Quantum chemical and physicochemical influences on structure–activity relations and drug design

Quantum chemical results will be presented on drugs, carcinogens, teratogens, and endogenous biomolecules using our new nonempirical ab initio MODPOT /VRDDO method, which incorporates as options to our ab initio LCAO -MO -SCF /CI programs ab initio effective core model potentials (MODPOT ) permitting one to calculate only the valence electrons explicitly yet accurately and an integral prescreening technique (VRDDO , variable retention of diatomic differential overlap) especially effective for spatially extended molecules. For molecules of the size of those of interest the MODPOT /VRDDO calculations run an order-of-magnitude faster than with our own fast ab initio programs and still retain accuracy to the third decimal place for the valence electron properties. We have also just implemented a new efficient MERGE technique which allows us to reuse integrals from a common skeletal fragment and only to have to recalculate those for a new atom or group or a change in its position. Examples will be presented of the use of this technique on a carcinogenic polycyclic aromatic hydrocarbon and its metabolites. The pK_a's, oil-water partition, and drug distribution coefficients as a sensitive function of pH have been measured for a number of drugs as well as for relevant endogenous biomolecules. The pH dependence of the lipophilicities of such molecules has profound implication on appropriate use of such data in QSAR studies.     

Molecular calculations with the MODPOT,VRDDO, and MODPOT/VRDDO procedures. IV. Boron hydrides and carboranes

Reference completely ab initio 6–3G and nonempirical 3G/MODPOT (ab initio effective core model potential) LCAO -MO -SCF calculations (using the same valence atomic orbital basis) were performed for a series of boron hydrides (B₄H₁₀, B₅H₉, B₅H₁₁, and B₆H₁₀) and a test 3G/MODPOT + VRDDO (variable retention of diatomic differential overlap for charge conserving integral prescreening) calculation were also performed for B₅H₉, B₆H₁₀, and B₁₀H₁₄. The agreement between the ab initio 6–3G and the corresponding 3G/MODPOT calculations was excellent for valence orbital energies, gross atomic populations, and dipole moments. The results also compared favorably to previous ab initio minimum STO basis results of Lipscomb and coworkers. The 3G/MODPOT + VRDDO calculations verified that for such spatially compact molecules (such as boron hydrides, which are fragments of polyhedra), the VRDDO procedure does not result in a noticeable savings in computer time for molecules of the size and shape of B₅H₉ and B₆H₁₀, in contrast to the savings previously realized for organic molecules of comparable atomic size. However, the agreement in calculational results between the 3G/MODPOT and the 3G/MODPOT +VRDDO results was still as extremely close as it had been for the organic molecules. 3G/MODPOT calculations were also carried out for B₈H₁₂, B₉H₁₅, B₁₀H₁₄, B₁₀H₁₄^?2, 1,2-C₂B₄H₆, and 1,6-C₂B₄H₆ and the results compared to the previous minimum STO basis results. For B₁₀H₁₄, the 3G/MODPOT +VRDDO method led to savings in computer time of 28% over the 3G/MODPOT method itself. The agreement of the 3G/MODPOT results with available experimental photoelectron spectral data for B₅H₉ and 1,6-C₂B₄H₆ was as good as that of the previous ab initio minimum STO basis calculations.     

Molecular calculations with the nonempirical ab initioMODPOT,VRDDO, and MODPOT/VRDDO procedures. IX. Carcinogenic benzo(a)pyrene and its metabolites using a MERGE technique

Ab initio MODPOT /VRDDO calculations have been carried out on carcinogenic benzo(a)pyrene and its metabolites. The MODPOT /VRDDO method incorporates two very desirable options into our fast ab initio Gaussian programs: MODPOT —ab initio effective core model potentials—and a charge-conserving integral prescreening approximation which we named VRDDO (variable retention of diatomic differential overlap). For orbital energies and population analyses the MODPOT /VRDDO results agree to essentially three decimal places with completely ab initio calculations using the same valence atomic basis set. For this series of very closely related congeners a new MERGE technique was implemented that allows reuse of integrals of a common skeletal fragment. Since our program computes integrals efficiently by blocks, reusing information common to the block, it was more difficult to implement a MERGE technique than for integral programs which calculate the integrals one-byone. The MODPOT /VRDDO calculations were performed for benzo(a)pyrene (BP), BP oxides, BP dihydrodiols, and BP dihydrodiol epoxides. The metabolites investigated were BP-7,8-oxide, BP-4,5-oxide, BP-7,8-dihydrodiol [cis(e, a), cis(a, e), trans(e, e), and trans(a, a)], and BP-7,8-dihydrodiol-9,10-epoxide [β,β,β (the most stable), β,β,α; α,α,β, and α,α,α all derived from cis-BP-7,8-dihydrodiol and β,α,β; α,β,β and α,β,β derived from trans-BP-7,8-dihydrodiol]. Several different conformations were calculated for each of the BP dihydrodiols and BP dihydrodiol epoxides. Calculations were carried out for the opening of the C₉—O—C₁₀ epoxide ring both toward C₉ and C₁₀ for the, most stable β,β,β isomer of BP-7,8-dihydrodiol-9,10-epoxide. Opening the epoxide ring between C₁₀ and O leads to a more stable intermediate than opening the epoxide ring between C₉ and C₁₀. However, there is no buildup of positive charge in C₁₀ as has been postulated by some cancer researchers, but rather the C₁₀ becomes slightly more negative. Nor is there a buildup of negative charge on the O atom. rather it becomes slightly less negative. As the epoxide ring is opened further than 90° for the O—C₉—C₁₀ or O—C₁₀—C₉ angles, there appears to be a possible mixing of configurations that is being investigated further.     

Molecular calculations with the nonempirical ab initioMODPOT,VRDDO, and MODPOT/VRDDO procedures. XII. Carcinogenic 3-methylcholanthrene and its metabolites using a MERGE technique

Ab initio MODPOT/VRDDO/MERGE calculations were carried out on carcinogenic 3-methylcholanthrene (3-MCA) and its metabolites. The results for 3-MCA were compared to our earlier similar calculations for carcinogenic benzo(a)pyrene (BP). Both compounds 3-MCA and BP are carcinogenic and are metabolically activated by similar mechanisms but in different positions. Both the calculated wave functions for 3-MCA and BP and the electrostatic molecular potential contour maps generated from these wave functions correctly reflect the similarity of mechanisms of metabolic activation and the differences in position. Our calculated results both for BP and for 3-MCA reflect accurately their experimentally observed behavior. Thus this combination of theoretical techniques can be used with confidence to describe the behavior of the polycyclic aromatic hydrocarbons (PAH's) and their metabolites. The ab initio MODPOT/VRDDO method incorporates two very desirable options into our fast ab initio Gaussian programs: MODPOT –ab initio effective core model potentials—and a charge-conserving integral prescreening approximation which we named VRDDO (variable retention of diatomic differential overlap). For orbital energies and population analysis the MODPOT/VRDDO results agree to essentially three decimal places with completely ab initio calculations using the same valence atomic basis set. For this series of very closely related congeners our recent MERGE technique which allows reuse of integrals from a common skeletal fragment was used. The ab initio MODPOT/VRDDO/MERGE calculations were carried out for 3-MCA, 3-MCA oxides, 3-MCA dihydrodiols, and 3-MCA dihydrodiolepoxides. The metabolites investigated were 3-MCA 9,10-oxide; 3-MCA 7,8-oxide; 3-MCA 9,10-dihydrodiol [trans(axial, axial); trans(equatorial, equatorial); cis(axial, equatorial); cis(equatorial, axial)]; and 3-MCA 9,10-dihydrodiol–7,8-epoxide [for both conformations A and B of the dihydrodiol and for all stereoisomers of the dihydrodiolepoxides relative to below and above the plane: ααα, and ααβ αβα αββ βαα βαβ ββα and βββ (most stable)]. Calculations were also carried out for opening of the C₇? O? C₈ epoxide ring both towards C₇ and C₈ for the most stable isomer Aβββ (above the ring). Opening the epoxide ring between C₇ and O leads to a more stable intermediate than opening the epoxide ring between C₈ and O. Again, however, as with opening the epoxide ring in BP 7,8-dihydrodiol–9,10-epoxide there is no buildup of positive charge on C₇ in the 3-MCA metabolites as postulated by some cancer researchers, but rather the C₇ becomes slightly more negative. Nor is there a buildup of negative charge on the O atom, but rather it becomes slightly more positive. As the epoxide ring is opened further than 90° for the O? C₇? C₈ or O? C₈? C₇ angles, there appears to be a possible mixing of configurations that is being investigated further.     

Molecular calculations with the nonempirical ab initioMODPOT,VRDDO, and MODPOT/VRDDO procedures. XI. Theoretical study of the [C6H5OH ⃛OC6H5]− molecular complex: Ab initioMODPOT/VRDDO calculations and electrostatic molecular potential contour maps

The transport of C₆H₅O^? (or similarly charged moieties) through a lipoidal membrane may possibly be facilitated by forming complexes with the neutral compound. Thus, theoretical studies were performed on the model [C₆H₅OH ?OC₆H₅]^? molecular complex to obtain some information concerning the possible molecular and electronic structure of such complexes. Ab initio MODPOT /VRDDO SCF calculations were carried out on the neutral-anion dimer [C₆H₅OH ?OC₆H₅] to optimize the equilibrium geometry. Electrostatic molecular potential contour maps have been generated from the ab initio MODPOT /VRDDO results in the molecular plane and in the plane perpendicular to the molecular plane and intersecting the hydrogen bond O ?H? O. Difference maps have also been generated showing the change of potential on complex formation. There is a decrease of electrostatic interactions of the phenoxide anion upon complex formation with the neutral phenol. Counterpoise corrections for basis set size could not be made since calculation of the phenoxide anions in the basis set of the phenol plus the phenoxide anion led to an excited state for the phenoxide anion. This behavior is somewhat similar to that occurring in the stabilization method for excited states of negative ions as the size of the basis set is increased.     

Ab initioMODPOT/VRDDO/MERGE calculations on energetic compounds. IV. Nitrocubanes: Mononitro to octanitro quantum chemical calculations and electrostatic molecular potential contour maps

Ab initio MODPOT /VRDDO /MERGE calculations have been carried out for all the different position isomers of nitrocubane from mononitrocubane through octanitrocubane for a perfect symmetrical cubic cubane skeleton and for mononitrocubane through septanitrocubane for the almost cubic experimentally determined cubane skeleton. These calculations were carried out with our own rapid efficient ab initio programs which also incorporate a number of desirable computational strategies for calculations on large molecules. The skeletal total overlap population of the cubane skeleton (a theoretical index we showed years ago to be sensitive and predictive of stability of energetic molecular frameworks) indicates that successive nitration seems to increase the stability of the cubane skeleton. Successive nitration also seems to increase the total overlap population of the C? NO₂ bond. There are subtle differences depending on the exact positional isomer for a constant number of nitro groups—but the overall trend is definite. We have also generated electrostatic molecular potential contour (EMPC ) maps around these nitrocubanes. These maps are indicative of preferred positions of electrophilic and nucleophilic attack as a function of the number of nitro groups or their positions. These EMPC maps can also indicate, to a first approximation, a limit on how close these molecules may be able to approach each other in a crystal.     

Ab initioMODPOT/VRDDO/MERGE calculations on energetic compounds. III. Nitroexplosives: Polyaminopolynitrobenzenes (including DATB,TATB, and tetryl)

Quantum chemical ab initio MODPOT /VRDDO calculations have been carried out on the following aminonitrobenzenes for which crystal structures had been determined experimentally: 4-nitroaniline; N,N-dimethyl-p-nitroaniline; 2,4,6-trinitroaniline; 1,3-diamino-2,4,6-trinitrobenzene (DATB—Form I); 1,3,5-triamino-2,4,6-trinitrobenzene (TATB); 2,3,4,6-tetranitroaniline; N-methyl-N,2,4,6-tetranitroaniline (Tetryl); and N-(β,β,β-trifluoroethyl)-N,2,4,6-tetranitroaniline. These quantum chemical calculations were performed on the molecules in their conformations as found in their crystal structures. The calculations were carried out with our own ab initio programs which also incorporate as options several desirable features for calculations on large molecules: ab initio effective core model potentials (MODPOT) which enable calculations of valence electrons only explicitly, yet accurately, and a charge conserving integral prescreening evaluation (which we named VRDDO-variable retention of diatomic differential overlap) especially effective for spatially extended molecules. Aminonitrobenzenes are especially interesting since there are inherent intramolecular ring distortions and deviations from planarity and intramolecular hydrogen bonds as well as intermolecular hydrogen bonds causing further deviations from planarity. The theoretical indices resulting from the quantum chemical calculations are relevant to a number of properties and behavioral characteristics of these molecules, both intramolecular and intermolecular. The charges on the atoms [from the gross atomic populations (GAP 's)] are needed for calculation of the atomic multipole–atomic multipole electrostatic contributions (a dominant factor) to the intermolecular interaction energies. These electrostatic interaction energies are part of the input necessary for calculations on the crystal packing and densities of these molecules. These GAP 's are also of value in interpreting the experimental photoelectron and ESCA spectra of these molecules. The total overlap populations (TOP 's) between atoms are related to the inherent bond strengths and can serve as a quantitative replacement for the old empirical bond length-bond order-bond energy relationship still used by explosives chemists to identify the “target bonds” (the weakest bonds). The TOP 's are of considerable value in predicting and tracing initiation and subsequent steps of explosive phenomena. The molecular orbital energies of the lowest unoccupied orbitals are of interest since nitroexplosives have been implicated in testicular toxicity and the initial metabolic activation appears to proceed through a one-electron reduction of the nitroexplosive.     

Principles for a direct SCF approach to LICAO–MOab-initio calculations

The principles and structure of an LCAO -MO ab-initio computer program which recalculates all two-electron integrals needed in each SCF iteration are formulated and discussed. This approach—termed “direct SCF ”—is found to be particularly efficient for calculations on very large systems, and also for calcuations on small and medium-sized molecules with modern minicomputers. The time requirements for a number of sample calculations are listed, and the distribution of two-electron integrals according to magnitude is investigated for model systems.     

Fast semiempirical calculations

Most quantum chemists regard semiempirical methods as ephemeral and computationally cost efficient. For this reason, an article dealing with computational efficiency of semiempirical methods is probably very unfashionable. However, experience at a big computer installation, shared by ab-initio and semiempirical quantum chemists shows that the second group actually consumes more computer time than the first. Obviously, the greater size of the molecules in semiempirical calculations outweighs the inherent efficiency of these methods. The present article describes a simple method for accelerating SCF -type semiempirical methods.     

The structure and acid–base properties of methyl and silyl amines and phosphines: An ab-initio SCF study

The structures of the methyl and silyl amines and phosphines and their ions have been calculated using ab-initio SCF theory and the 3-21G basis set. The computed structures give excellent agreement with the available experiment data without the inclusion of d functions, with the exception of (SiH₃)₂N– and the isoelectronic molecules (SiH₃)₂O and (SiH₃)₂C^2? where d functions are essential. The observed trends in computed basicities and acidities are reproduced by the calculations.     

A general ab initio molecular multi-configuration self-consistent field algorithm

The ab initio multiconfiguration self-consistent-field (MC SCF ) techniques and computer programs of Basch [1, 2] and the ab initio configuration interaction (CI ) techniques and programs of Whitten and Hackmeyer [3] have been combined and generalized to form a general technique and program to yield optimized ab initio MC SCF wavefunctions for any set of Slater determinants. The Slater determinants are read in as input data to the program along with the spin parity that is being considered (optional) and the program successively does the CI calculation and one iteration of the SCF calculation, constructing the proper Fock–Hamiltonians by examining the set of Slater determinants and their CI coefficients. The Fock–Hamiltonian matrices are calculated and diagonalized in succession, a single two-dimensional array being used to store these matrices. The basis function integrals are read from a tape only once during each MC SCF iteration (one MC SCF iteration = a CI calculation followed by one iteration of the SCF calculation).     

Electrostatic molecular potential contour maps generated from ab initioMODPOT/VRDDO/MERGE wave functions of carcinogenic 3-methylcholanthrene and its metabolites

The electrostatic molecular potential contour maps were calculated for carcinogenic 3-methylcholanthrene (3-MCA) and a number of its metabolites {3-MCA 7,8-oxide and 3-MCA 9,10-oxide; 3-MCA 7,8-dihydrodiols[several stereoisomers: A trans(equatorial, equatorial) and A cis(equatorial, axial)]; 3-MCA 9,10-dihydrodiol–7,8-epoxide A βββ and 3-MCA 9,10-dihydrodiol–7,8-epoxide A αβα}. The maps were generated from our ab initio MODPOT/VRDDO/MERGE wave functions calculated for these species. The results of these maps for 3-MCA [similarly to our results for the maps we generated for benzo(a)pyrene (BP)] show that these electrostatic molecular potential contour maps can be used to indicate favored positions of attack for electrophilic species, such as “electrophilic” oxygen to form an epoxide as well as for positive ion attack. The 3-MCA maps indicate the favored site for attack and the pathways. The maps around 3-MCA 9,10-oxide and around 3-MCA 9,10-dihydrodiol-7,8-epoxide indicate the directional preferences for proton assisted epoxide ring opening. The maps around the 3-MCA dihydrodiols indicate that while for certain stereoisomers the “electrophilic” oxygen will prefer to attack from below, for other isomers it will prefer to attack from above. This gives great insight into the stereochemical preference for formation of different 3-MCA 9,10-dihydrodiol–7,8-epoxides.     

Ab-initio electrostatic molecular potential contour maps for initiation step and Ab-Initio MRD-CI calculations for propagation step of cationic polymerization of oxetanes

The initiation step in the cationic polymerization of cyclic ethers is influenced by basicity and ring strain. We carried out ab-initio MODPOT/VRDDO/MERGE calculations on a variety of substituted oxetanes and generated electrostatic molecular potential contour (EMPC) maps in three-dimensions around the molecules. The size of the negative EMPC map region around the oxygen enabled us to predict the propensity to polymerize prior to the syntheses of the actual monomers themselves. We carried out ab-initio MODPOT/VRDDO/MERGE MRD-CI calculations for the propagation step of oxetane reacting with protonated oxetanes to cause ring opening of protonated oxetane. Similar MRD-CI calculations on variously substituted oxetanes will shed insight into relative copolymerization preferences.     

Minimal basis study of inner-shell ionization potentials for molecules containing sulfur: S,S-Diphenyl-N-p-Tolylsulfonyl-Sulfilimine

Ab initio calculations with a minimal (STO -3G) basis set on a number of sulfur-containing molecules are used to show that Koopmans' theorem and minimal basis calculations may be a simple but adequate way of obtaining inner-shell ionization potentials and chemical shifts of large molecules. The x-ray photoelectron spectrum of (C₆H₅)₂SNSO₂C₆H₄CH₃ is discussed with reference to an ab initio SCF minimal basis calculation on the model molecule H₂SNSO₂H.     

An investigation of the relative stabilities of the isomers of CF2N2: Comparison of ab initio and MNDO calculations

Ab initio SCF calculations at the HF/3-21G level and semi-empirical MNDO calculations have been used to locate the stationary points on the CF₂N₂ energy surface. Perfluorodiazomethane is predicted to be most stable isomer, but perfluorodiazirine is predicted to lie only ca 41 kJ higher in energy at the SCF level. There are significant differences between the ab initio and MNDO results for the ordering of some of the isomers. Frequency calculations give results in good agreement with the limited experimental data on these molecules.     

Bond–antibond analysis of internal rotation barriers in glyoxal and related molecules: Where INDO fails

Ab initio and INDO LCBO–MO calculations are carried out on glyoxal, 1,3-butadiene, and acrolein in order to analyze the qualitative failure of INDO -like methods to describe conformation energies in these molecules. Following the method of Brunck and Weinhold for ethanelike systems we identify the principal bond–antibond interactions contributing to the glyoxal barrier, their dependence on dihedral angle and substituent, and their relative magnitudes as calculated by ab initio and INDO SCF–MO theory. We find a gross disparity in the INDO representation of π* interactions which leads to a grossly exaggerated estimate of the stability of gauche conformers in these molecules. These findings appear to have serious implications for the applicability of INDO -like theories to conformational problems in π-bonded molecules, including those of biological interest.     

Ab initio studies on vibrational spectra of XSO2NCO (X = F,Cl): harmonic force fields and frequency assignments

The harmonic vibrational force fields and the IR spectrum of XSO₂NCO (X= F, C1) molecules have been studied usingab initio HF/SCF method with the 6-31G’ basis set. Theab initio harmonic force fields are scaled empirically using the scaled quantum mechanical (SQM) method of Pulay. A set of scale factors are optimized by the least-squares fitting to the experimental frequencies of FSO₂NCO and then are transferred to CISO₂NCO to give ana priori prediction of its fundamental frequencies. The average deviations between the theoretical frequencies and the experimental values for FSO₂NCO and C1SO₂NCO are 3 and 5 cm^-1, respectively. The assignments of the fundamentals for these two molecules are also made atcording to the potential energy distributions and theab initio IR intensities Project supported by the National Natural Science Foundation of China (Grant No. 29673029)     

Comparison of minimization procedures for UHF wave functions

The Roothaan, McWeeny and Fletcher methods of minimizing the electronic energy in the SCF method are compared. The CN radical is used as an example using the abinitio UHF method. It is concluded that a combination of the Fletcher and Roothaan methods should be generally applicable and also highly efficient.     

Accuracy and limitations of the pseudopotential method

Molecular model potential calculations have been performed within the SCF approximation on nine di- and triatomic molecules from the first row of the periodic table. We compare the molecular constants with ab initio SCF values and with model potential results obtained by other authors. Our results are accurate to a few per cent. The three most significant approximations in molecular model potential theory are: 1) The molecular model potential is the sum of atomic model potentials; 2) The atomic model potential is energy-independent; 3) The electron interaction model operator is l/r ₁₂. We arrive at the following general conclusions concerning these approximations: 1) The first approximation does not hold for strongly ionic molecules and for some highly excited molecular states. 2) Approximations 2 and 3 cancel to a large extent in molecules as they do in atoms, except in the case where approximation 1 breaks down. 3) Although various model- and pseudo-potentials yield reasonable results for atoms, not all of them are suitable for molecular calculations.