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.     

Ab initio MRD–CI calculations on cubane (neutral,carbocation, carboanion) and dissociation of nitrocubanes based on localized orbitals

Ab initio MRD –CI calculations based on localized orbitals were carried out for cubane (neutral, carbocation, carboanion) both in our customary MODPOT basis set and in an all-electron 4–31G basis set. The calculated MRD –CI charge distributions on C1 (the skeletal atom from which the H^? or H⁺ was removed) (ab initio MODPOT neutral 4.221, carbocation 3.796, carboanion 4.282; all-electron 4–31G neutral 6.171, carbocation 5.717, carboanion 6.078) indicate that the + or - charge does not remain localized on C1 but redistributes itself. This has significant implications for preparative reactions of energetically substituted cubanes. The MRD –CI population analyses differ somewhat from the SCF population analyses, especially in the calculated total overlap populations. To investigate this effect on electrostatic molecular potential contour (EMPC ) maps generated from SCF or MRD –CI wave functions, we wrote additional routines to calculate EMPC maps from MRD –CI wave functions. The EMPC maps generated from SCF or MRD –CI wave functions are different if the molecule needs an MRD –CI multideterminant wave function to describe it adequately. The EMPC map is a one-electron property. One-electron properties are derived from the 1-matrix. The 1-matrix is different for SCF or MRD –CI wave functions. Thus, all the one-electron properties (EMPC maps, population analyses, bond deviation indices, etc.) are different when calculated from SCF or MRD –CI wave functions if MRD –CI wave functions are necessary to describe a system properly. We calculate these one-electron properties from the 1-matrix from the final natural orbitals. Our preliminary calculations for the dissociation pathway indicate it takes more energy to dissociate a bond in 1-nitrocubane than in octanitrocubane. Even in their ground electronic states at equilibrium geometry, both 1-nitrocubane and octanitrocubane require MRD –CI wave functions to describe them properly. The c² of the single determinant SCF wave function is only 0.8401 for 1-nitrocubane and 0.8300 for octanitrocubane. There are contributions from skeletal excitations as there are for cubane itself as well as excitations involving the nitrogroup. As the bond in nitrocubane is dissociated to 8.00 bohrs, the c² of the SCF contribution drops to only 0.4606 (1-nitrocubane) and 0.4445 (octanitrocubane). At this C₁? N₁ intermolecular distance, the largest excitations are in the C₁? N₁ bond: (C₁? N₁)² → (C₁? N₁*)², (C₁? N₁) → (C₁? N₁*). We also calculated the first electronically excited state for the dissociation pathway for selected points for both 1-nitrocubane and octanitrocubane.     

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.     

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.     

Cage strain in nitro-substituted 1,3,5,7-tetraazacubanes

Homodesmotic reactions were designed for the computation of strain energies (SE) for four nitro-substituted 1,3,5,7-tetraazacubane derivatives. Total energies of the optimized geometric structures at the DFT-B3LYP/6-31G* and DFT-B3LYP/6-311G** levels were used to derive the SE. The variation of SE with respect to the number of substituents is similar with both basis sets. The SE value is 237.32 kcal/mol at the B3LYP/6-311G** level for 2,4,6,8-tetranitro-1,3,5,7-tetraazacubane, which is unexpectedly much larger than that of its cubane analogue. The SE increases remarkably with more nitro groups being attached to the cage skeleton of tetraazacubane. The ‘bending’ of the bonds within the cubic skeleton attributes to the increase of strains as the attached number of nitro groups increases.     

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.     

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.     

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.     

Ab initio calculations, electronegativity equalisation and group electronegativity

A correspondence betweenab initio calculations, the principle of electronegativity equalisation and group electronegativity has been established within the framework of Mulliken population analysis. Using this we have calculated electronegativities of some 37 groups/atoms. These electronegativities show excellent linear correlation with¹ J _CC coupling constants in monosubstituted benzenes and Inamoto’si scale and a satisfactory one with Wells’ group electronegativity data. The correspondence however required a scaling of charge (obtained byab initio calculations) and a proportionality between the electronegativity of the neutral group and its hardness. It is shown that using these electronegativity values it is possible to calculate group charges in molecules where groups under consideration interact with each other through σ bond only.     

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.     

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.     

Bond polarization in the FeCO system: Semiempirical MO–SCF (BMV) calculations

Charge distributions in FeCO for different Fe–C distances and the Fe–C–O angle equal to 180° and 90° have been computed by the BMV method, a semiempirical SCF scheme including overlap and especially suited for transition-metal atoms. A comparison with available EHT and ab initio calculations suggests that the BMV method is a useful complement to ab initio calculations. The information obtained on the dependence of the binding in FeCO on the Fe–C distance is also briefly discussed in connection with the views of experimentalists of the state of CO absorbed on iron.     

Ab initio calculations on porphin

Ab initio SCF calculations are reported for the porphin molecule. The positions of the central protons have been optimized, and the equilibrium geometry is found to be a linear NH ? HN arrangement. The NH vibrational frequencies have been computed and are compared to experimentally measured quantities. Several low ionized states have also been studied in separate spin-restricted SCF calculations. The lowest state is found to have B_1u symmetry with an ionization potential of 8.0 eV.     

Toward similarity measures for macromolecular bodies: Medla test calculations for substituted benzene systems

A new method is proposed for the evaluation of numerical similarity measures for large molecules, defined in terms of their electron density (ED) distributions. The technique is based on the Molecular Electron Density Lego Assembler (MEDLA) approach, proposed earlier for the generation of ab initio quality electron densities for proteins and other macromolecules. The reliability of the approach is tested using a family of 13 substituted aromatic systems for which both standard ab initio electron density computations and the MEDLA technique are applicable. These tests also provide additional examples for evaluating the accuracy of the MEDLA technique. Electron densities for a series of 13 substituted benzenes were calculated using the standard ab initio method with STO-3G, 3-21G, and 6-31G** basis sets as well as the MEDLA approach with a 6-31G** database of electron density fragments. For each type of calculation, pairwise similarity measures of these compounds were calculated using a point-by-point numerical comparison of the EDs. From these results, 2D similarity maps were constructed, serving as an aid for quick visual comparisons for the entire molecular family. The MEDLA approach is shown to give virtually equivalent numerical similarity measures and similarity maps as the standard ab initio method using a 6-31G** basis set. By contrast, significant differences are found between the standard ab initio 6-31G** results and the standard ab initio results obtained with smaller STO-3G and 3-21G basis sets. These tests indicate that the MEDLA-based similarity measures faithfully mimic the actual, standard ab initio 6-31G** similarity measures, suggesting the MEDLA method as a reliable technique to assess the shape similarities of proteins and other macromolecules. The speed of the MEDLA computations allows rapid, pairwise comparisons of the actual EDs for a series of molecules, requiring no more computer time than other simplified, less detailed representations of molecular shape. The MEDLA method also reduces the need to store large volumes of numerical density data on disk, as these densities can be quickly recomputed when needed. For these reasons, the proposed MEDLA similarity analysis technique is likely to become a useful tool in computational drug design. © 1995 John Wiley & Sons, Inc.     

A comparison of the results of PCILO andab initio SCF calculations for the molecules glycine,cysteine and N-acetyl-glycine

Conformational energy maps for glycine, cysteine and N-acetyl-glycine obtained using PCILO andab initio SCF calculations are compared.     

Cubic-grid Gaussian basis sets for electron scattering calculations. I. Definition and construction

We propose a new type of Gaussian basis sets for use in calculations of electron scattering by molecules. Instead of locating the basis-set functions on the atomic centers of the target molecule, we place primitive s-type Gaussians at the positions of a cubic lattice with a regular grid. The grid and the Gaussian exponent are fixed so as to give the best representation of the plane-wave function. Plane-wave functions and Green functions obtained by means of the cubic-grid basis set are tested graphically against exact functions and functions expressed by means of a conventional Gaussian basis set. © 1995 John Wiley & Sons, Inc.     

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.     

Theoretical Study of the Mechanism of the Nitro-Nitrite Rearrangement and Its Role in Gas-Phase Monomolecular Decomposition of C-Nitro Compounds

Semiempirical, ab initio, and density functional theory calculations were used to study the primary act of gas-phase monomolecular decomposition of certain C-nitro compounds and their radical cations, associated with the nitro-nitrile rearrangement. It was shown that the reaction fails to occur with all neutral molecules of aliphatic nitro compounds (except for fluoronitromethane and fluoronitroethene) and has a much lower barrier with the corresponding radical cations. An important role of the nitro-nitrile rearrangement in gas-phase decomposition of aromatic nitro compounds was demonstrated.     

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.     

Accurate molecular electrostatic potentials based on modified PRDDO/M wave functions. I. Electrostatic potential derived atomic charges

A new approach for the calculation of electrostatic potential derived atomic charges is presented. Based on molecular orbital calculations in the PRDDO/M approximation, the new parametrized electrostatic potential (PESP) method is parametrized against ab initio MP2/6-31G** calculations. For a data set of 820 atoms in 145 molecules containing H, C, N. O, F, P, S, Cl, and Br (including hypervalent species), the PESP method achieves a mean absolute error of 0.037 e⁻ with a correlation coefficient of 0.990. Unlike other approximate approaches, no scaling factor is required to improve the agreement between PESP charges and the underlying ab initio results. PESP calculations are an order of magnitude faster than the simplest ab initio calculation (STO-3G) on large molecules while achieving a level of accuracy that rivals much more elaborate ab initio methods. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 955–969, 1997