Big data analysis of ab Initio molecular integrals in the neglect of diatomic differential overlap approximation

Most modern semiempirical quantum-chemical (SQC) methods are based on the neglect of diatomic differential overlap (NDDO) approximation to ab initio molecular integrals. Here, we check the validity of this approximation by computing all relevant integrals for 32 typical organic molecules using Gaussian-type orbitals and various basis sets (from valence-only minimal to all-electron triple-ζ basis sets) covering in total more than 15.6 million one-electron (1-e) and 10.3 billion two-electron (2-e) integrals. The integrals are calculated in the nonorthogonal atomic basis and then transformed by symmetric orthogonalization to the Löwdin basis. In the case of the 1-e integrals, we find strong orthogonalization effects that need to be included in SQC models, for example, by strategies such as those adopted in the available OMx methods. For the valence-only minimal basis, we confirm that the 2-e Coulomb integrals in the Löwdin basis are quantitatively close to their counterparts in the atomic basis and that the 2-e exchange integrals can be safely neglected in line with the NDDO approximation. For larger all-electron basis sets, there are strong multishell orthogonalization effects that lead to more irregular patterns in the transformed 2-e integrals and thus cast doubt on the validity of the NDDO approximation for extended basis sets. Focusing on the valence-only minimal basis, we find that some of the NDDO-neglected integrals are reduced but remain sizable after the transformation to the Löwdin basis; this is true for the two-center 2-e hybrid integrals, the three-center 1-e nuclear attraction integrals, and the corresponding three-center 2-e hybrid integrals. We consider a scheme with a valence-only minimal basis that includes such terms as a possible strategy to go beyond the NDDO integral approximation in attempts to improve SQC methods. © 2018 Wiley Periodicals, Inc.     

A re-examination of the justification of neglect of differential overlap approximations in terms of a power series expansion inS

Neglect of differential overlap methods are treated as approximations to calculations in a symmetrically orthogonalized basis. The accuracy of this approximation is investigated in terms of a power series expansion of the overlap matrix. TheS-matrix can be transformed into a matrix which will give a convergent series, and this series is used in the examination. The only approximation having any justification from this point of view is the NDDO method and even this neglects certain important three-electron integrals. Corrected expressions for the repulsion integral scaling factors introduced by Chandrasekharet al. are also derived. On leave from The Chemistry School, University of Western Australia.     

DFT and ab initio quantum chemical studies on p-cyanobenzoic acid

The Fourier transform infrared (FTIR) and FT-Raman spectra of p-cyanobenzoic acid (CBA) have been recorded in the range 4000-400 and 4000-100 cm(-1), respectively. The complete vibrational assignment and analysis of the fundamental modes of the compound were carried out using the observed FTIR and FT-Raman data. The vibrational frequencies determined experimentally were compared with theoretical wavenumbers obtained from ab initio HF and DFT-B3LYP gradient calculations employing 6-31G**, 6-311++G** and cc-pVTZ basis sets for the optimised geometry of the compound. The geometry and normal modes of vibration obtained from the HF and DFT methods are in good agreement with the experimental data. The normal coordinate analysis was also carried out with ab initio force fields utilising Wilson's FG matrix method. The interactions of cyano and carboxylic acid groups with the skeletal vibrational modes were investigated.     

Problems and prospects in the ab initio treatment of pure and defective crystals

Accurate Hartree-Fock LCAO calculations for moderately complex crystalline systems are now feasible; a number of important applications may be envisaged in the areas of material science and technology. Some critical aspects of the corresponding computer schemes are discussed which are of fundamental importance in determining the cost of the computation. Data are provided concerning actual computations which are indicative of the kind of periodic systems that can (or cannot) be treated at present. The result of a perfect-crystal ab initio HF study can be used as an input for treating with the same approximation local-defect problems, by use of suitable embedding techniques. A scheme of this kind is presented, and its computational implications are discussed: due to the intrinsic complexity of this problem, it may be foreseen that the study of defects in crystals will be a typical application of supercomputers in the area of quantum chemistry.This paper was presented at the International Conference on The Impact of Supercomputers on Chemistry, held at the University of London, London, UK, 13–16 April 1987     

A comparative ab initio study of ethylene,acetylene and benzene

Ground state properties have been calculated by use of a medium-sized Gaussian basis set and comparison with other bases has been made. Contraction to double-zeta of a comparatively small basis is found to be superior to a large set of primitive Gaussians contracted to minimal basis. Molecular optimization is not important for double-zeta bases. Inclusion of a balanced set of polarization functions is essential in all cases studied. Population analysis gives a certain insight in molecular properties but contour maps are found to be significantly superior. This is demonstrated on bonding properties of corresponding orbitals within the series. In case of benzene Slater's energyband plot is shown to be useful for classifying bonding properties.     

Ab initio program for treatment of related molecules. I. Integral part

Anab initio integral program is described. It utilizes the local symmetries to avoid the redundant computation of integrals over spatially equivalent subsets of the basis. The integrals are grouped in a particular way to facilitate their transfer. The program is very suitable for the treatment of related systems with model geometries. The computing times of different programs are compared and the efficiency of the presented one is demonstrated.     

Desolvation effects on the dissociation energy of diatomic molecules:Ab initio study of the dissociation of Li-F in polar media

Summary The potential curve of the ground state dissociation of Li-F in water has been studied by a combination of a standardab initio Hartree-Fock procedure and a perturbative reaction field approach. The electrostatic solute-solvent interaction is accounted for by the generalized Born formalism introduced through a perturbation approach. The calculations were carried out at a 6–311+G* basis set level. Diffuse functions ofs symmetry were included to model a desolvation potential. A double well potential curve was obtained for the dissociation of this molecule in the presence of a highly polarizable medium. The first minimum, corresponding to an ion pair, electrostatically bound, is found at aR(Li-F)<6.0 Å distance. As the two ions come together, a desolvation barrier of about 30 kcal/mol is to be overcome before the formation of the neutral Li-F at 1.56 Å. The barrier to ionization towards the ion pair is calculated to be about 14 kcal/mol. The dissociation of the ion pair towards the free ions is discussed in terms of the electrostatic solvation entropy changes.Contribution No 6 from Centro de Mecánica Cuantica Aplicada (CMCA)     

Multipole expansion of diatomic overlap

A systematic extension of Ruedenberg's expansion formula is applied to evaluate two-electron integrals occurring in calculations on molecular structure. Minimum STO basis sets are used for all SCF-calculations within the framework of the MEDO-method (Multipole Expansion of Diatomic Overlap). The errors due to this approximation scheme are almost negligible compared to those introduced by the truncated basis set: LiH, Li₂ and N₂ are chosen as examples.     

Ab initio calculations on large molecules using molecular fragments. Characterization of the zwitterion of glycine

The ab initio molecular fragment approach is applied to a characterization study of the ground state of the zwitterion of glycine. Included among the properties studied are the — conformational energy surface, the electronic structure, and the magnitude and direction of the dipole moment. The results of the present study are compared to the results of other theoretical and experimental studies.This work was supported in part by the National Science Foundation, the University of Kansas, and the Upjohn Company, Kalamazoo, Michigan 49001.NSF Trainee (1969-1972).Alfred P. Sloan Research Fellow (1971–1973).     

An ab initio CI study of the ground and excited states of p-quinodimethane

Configuration interaction (CI) studies of the ground, electronically excited singlet and triplet states and of the ionized states (cations) are reported for p- quinodimethane (p-xylylene). The calculated ionization potentials are compared with the experimental photoelectron spectrum for the low-energy ionization region. The two high-energy low-intensity flanks of the second and third band observed in the photoelectron spectrum are assigned to be due to the two non-Koopmans' cation states, ascribing to shake-up ionizations.The calculated singlet-singlet and singlet-triplet excitation energies are compared with previous semiempirical MO results and experimental data.     

Note on the ab initio PUHF treatment of open-shell systems

Ab initio projected-unrestricted Hartree-Fock calculations have been carried out on a number of excited and ionic states of the water molecule. Results have been compared with large-scale CI calculations, with IVO calculations, and with those of Mrozek and Golebiewski obtained by the 2 × 2 rotation method applied to orbitals. It is concluded that the PUHF method may provide the most useful alternative to large-scale CI for calculating properties of open-shell systems. But it will not be generally useful for calculating spectral transition energies.     

The structures of HCOO−, CH3COO−, C2H5COO− and CH3O− in gas phase and in crystal structure by ab initio and resonance theory

The purpose of this report is to quantitatively find the cause for the elongation of the R-C bond in R-COO^– (R = H, CH₃ and C₂H₅) and the shortening of the C-O bond in CH₃-O^– upon deprotonation in the gas phase. These elongations and shortenings result from the contributions of R^–---CO₂ and H^–---CH₂=O as resonance structures to the systems. Because these structures must make only a small contribution in the crystal, the R-C bond lengths of R-COO^– (R= H and CH₃) in the crystal structure are shorter than those in the gas phase.     

Ab initio molecular orbital calculations of the infrared spectra of hydrogen-bonded complexes of water,ammonia and hydroxylamine

Summary The geometries of three hydrogen-bonded dimers of hydroxylamine have been optimized, at the MP2 level of theory, using the 6-31G** basis set. These calculations yielded three separate local minima on the dimer potential energy surface. The interaction energies of these three species have been calculated, and corrected for basis set superposition error. The infrared band wavenumbers and intensities have been computed, and the monomer-dimer wavenumber shifts and intensity enhancements rationalized in terms of the types and strengths of hydrogen bonds present. The predicted wavenumbers have been correlated with those measured in a recent matrix isolation spectroscopic study, and an argument for the structure of the preferred dimer has been presented.     

Ab initio calculation of the band structure of some boron polymers

Ab initio calculations using a STO-3G basis set have been performed on the polymer systems (HBX) _n where X = Be, BH, CH₂, NH, and O. Energy band diagrams and accompanying density-of-states plots have been obtained. The highest filled orbital of (HBNH) _n and (HBO) _n occurs at the X-point and possesses character while the - framework orbital at the X- point is the highest filled level for (HBBe) _n , (HBBH) _n , and (HBCH₂) _n . The conduction band for all five species has symmetry and the band gap of the (HBX) _n species increases in the order X = Be < BH < NH < O < CH₂. An estimate of the energy of polymerisation of the (HBX) _n systems suggests that HBNH is particularly stabilised by polymerisation. The electron distribution in (HBBe) _n shows a - electron drift towards boron, while in the other four systems the net electron transfer is directed away from boron. There is significant electron back-donation to boron in (HBO) _n and (HBNH) _n .     

FTIR and FT-Raman spectra, assignments, ab initio HF and DFT analysis of xanthine

The molecular vibrations of xanthine were investigated in polycrystalline sample, at room temperature by Fourier transform infrared (FTIR) and FT-Raman spectroscopies. The spectra of the molecule have been recorded in the regions 4000-50 cm(-1) and 3500-100 cm(-1), respectively. Theoretical information on the optimized geometry, harmonic vibrational frequencies, infrared and Raman intensities were obtained by means of ab initio Hartree-Fock (HF) and density functional theory (DFT) gradient calculations with complete relaxation in the potential energy surface using 6-311++G(d,p) basis set. The vibrational frequencies which were determined experimentally from the spectral data are compared with those obtained theoretically from ab initio and DFT calculations. A close agreement was achieved between the observed and calculated frequencies by refinement of the scale factors. The infrared and Raman spectra were also predicted from the calculated intensities. Thermodynamic properties like entropy, heat capacity, zero point energy have been calculated for the molecule. Unambiguous vibrational assignment of all the fundamentals was made using the potential energy distribution (PED).     

An efficient ab initio gradient program

An ab initio Hartree-Fock gradient program is described. It is characterized by (1) efficiency of the gradient evaluation, and (2) capability of handling higher angular momentum (d andf) basis functions. The latter are constructed from shifted Cartesian Gaussian p-type primitives. A satisfactory solution is presented for the problems connected with the neglect of small integrals in a gradient program. Methods for increasing the efficiency of the SCF procedure are discussed.     

Hydration of the carboxylate group: Anab initio molecular orbital study of acetate-water complexes

The hydration of the carboxylate group in the acetate anion has been investigated by performingab initio molecular orbital calculations on selected conformers of complexes with the form CH₃CO₂ ^– ·nH₂O·mH₂O, wheren andm denote the number of water molecules in the first and second hydration spheres around the carboxylate group, andn + m 7. The results of RHF/6–31G^* optimizations for all the complexes and MP2/6–31+G^** optimizations for several one-water complexes are reported. The primary consequence of hydration on the structure of the acetate anion is a decrease in the length of the C-C bond. Enthalpy and free energy changes calculated at the MP2/6–31+G^** and MP2/6–311+ +G^** levels are reported for the reactions CH₃CO₂ ^– + [H₂O] _P CH₃CO₂ ^– ·nH₂O ·mH₂O where [H₂O] _P is a water cluster containingp water molecules andp=n+m 7. The calculations show that conformers with the lowest enthalpy change on complex formation are often not those with the lowest free energy change, due to a greater entropic loss in complexes with tighter and more favorable enthalpic interactions. Hydrogen bonding of six water molecules directly to the carboxylate group in CH₃CO₂ ^– is found to account for approximately 40% of the enthalpy change and 37% of the free energy change associated with bulk solvation.     

Structure and vibrational modes of AgI-doped AsSe glasses: Raman scattering and ab initio calculations

We report an investigation of the structure and vibrational modes of (AgI)_x (AsSe)_100−x, bulk glasses using Raman spectroscopy and first principles calculations. The short- and medium-range structural order of the glasses was elucidated by analyzing the reduced Raman spectra, recorded at off-resonance conditions. Three distinct local environments were revealed for the AsSe glass including stoichiometric-like and As-rich network sub-structures, and cage-like molecules (As₄Se_n, n=3, 4) decoupled from the network. To facilitate the interpretation of the Raman spectra ab initio calculations are employed to study the geometric and vibrational properties of As₄Se_n molecular units that are parts of the glass structure. The incorporation of AgI causes appreciable structural changes into the glass structure. AgI is responsible for the population reduction of molecular units and for the degradation of the As-rich network-like sub-structure via the introduction of As-I terminal bonds. Ab initio calculations of mixed chalcohalide pyramids AsSe_mI_3−m provided useful information augmenting the interpretation of the Raman spectra.     

Multipole expansion of diatomic overlap

The systematic extension of Ruedenberg's expansion formula proposed in Part I [1] is applied to a series of diatomic and polyatomic molecules (BH, NH, HF, Be₂, C₂, F₂, CO, BH₃, CH₄, NH₃, H₂O, HCN and H₂CO). In general, good agreement with the results of full SCF calculations with the same minimum STO basis set is achieved. Thus, the errors due to this integral approximation scheme called MEDO (Multipole Expansion of Diatomic Overlap) are almost negligible compared to those introduced by basis set truncation.     

An ab initio study of O2 and CO2 transport by perfluorocarbons

Fluorocarbons have been successfully applied as oxygen carriers replacing blood. In order to understand the nature of the interaction between fluorocarbons and hydrocarbons on the one hand and O₂, N₂ and CO₂ on the other, STO-3G calculations have been performed on their complexes. The very slight energies of interaction that were obtained seem to substantiate the contention that O₂, N₂ and CO₂ are physically dissolved in fluorocarbons. This energy of interaction is, however, distinctly larger for fluorocarbons than for hydrocarbons. Electrostatic potentials have been computed around several fluorocarbons. They make it possible to predict the geometries of the complexes that are formed.