o u r latest a n d l a r g e s t t r a i n i n g set, e x c l u d i n g p h o s p h o r u s - c o n t a i n i n g c o m p o u n d s , e x c e p t t h a t i n T a b l e s 2, 3, a n d 5, t h e S M 5 . 4 / P M 3 r e s u l t s are b a s e d o n o n e less d a t a p o i n t b e c a u s e h y d r a z i n e is e x c l u d e d w h e n P M 3 is u s e d to o p t i m i z e geometries. Tables 2-5 show that we have uniformly small


132

Table 7. Free Energy of Solvation and Partition Coefficient Results for Thioanisole.

A G

Model

ENP

G

CDS

A

G

S

l o

g ôrg/water

theory

experiment



-3.9 -3.0 -1.0 -1.0 -3.8 -2.7


-3.5 -2.7 -0.9 -0.9 -3.4 -2.4

0.7 -0.3 -1.7 -1.9 0.8 -0.3

-3.3 -3.3 -2.7 -2.9 -3.0 -3.0 -3.4

-3.9 -4.6 -5.2 -5.5 -3.0 -4.1

-7.4 -7.3 -6.1 -6.4 -6.4 -6.5 -6.4

3.0 2.9 2.5 2.6 2.5 2.6 2.2

-6.9 -7.0 -6.1 -6.3 -6.1 -6.3 -6.3

2.6 2.7 2.5 2.5 2.3 2.4 2.1

-7.8 -8.0 -7.3 -7.4 -7.7 -7.7 -7.4

3.3 3.4 3.3 3.3 3.4 3.4 2.9

1-octanol


hexadecane -1.8 -5.1 -1.4 -5.7 -0.5 -5.6 -5.8 -0.5 -1.8 -4.3 -1.2 -5.0 chloroform -4.8 -2.9 -2.3 -5.7 -0.8 -6.5 -0.8 -6.7 -2.9 -4.8 -2.0 -5.7

m e a n e r r o r s . N o t i c e t h a t s o m e s o l u t e classes are n o t w e l l r e p r e s e n t e d i n the d a t a sets f o r s p e c i f i c s o l v e n t s , a n d i n fact s o m e s o l u t e c l a s s e s a r e n o t r e p r e s e n t e d at a l l i n s o m e s o l v e n t s . T h e S M 5 s o l v a t i o n m o d e l s are a b l e to treat s u c h cases b e c a u s e a l l t h e d a t a for free e n e r g i e s o f s o l v a t i o n i n o r g a n i c s o l v e n t s a r e fit s i m u l t a n e o u s l y , a n d t h e n u m b e r o f s o l v e n t d e s c r i p t o r s is m u c h s m a l l e r t h a n t h e t o t a l n u m b e r (90) o f o r g a n i c s o l v e n t s . W e b e l i e v e i n t h i s w a y w e h a v e c a p t u r e d a l l t h e m a j o r p h y s i c a l effects. T a b l e s 6-8 w e r e i n c l u d e d to e x a m i n e a c o u p l e o f i n d i v i d u a l e x a m p l e s , namely, 1,2-ethanediol, thioanisole, a n d p - d i c h l o r o b e n z e n e . These tables s h o w the p a r t i t i o n i n g of the p r e d i c t e d s o l v a t i o n free energy


133

Table 8. Free Energy of Solvation and Partition Coefficient Results for p-Dichlorobenzene.

A G

Model

ENP

G

CDS

A

G

S

l o

g ôrg/water

theory

experiment



-2.1 -1.3 -1.0 -1.4 -2.5 -1.8


-1.9 -1.2 -0.9 -1.3 -2.2 -1.6

1.1 0.2 -0.6 -0.3 1.5 0.2

-1.0 -1.2 -1.6 -1.7 -1.0 -1.6 -1.0

-3.7 -4.5 -5.0 -4.8 -3.2 -4.2

-5.6 -5.7 -5.9 -6.1 -5.5 -5.8 -5.6

3.3 3.3 3.2 3.2 3.3 3.1 3.4

-5.7 -5.7 -5.9 -5.9 -5.5 -5.8 -5.8

3.4 3.3 3.1 3.1 3.3 3.1 3.5

-5.9 -6.1 -6.8 -6.9 -6.6 -6.9 -6.6

3.6 3.6 3.8 3.8 4.1 3.9 4.2

1-octanol


hexadecane -1.0 -4.7 -0.6 -5.1 -0.5 -5.4 -0.7 -5.2 -1.2 -4.3 -0.9 -4.9 chloroform -1.6 -4.3 -1.0 -5.1 -0.8 -6.1 -1.1 -5.9 -1.9 -4.7 -1.4 -5.5

b e t w e e n the electrostatic (AGENP) and non-electrostatic (G ) c o m p o n e n t s as w e l l as t h e l o g a r i t h m o f t h e p a r t i t i o n c o e f f i c i e n t b e t w e e n selected o r g a n i c solvents a n d water. T h e S M 5 . 4 m o d e l s utilize class I V c h a r g e s a n d are d e s i g n e d t o o p t i m i z e s o l u t e g e o m e t r y i n t h e p r e s e n c e o f t h e s o l v e n t r e a c t i o n f i e l d . N o t e t h a t the a b s o l u t e v a l u e o f t h e A G E N P t e r m is generally m u c h larger for the S M 5 . 4 p a r a m e t e r i z a t i o n s t h a n for the S M 5 . 2 R m o d e l s w h i c h i n c o r p o r a t e t h e l e s s - a c c u r a t e c l a s s II c h a r g e s . I n g e n e r a l , class I V c h a r g e s l e a d to g r e a t e r c h a r g e s e p a r a t i o n w i t h i n a s o l u t e m o l e c u l e , w h i c h results i n a larger |AGENP|O u r m e t h o d of p a r a m e t e r i z i n g the C D S


134


Table 9. Absolute Value (kcal/mol) of the A G g ^ p and G Terms in Selected S M x M o d e l s

0

Model

|)

(|AG

SM5.4/AM1 SM5.4/PM3 SM5.2R/MNDO(d) SM5.2R/MNDO SM5.2R/AM1 SM5.2R/PM3 SM5.0R SM5.4/AM1 SM5.4/PM3 SM5.2R/MNDO(d) SM5.2R/MNDO SM5.2R/AM1 SM5.2R/PM3 SM5.0R SM5.4/AM1 SM5.4/PM3 SM5.2R/MNDO(d) SM5.2R/MNDO SM5.2R/AM1 SM5.2R/PM3 SM5.0R SM5.4/AM1 SM5.4/PM3 SM5.2R/MNDO(d) SM5.2R/MNDO SM5.2R/AM1 SM5.2R/PM3 SM5.0R

E

N

P

(|G

water 4.5 3.7 1.7 1.7 3.2 2.4 0.0 1-octanol 4.0 3.4 1.5 1.5 2.8 2.1 0.0 hexadecane 2.1 1.8 0.8 0.8 1.5 1.1 0.0 chloroform 3.4 2.9 1.3 1.3 2.4 1.8 0.0

C D S

(

|)

1.5 1.3 2.3 2.3 1.9 2.0 3.7 2.0 2.5 4.2 4.2 2.9 3.6 5.7 2.4 2.8 3.6 3.6 2.9 3.3 4.5 2.6 3.1 4.4 4.4 3.5 4.0 5.5

a

Reported averages are for 67 organic solutes for which experimental solvation free energies are available i n water, hexadecane, octanol, and chloroform. ( A total of 268 data points.)

remaining non-electrostatic term ( G energies expensive

allows the

C D S

) t o t h e e x p e r i m e n t a l s o l v a t i o n free

d i m i n i s h e d electrostatics

S M 5 . 2 R m o d e l s to be

compensated

obtained

with

for b y the

G

the C

D

S

less term,

r e s u l t i n g i n f a i r l y a c c u r a t e a b s o l u t e s o l v a t i o n free e n e r g i e s a n d p a r t i t i o n coefficients.

T h i s a p p r o a c h was t a k e n to the l i m i t i n the S M 5 . 0 R m o d e l


135

Table 10. Mean Unsigned Errors in Predicted Solvation Free Energies, Organic/Water Partition Coefficients, and Free Energy of Transfer for Selected S M x methods* Model

MUE


A G

SM5.4/AM1 SM5.4/PM3 SM5.2R/MNDO(d) SM5.2R/MNDO SM5.2R/AM1 SM5.2R/PM3 SM5.0R SM5.4/AM1 SM5.4/PM3 SM5.2R/MNDO(d) SM5.2R/MNDO SM5.2R/AM1 SM5.2R/PM3 SM5.0R SM5.4/AM1 SM5.4/PM3 SM5.2R/MNDO(d) SM5.2R/MNDO SM5.2R/AM1 SM5.2R/PM3 SM5.0R SM5.4/AM1 SM5.4/PM3 SM5.2R/MNDO(d) SM5.2R/MNDO SM5.2R/AM1 SM5.2R/PM3 SM5.0R

S°

MUE A A G

water 0.54 0.47 0.45 0.44 0.43 0.39 0.46 1-octanol 0.56 0.51 0.43 0.42 0.47 0.41 0.40 hexadecane 0.29 0.29 0.27 0.26 0.27 0.26 0.30 chloroform 0.32 0.27 0.45 0.46 0.47 0.44 0.50

o°rg/water

MUE l o

g ^rg/water

0.63 0.54 0.38 0.38 0.42 0.37 0.40

0.46 0.40 0.28 0.28 0.31 0.27 0.38

0.49 0.49 0.45 0.45 0.51 0.47 0.30

0.36 0.36 0.33 0.33 0.38 0.35 0.43

0.46 0.39 0.45 0.45 0.45 0.41 0.50

0.33 0.28 0.33 0.33 0.33 0.30 0.41

^Reported averages are for 67 organic solutes from our training set for which experimental solvation free energies are available in water, hexadecane, octanol, and chloroform. ( A total of 268 data points.)

w h i c h c o n t a i n s n o e x p l i c i t e l e c t r o s t a t i c o r S C F t r e a t m e n t . A l t h o u g h i t is likely that the very i n e x p e n s i v e S M 5 . 0 R a p p r o a c h w i l l have difficulty p r e d i c t i n g s o l v a t i o n free e n e r g i e s i n c a s e s w h e r e t h e c h a r g e d i s t r i b u t i o n w i t h i n a g i v e n s o l u t e differs s i g n i f i c a n t l y f r o m t h e i m p l i c i t d i s t r i b u t i o n s p a r a m e t e r i z e d i n t o the m o d e l , S M 5 . 0 ' s p r e d i c t i o n s for the e x a m p l e m o l e c u l e s a n d o v e r a l l t r a i n i n g set are r e a s o n a b l y s i m i l a r t o t h o s e p r e d i c t e d b y S M 5 m o d e l s w i t h m o r e rigorous electrostatic treatments.


136

To compare the performance of the S M J C models i n water, 1-octanol, hexadecane, and chloroform, we selected the subset of organic solutes from the training set for these solvation models for which the experimental free energy of solvation is known for all four solvents. This subset contains 6 8 molecules. Table 9 compares the average absolute value of the A G E N P andG

C D S

terms for various S M J C models i n 4 solvents. As mentioned earlier,

the SM5.4 methods typically have the largest

( | A G E N P | ) , while the SM5.2


methods with the usually smaller class II charges have ( I A G E N P I )

that are

only one half to o n e - t h i r d as large as the SM5.4 counterpart. It is interesting to note that the class II charges p r o d u c e d b y the A M I Hamiltonian appear to be the most similar to the class IV charges, while the M N D O a n d M N D O ( d ) Hamiltonians produce m u c h less charge separation. The

(|G

CDS

| ) terms have opposite trends to make up for the differences i n

the electrostatics. Table 10 contains the m e a n unsigned errors i n the absolute free energies of solvation from the gas phase into each of our four considered solvents as well as the unsigned error i n the free energy of transfer from water to an organic solvent a n d the resulting error i n the log of the estimated partition coefficient. Note that i n general the SM5.4 a n d SM5.2 models perform similarly i n both the m e a n unsigned error of the absolute free energies a n d the m e a n unsigned error of the log of the partition coefficient. The results i n chloroform are an exception to this trend. The SM5.4 models were especially reparameterized for chloroform a n d hence they do achieve a significantly i m p r o v e d m e a n u n s i g n e d error i n the absolute free energies of solvation. (The SM5.2R and SM5.0R models are parameterized for chloroform solvent at the same time as 8 9 other organic solvents, although a solvent descriptor is included which helps distinguish electronegative-halogen-containing solvents.) However, b o t h the SM5.4 and SM5.2R models are shown to perform similarly i n their ability to predict chloroform/water partition coefficients. SM5.0R generally is shown to have slightly larger errors than the SM5.4 and SM5.2R parameterizations, but still produces answers that are within reason considering the simplicity of the model. 4. C o n c l u d i n g remarks We have developed a number of universal solvation models based o n q u a n t u m m e c h a n i c a l treatment of the solutes, with solute polarizability i n c l u d e d self-consistently. B o t h electrostatics a n d first-solvation-shell effects are treated by 3-D modeling. Hydrogen b o n d i n g of solute with solvent a n d solute disruption of solvent-solvent hydrogen b o n d i n g are both included. Solute functionality is recognized o n the basis of atomic n u m b e r s a n d geometry only; thus the i n c o n v e n i e n c e (and occasional ambiguity) of assigning atomic types is avoided. The solvation models are parameterized directly i n terms of free energies, w h i c h are the critical thermodynamic quantities for predicting equilibria. One possible application is the prediction of log Poctanol-water> which is a widely used measure of lipophilicity, the movement of organic


137

compounds through cells, a n d drug activity. We hope the models will be useful for a variety of purposes i n the humanistic endeavor of designing better drugs. 5. Acknowledgments T h i s work Foundation.

was

supported

i n part

b y the

National

Science


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Rational Drug Design - American Chemical Society

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