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.     

Theoretical studies of molecular conformation. Derivation of an additive procedure for the computation of intramolecular interaction energies. Comparison withab initio SCF computations

An additive procedure (SIBFA) is developed for the rapid computation of conformational energy variations in very large molecules. The macromolecule is built out of constitutive molecular fragments and the intramolecular energy is computed as a sum of interaction energies between the fragments. The electrostatic and the polarization components are calculated using multicenter multipole expansions of theab initio SCF electron density of the fragments. The repulsion component is obtained as a sum of bond and lone pair interactions.Tests of the procedure on a series of model compounds containing ether oxygens and pyridine-like nitrogens are reported and compared with the results of correspondingab initio SCF calculations. The resulting methodology is compatible with the simultaneous computation of intermolecular interactions.     

Atomic forces for geometry‐dependent point multipole and Gaussian multipole models

In standard treatments of atomic multipole models, interaction energies, total molecular forces, and total molecular torques are given for multipolar interactions between rigid molecules. However, if the molecules are assumed to be flexible, two additional multipolar atomic forces arise because of (1) the transfer of torque between neighboring atoms and (2) the dependence of multipole moment on internal geometry (bond lengths, bond angles, etc.) for geometry‐dependent multipole models. In this study, atomic force expressions for geometry‐dependent multipoles are presented for use in simulations of flexible molecules. The atomic forces are derived by first proposing a new general expression for Wigner function derivatives . The force equations can be applied to electrostatic models based on atomic point multipoles or Gaussian multipole charge density. Hydrogen‐bonded dimers are used to test the intermolecular electrostatic energies and atomic forces calculated by geometry‐dependent multipoles fit to the ab initio electrostatic potential. The electrostatic energies and forces are compared with their reference ab initio values. It is shown that both static and geometry‐dependent multipole models are able to reproduce total molecular forces and torques with respect to ab initio, whereas geometry‐dependent multipoles are needed to reproduce ab initio atomic forces. The expressions for atomic force can be used in simulations of flexible molecules with atomic multipoles. In addition, the results presented in this work should lead to further development of next generation force fields composed of geometry‐dependent multipole models. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

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.     

Ab initio crystal structure predictions for flexible hydrogen‐bonded molecules. Part II. Accurate energy minimization

A method is described to perform ab initio energy minimization for crystals of flexible molecules. The intramolecular energies and forces are obtained directly from ab initio calculations, whereas the intermolecular contributions follow from a potential that had been parameterized earlier on highly accurate quantum‐chemical calculations. Glycol and glycerol were studied exhaustively as prototypes. Lists of hypothetical crystal structures were generated using an empirical force field, after which ab initio energy minimizations were performed for a few hundreds of these. The experimental crystal structures were found among the structures with lowest energy, provided that sufficiently large basis sets were used. Moreover, their crystal geometries were well reproduced. This approach enables a systematic comparison between the merits of force fields at various levels of sophistication. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 805–815, 2001     

A charge-conserving approximation method for ab initio calculations

A new method is presented for approximate ab initio calculations in quantum chemistry. It is called CCAM (charge conserving approximation method). The calculation method does not include the use of empirical parameters. We use Slater type orbitals as basis set, replacing STO's by STO-2G functions to evaluate three- and four-center integrals and making the STO-2G two-orbital charge distributions have the same total charge as STO. The results are presented for test calculations on five molecules. In view of these results, CCAM is better than ab initio calculations over STO-6G in the results on total energies, kinetic energies and occupied orbital energies. In atomic populations, dipole moments and unoccupied orbital energies, CCAM is also satisfactory. We estimate that CCAM would be as fast as ab initio calculations over STO-2G in evaluating molecular integrals.     

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.     

A CNDO/INDO molecular orbital formalism for the elements H to Br. applications

The CNDO/INDO molecular orbital formalism introduced in the preceding paper has been applied to a large number of atom combinations up to bromine under the inclusion of the first transition metal series. The results are compared with experimental data (geometries, ionization potentials, dipole moments) or with the results of sophisticatedab initio calculations (one electron energies, net charges, atomic populations). The semiempirical model reproduces for a wide range of molecules the experimental andab initio data with remarkable success.     

Atomic multipoles: Electrostatic potential fit,local reference axis systems,and conformational dependence

Currently, all standard force fields for biomolecular simulations use point charges to model intermolecular electrostatic interactions. This is a fast and simple approach but has deficiencies when the electrostatic potential (ESP) is compared to that from ab initio methods. Here, we show how atomic multipoles can be rigorously implemented into common biomolecular force fields. For this, a comprehensive set of local reference axis systems is introduced, which represents a universal solution for treating atom‐centered multipoles for all small organic molecules and proteins. Furthermore, we introduce a new method for fitting atomic multipole moments to the quantum mechanically derived ESP. This methods yields a 50–90% error reduction compared to both point charges fit to the ESP and multipoles directly calculated from the ab initio electron density. It is shown that it is necessary to directly fit the multipole moments of conformational ensembles to the ESP. Ignoring the conformational dependence or averaging over parameters from different conformations dramatically deteriorates the results obtained with atomic multipole moments, rendering multipoles worse than partial charges. © 2012 Wiley Periodicals, Inc.     

Ab-initio and approximately rigorous calculations on small,medium, and large systems

We have explored two areas of approximately rigorous calculations for computing nonempirical wave functions for heavy and/or large molecules orders of magnitude faster than with conventional ab-initio methods but with the same chemical accuracy. First, we have developed and used a series of programs (starting from our new fast sets of ab-initio Gaussian SCF and SCF -CI programs) incorporating ab-initio effective core model potentials (MOD -POT ) which allow one to treat only the valence electrons explicitly, plus a charge conserving integral prescreening, which cuts down significantly on the number of integrals that have to be calculated, stored, or processed for a large molecule. We have named this latter procedure VRDDO (variable retention of diatomic differential overlap). With these MODPOT and MODPOT /VRDDO methods we have explored a variety of small, medium, and large systems ranging from electron affinities of atoms through to molecules of biological interest and large boron hydrides. The results compared to ab-initio SCF or SCF /CI calcuations are very good, usually within 0.001 to 0.002 a.u. for orbital energies and gross atomic populations (GAPS ) and even better along potential energy curves. Secondly, we have explored the use of the MS -Xα method for less conventional molecules and properties than those for which it is customarily employed.     

Intermolecular and intramolecular interactions calculated with ab initio perturbative configuration interaction method using strongly localized orbitals

We have applied the ab initio formulation of the perturbative configuration interaction using localized orbitals (PCILO ) method up to third order to calculate intermolecular and intramolecular interaction energies going beyond the ab initio Hartree–Fock calculation. For the rotational barrier in ethane our results agree well with the experimental value and the cis- and even the trans-barriers in HOOH are at least qualitatively reproduced with the aid of the STO -3G basis set. In the case of the water dimer we obtain an equilibrium intermolecular distance and interaction energy which are confirmed by other calculations. We can further conclude from our studies that one has to include higher orders in the perturbation expansion as the system becomes more complicated. It is especially the last aspect which hinders the application of the ab initio PCILO to estimate the major part of the electron correlation energy for large molecules.     

“Spectroscopic” Calculations of CH Bond Dissociation Energies for Ethane, Propane, Butane, Isobutane, Pentane, Hexane, and Neopentane Using Fundamental Vibration Frequencies

The fundamental spectrum and the parameters of the potential function of a number of saturated hydrocarbon molecules are calculated in an anharmonic approximation. The calculation is performed by the variational technique using a minimal Morse-harmonic basis. The potential function is taken as the sum of the Morse function for CH bonds and the harmonic function for the skeletal and deformation vibrations. The initial approximation for the potential function is found by ab initio calculations in a 6-31G basis and refined by solving the inverse problem. The calculated CH bond dissociation energies depend significantly on the molecular structure and on the position of CH bonds in the molecule. These energies correlate well with the experimental cleavage energies of these bonds. The changes in the dipole moment of the molecule induced by vibrations were found by ab initio calculations in a 6-31G basis. The calculated IR transmission curves are in good agreement with the experimental curves.     

Conformational properties and homolytic bond cleavage of organic peroxides. I. An empirical approach based upon molecular mechanics and ab initio calculations

The conformational features of a large number of hydroperoxides ROOH and peroxides ROOR′, where R and R′ are alkyl groups of different and increasing size and phenyl rings, including ortho substituted derivatives, were obtained from molecular mechanics calculations by employing a standard package. For the molecules of small molecular size, comparison was carried out with the results of ab initio calculations. Heats of formation were also obtained from molecular mechanics for hydroperoxides and peroxides: The values are, in general, overestimated. For the molecules containing the CF₃ group, the calculated values are subject to large errors and heats of formation were obtained from ab initio total energies in the “atom equivalents” scheme. To estimate the homolytic dissociation energies of the different bonds in the peroxide molecules, heats of formation of R·, ·OR, and ·OOR radicals were employed and several of them had to be calculated. Different approaches were employed—molecular mechanics calculations, ab initio energies within the atom equivalent and isodesmic reaction schemes, and Benson's group additivity rule; values consistent within the different calculation methods were chosen for estimating dissociation energies. The bond dissociation energies indicate different trends in these molecules as a function of the nature of the R and R′ groups and the possible electronic effects operating in these molecules are discussed. © 1993 John Wiley & Sons, Inc.     

Compact contracted Gaussian-type basis sets for halogen atoms. Basis-set superposition effects on molecular properties

Compact, contracted Gaussian basis sets for halogen atoms are generated and tested in ab initio molecular calculations. These basis sets have similar structure to that of Huzinaga and co-workers' (HTS ) sets; however, they give both better atomic total energies and better properties of atomic valence orbitals. These sets, after splitting of valence orbitals and augmenting with polarization functions, provide molecular results that agree well with those given by extended calculations. Basis set superposition error (BSSE ) is calculated using the counterpoise method. BSSE has only slight influence on calculated equilibrium geometry, shape of potential curve, and electric properties (dipole and quadrupole moments) of molecules. However, atomization energies may be significantly changed by the BSSE .     

Base stacking in cytosine dimer. A comparison of correlated ab initio calculations with three empirical potential models and density functional theory calculations

Ab initio MP2/6-31G* interaction energies were calculated for more than 80 geometries of stacked cytosine dimer. Diffuse polarization functions were used to properly cover the dispersion energy. The results of ab initio calculations were compared with those obtained from three electrostatic empirical potential models, constructed as the sum of a Lennard-Jones potential (covering dispersion and repulsion contributions) and the electrostatic term. Point charges and point multipoles of the electrostatic term were also obtained at the MP2/6-31G* level of theory. The point charge MEP model (atomic charges derived from molecular electrostatic potential) satisfactorily reproduced the ab initio data. Addition of π-charges localized below and above the cytosine plane did not affect the calculated energies. The model employing the distributed multipole analysis gave worse agreement with the ab initio data than the MEP approach. The MP2 MEP charges were also derived using larger sets of atomic orbitals: cc-pVDZ, 6-311 + G(2d, p), and aug-cc-pVDZ. Differences between interaction energies calculated using these three sets of point charges and the MP2/6-31G* charges were smaller than 0.8 kcal/mol. The correlated ab initio calculations were also compared with the density functional theory (DFT) method. DFT calculations well reproduced the electrostatic part of interaction energy. They also covered some nonelectrostatic short-range effects which were not reproduced by the empirical potentials. The DFT method does not include the dispersion energy. This energy, approximated by an empirical term, was therefore added to the DFT interaction energy. The resulting interaction energy exhibited an artifact secondary minimum for a 3.9-4.0 vertical separation of bases. This defect is inherent in the DFT functionals, because it is not observed for the Hartree-Fock + dispersion interaction energy.© 1996 John Wiley & Sons, Inc.     

Mixed ab initio QM/MM modeling using frozen orbitals and tests with alanine dipeptide and tetrapeptide

Methodology is discussed for mixed ab initio quantum mechanics/molecular mechanics modeling of systems where the quantum mechanics (QM) and molecular mechanics (MM) regions are within the same molecule. The ab initio QM calculations are at the restricted Hartree–Fock level using the pseudospectral method of the Jaguar program while the MM part is treated with the OPLS force fields implemented in the IMPACT program. The interface between the QM and MM regions, in particular, is elaborated upon, as it is dealt with by “breaking” bonds at the boundaries and using Boys-localized orbitals found from model molecules in place of the bonds. These orbitals are kept frozen during QM calculations. Results from tests of the method to find relative conformational energies and geometries of alanine dipeptides and alanine tetrapeptides are presented along with comparisons to pure QM and pure MM calculations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1468–1494, 1999     

Pyrrolizidine alkaloids necine bases: Ab initio,semiempirical, and molecular mechanics approaches to molecular properties

The structural stabilities of endo and exo conformations of retronecine and heliotridine molecules were analyzed using different ab initio, semiempirical, and molecular mechanics methods. All electron and pseudopotential ab initio calculations at the Hartree-Fock level of theory with 6-31G* and CEP-31G* basis sets provided structures in excellent agreement with available experimental results obtained from X-ray crystal structure and ¹H-NMR (nuclear magnetic resonance) studies in D₂O solutions. The exo conformations showed a greater stability for both molecules. The most significant difference between the calculations was found in the ring planarity of heliotridine, whose distortion was associated with the interaction between the O(11)H group and the C(1)-C(2) double bond as well as with a hydrogen bond between O(11)H and N(4). The discrepancy between pseudopotential and all-electron optimized geometries was reduced after inclusion of the innermost electrons of C(1), C(2), and N(4) in the core potential calculation. The MNDO, AM1, and PM3 semiempirical results showed poor agreement with experimental data. The five-membered rings were observed to be planar for AM1 and MNDO calculations. The PM3 calculations for exo-retronecine showed a greater stability than the endo conformer, in agreement with ab initio results. A good agreement was observed between MM3 and ab initio geometries, with small differences probably due to hydrogen bonds. While exo-retronecine was calculated to be more stable than the endo conformer, the MM3 calculations suggested that endo-heliotridine was slightly more stable than the exo form. © 1996 by John Wiley & Sons, Inc.