Quantum similarity measures under atomic shell approximation: First order density fitting using elementary Jacobi rotations

The elementary Jacobi rotations technique is proposed as a useful tool to obtain fitted electronic density functions expressed as linear combinations of atomic spherical shells, with the additional constraint that all coefficients are kept positive. Moreover, a Newton algorithm has been implemented to optimize atomic shell exponents, minimizing the quadratic error integral function between ab initio and fitted electronic density functions. Although the procedure is completely general, as an application example both techniques have been used to compute a 1S-type Gaussian basis for atoms H through Kr, fitted from a 3-21G basis set. Subsequently, molecular electronic densities are modeled in a promolecular approximation, as a simple sum of parameterized atomic contributions. This simple molecular approximation has been employed to show, in practice, its usefulness to some computational examples in the field of molecular quantum similarity measures. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2023–2039, 1997     

The surface charge density/surface potential relationship and the Poisson-Boltzmann equation

A procedure is described which provides an approximate analytic expression for the relationship between the surface charge density and the surface potential of a spherical or cylindrical colloidal particle in a general type of electrolyte. The first approximation is found and the approximation error is given. Also derived are the fourth approximation for a symmetric z-z type electrolyte and the second approximation for a symmetric z-z, 2z-2z type electrolyte.     

Systematicab initio calculations on one- and three-dimensional polyethylene

The electronic structure of polyethylene has been re-examined using Gaussian basis sets in anab initio solid-state method. Previous calculations were shown to possess a minor error in unit-cell coordinates and were corrected. Six basis sets were used and the results compared within the nearest-neighbour approximation. The effect on the calculation of increasing the number of interacting unit cells to five was studied. The latter produces no significant change in the C-H polarity; the overall conduction band width remains essentially the same but the Koopmans' ionization potential is displaced more towards the experimental value. An investigation was made into the effects of neighbouring strands on a central filament. We find that the Point Charge Perturbation model is a useful one in this context and yields a realistic interstrand distance. This is dominated by the hydrogen atoms. It is essentially unaffected by extension of the perturbing field to second neighbour strands.     

X-ray spectra and electronic energy structure of carboaluminides Ti-Al-C

The electronic energy structure, TiL_2,3 X-ray emission, and TiL2j XANES spectra of diamond and titanium carboaluminides Ti-Al-C are calculated by the local coherent potential method in terms of multiple scattering theory. The cluster version of the MT approximation is used to calculate the crystal potential. The electronic energy structures of diamond and the ternary and binary titanium carbide systems are compared in a single approximation. The broadening of the hybridized band in Ti-Al-C is discussed and compared with the experimental CK_α emission spectra. The specifics of chemical binding in the compounds is explained by delocalization of the carbon sp³ configuration and formation of a metal bond in carboaluminides. Translated fromZhurnal Strukturnoi Khimii, Vol. 41, No. 3, pp. 505-514, May–June, 2000.     

X-Ray Spectra and Electronic Structure of 3C SiC and BN Based Solid Solutions

The local coherent potential approximation is used in the framework of multiple-scattering theory to calculate the electronic energy structure of solid solutions of silicon carbide Si_1-xCR_x and boron nitride BN_1-xR_x and B_1-xNR_x (x = 0-0.75, R = C, Al, Ti) in a diamond-like modification. The total and partial densities of states are calculated for each atom in the solid solutions. The crystal potential is evaluated in an MT approximation. The lattice parameter is determined by Vegard's rule. The electronic energy structures of the solid solutions are compared with each other and with binary analogs in the framework of one approximation. The calculated partial densities of states are compared with the experimental X-ray spectra of silicon in the compounds. The calculation of the partial charges of atoms at the top of the valence band showed that the charge transfer (0.35 e) from boron to nitrogen in binary 3C BN changes sign in B_0.75NC_0.25. In the latter system, nitrogen donates 0.19 e to boron, and carbon acts as a donor for the electronic configurations of boron and nitrogen. An electronic structure analysis of the solid solutions indicates that the quasicore resonance states inherent in the binary compounds are delocalized, probably because of the weakening of chemical binding in the solid solutions.     

X-Ray Photoelectron Spectra and Electronic Structure of Solid Solutions Based on Cubic Boron Nitride

The electronic energy structure of substitution solid solutions based on boron nitride B _1-x NR _x and BN _1-x R_x (R = C, O) (x=0.25) in a diamond-like modification of ZnS type has been investigated by the local coherent potential method in terms of multiple-scattering theory. The total and partial densities of states were calculated for each element in a solid solution. The crystalline potential was calculated using an MT approximation. The lattice parameter was chosen based on X-ray diffraction data for c-BN: 0.3615 nm. The electronic energy structures of the solid solutions and binary c-BN are compared in the framework of a single approximation. The calculated partial densities of states are compared with the experimental X-ray emission and photoelectron spectra of boron, nitrogen, and oxygen in these compounds. The calculated partial charges of electrons at the top of the valence band show that charge transfer from boron to nitrogen takes place in the solid solutions. An analysis of the electronic structures of the solid solutions of boron nitride indicates that the quasicore resonances inherent in binary c-BN are delocalized and that chemical bonding in the solid solutions of boron nitride is weakened.     

Functional derivative δE/δρ in calculation of chemical potential for the Kohn–Sham electronic system

A method for finding the chemical potential for an electronic system with density ρ = Σ_ρi represented within the Kohn–Sham approximation is proposed. To find the chemical potential of the system under consideration, we propose to refer to the definition μ = δE/δ_ρ and to apply the mathematical properties of functional derivatives. Particularly, in the case examined, the result μ = μ( r ) ≠ const has been obtained, which may be explained in the framework of the calculus of variation. Taking the limit lim_r→∞ μ( r ) as the best approximation to the proper equilibrium chemical potential of a free atom, one obtains μ = ?I, where I denotes first ionization energy. A possibility of further applications of the proposed method in relation to crystalline systems is also discussed. © 1994 John Wiley & Sons, Inc.     

New method for approximate Hartree-Fock calculations using density approximations and coulomb field corrections. II

The HF approximation method that was outlined in Paper I is tested with respect to several molecular properties. Three different levels of approximation a, b, and c are considered. Satisfactory results—compared to corresponding “exact” HF calculations—are obtained with the STO -3G basis and the approximation level a. At this level the error in the binding energy is 0.001–0.025 a.u. for all considered molecules which contain up to six first-row atoms as, e.g., cyclopentanone (C₅OH₈). The error in the reaction energies considered here is about 4 kcal/mol (the maximal error is 9 kcal/mol). Orbital energies, dipole moments, gross charges, equilibrium geometries, and barriers to internal rotation are well reproduced by the approximation method at all three levels.     

Simplified accurate approximation for the Kohn-Sham potential using the KLI method

The method of Krieger, Li, and Iafrate (KLI) [Phys. Rev. A46, 5453 (1992) and A47, 165 (1993)] is employed to calculate the Kohn-Sham (KS) potential, V_κσ, for the exchange-only case in which the electron-electron interaction between “core” electrons in the Hartree-Fock exchange energy functional is treated in the local-spin-density (LSD) approximation with and without self-interaction-correction (SIC). The resulting V_κσ(r) maintains the important analytic properties exhibited by the exact KS potential. When the core is taken to include all occupied states except those in the last two occupied subshells of the atom, we find that properties strongly dependent on the valence electron states continue to be accurately approximated. In particular, when the LSDSIC approximation is employed, we find the results of self-consistent calculations of the ionization potential and electron affinity are within 0.3 mRy of the exact KS results and that the energy eigenvalue corresponding to the highest energy occupied orbital and <r²> have an average error of a few tenths of 1% for both atoms and negative ions for Z ≤ 20. Similarly, slightly less accurate results are obtained when the LSD approximation is employed. These results suggest that the KLI method may be accurately and more easily applied to multiatom systems when this additional approximation is made. © 1997 John Wiley & Sons, Inc.     

How good is good agreement: Evaluating the reliability of quantum-mechanically calculated observables

The practical value of a wave function derives from its ability to estimate or predict the chemical and physical properties of the electronic structure which it describes. Reliability is defined as a property to be evaluated on the basis of (i) the magnitude of the difference between the measured and calculated values of the observable together with (ii) the sign of the difference, (ii) the number and nature of observables correctly estimated, and (iv) the number and type of electronic structures that are correctly estimated. Systematic statistical comparison implies the existence of both internally consistent sets of wave functions for homologous series of molecules and their corresponding experimental values together with reliable error estimates. The most complete data base currently available for comparison is the spectroscopic constants for the first and second row diatomic hydrides. Utilizing appropriate statistical comparison techniques, four approximations (CEPA , PNO -CI , GTO -SCF , and STO -SCF ) are compared among themselves and against experimentally measured values. The CEPA approximation yields differences from experiment that approximate a normal error distribution, while the other approximations show systematic departures from experiment. Two values, ω_e and ω_eχ_e, for SH exhibit differences large enough to cast doubt upon the calculated value, the experimental value, or both.     

Multiconfiguration Pair-Density Functional Theory for Transition Metal Silicide Bond Dissociation Energies,Bond Lengths,and State Orderings

Transition metal silicides are promising materials for improved electronic devices, and this motivates achieving a better understanding of transition metal bonds to silicon. Here we model the ground and excited state bond dissociations of VSi, NbSi, and TaSi using a complete active space (CAS) wave function and a separated-pair (SP) wave function combined with two post-self-consistent field techniques: complete active space with perturbation theory at second order and multiconfiguration pair-density functional theory. The SP approximation is a multiconfiguration self-consistent field method with a selection of configurations based on generalized valence bond theory without the perfect pairing approximation. For both CAS and SP, the active-space composition corresponds to the nominal correlated-participating-orbital scheme. The ground state and low-lying excited states are explored to predict the state ordering for each molecule, and potential energy curves are calculated for the ground state to compare to experiment. The experimental bond dissociation energies of the three diatomic molecules are predicted with eight on-top pair-density functionals with a typical error of 0.2 eV for a CAS wave function and a typical error of 0.3 eV for the SP approximation. We also provide a survey of the accuracy achieved by the SP and extended separated-pair approximations for a broader set of 25 transition metal–ligand bond dissociation energies.     

Quantum-mechanical exploration of the properties of the sugar rings

Theab initio SCF method is used for computing the main electronic properties of the ribose unit of the nucleic acids. The present study is devoted to the ribose in the C₃-endo,gg conformation. The properties investigated include the distribution of the electronic charges, the electrostatic molecular potential around the four oxygens of the unit, the hydration and the Na⁺ binding schemes studied in the supermolecule approximation. The possibilities of through-water binding of the cation to the sugar are also explored. The predictions of the computation in particular with regard to cation binding to the ribose ring are correlated with recent experimental results.     

The fundamental syntopy of quasi-symmetric systems: Geometric criteria and the underlying syntopy of a nuclear configuration space

Point symmetry is a discrete concept; A nuclear configuration for a given stoichiometry either has or has not a particular point symmetry. By contrast, both static and dynamic properties of actual molecules exhibit continuous features. Using the formalism of fuzzy-set theory, we had previously proposed the concept of syntopy as a continuous extension of the symmetry concept for quasi-symmetric systems: This was based on an energetic criterion taking into account the energy costs of nuclear rearrangements. This extension of symmetry was necessarily dependent on the considered electronic state: For a given geometric arrangement of the nuclei, the energy cost of some rearrangement is dependent on the actual potential surface, that is, on the electronic state, in the Born–Oppenheimer approximation. In the extension of the syntopy model reported in the present work, we consider a syntopy criterion that is common to all electronic states. The syntopy thus defined—called the fundamental syntopy of the reduced nuclear configuration space—is independent of the potential surface and of the electronic state: It is defined only in terms of a geometric condition, which makes it more appropriate to rationalize mesoscopic structures. This new syntopy model provides a connection between all possible syntopies generated by the various potential-energy surfaces supported by the considered family of atomic nuclei. © 1993 John Wiley & Sons, Inc.     

SC Cellular multiple scattering in molecular electronic structure calculations

Recent advances in the statistical exchange approximation to the one-electron potential and in the use of general potentials in multiple scattering are studied numerically and combined in a cellular multiple scattering calculation of the electronic structure of molecules. The particular examples of these calculations are SF₆, H, and H₂, the results being compared with those of previous approximations and other techniques. It is first seen that the Xαβ approximation or a similar one based on the use of a universal parametrization of the statistical exchange (and some effects of correlation) part of the potential will provide the maximum of freedom in the partition of the real space of the molecules into cells. This avoids arbitrariness in the assumed value of the parameters to be used in every cell. The usefulness of the Xαβ approximation in a muffin-tin and in a cellular calculation is discussed. It is also found that the usual limitation to muffin-tin-like potentials, while simpler as a first approximation, can be removed without unduly increasing the computing effort. However, an accurate evaluation of the real self-consistent potential in each cell (or even in a muffin-tin) will increase the length of the program, the storage necessities and the computing time by a factor estimated to be between three and ten according to the geometry considered. It is concluded that the cellular multiple scattering method offers the best possibilities for a systematic use of multiple scattering techniques in molecular calculations.     

Adjustment of Born‐Oppenheimer electronic wave functions to simplify close coupling calculations

Technical problems connected with use of the Born‐Oppenheimer clamped‐nuclei approximation to generate electronic wave functions, potential energy surfaces (PES), and associated properties are discussed. A computational procedure for adjusting the phases of the wave functions, as well as their order when potential crossings occur, is presented which is based on the calculation of overlaps between sets of molecular orbitals and configuration interaction eigenfunctions obtained at neighboring nuclear conformations. This approach has significant advantages for theoretical treatments describing atomic collisions and photo‐dissociation processes by means of ab initio PES, electronic transition moments, and nonadiabatic radial and rotational coupling matrix elements. It ensures that the electronic wave functions are continuous over the entire range of nuclear conformations considered, thereby greatly simplifying the process of obtaining the above quantities from the results of single‐point Born‐Oppenheimer calculations. The overlap results are also used to define a diabatic transformation of the wave functions obtained for conical intersections that greatly simplifies the computation of off‐diagonal matrix elements by eliminating the need for complex phase factors. © 2013 Wiley Periodicals, Inc.     

X-ray spectra and electronic structure of boron nitride in different crystallographic modifications

The electronic energy structure of boron nitride with ZnS (c-BN) and wurtzite (w-BN) type crystal lattices is calculated by the local coherent potential (LCPA) method in a multiple scattering approximation. The local partial 2p states of boron with c-BN and w-BN are compared with the boron K emission spectra in the corresponding compounds. Fine structure is first obtained in the region of the top of the valence band. Translated fromZhurnal Struktumoi Khimii, Vol. 39, No. 6, pp. 1083–1087, November–December, 1998.     

Accurate local-space treatment of hydrogen bonding in large systems

Tests of the local-space approximation for electronic structure are carried out on a variety of hydrogenbonded systems. Regardless of size they are all found to be well localized in the sense of this approximation. For a local space defined by the valence atomic orbitals on X? H ··· Y, one obtains a bond energy within 6% of the “exact” full-space value. The potential energy surface and the electronic charge distribution are also accurately determined. In contrast with cluster models the local-space approximation satisfactorily accounts for long-range electrostatic and polarization effects.     

Study of an approximate relation between the energy of an atom and the electronic potential at the nucleus

This paper provides an analysis of the reasons for the approximate validity of the relation \documentclass{article}\pagestyle{empty}\begin{document}$ E = \frac{3}{7}NV(0) $\end{document}, between the total energy E of a neutral atom, the number N of electrons, and the electronic potential at the nucleus V(0). Using the density functional formalism we find that the right-hand side of the above equation also appears (and is the leading term) in density functional approximations more sophisticated than the Thomas–Fermi (TF ) approximation (the above equation is exact in the TF approximation). Systematic improvements to the equation appear to be difficult because the main corrections come from those terms which are more difficult to handle in the density functional formalism. After this analysis we propose a kinetic energy functional for neutral atoms in the Hartree–Fock approximation. The first term of this new functional is a rescaled Thomas–Fermi term , where γ = ?0.0063 for light atoms and γ = 0.0085 for the others. The second term is the first gradient correction due to Kirzhnits . For lithium to krypton atoms, this new functional gives an average error of 0.22%.     

Spectrum and polarizability of polyphenyls in the Pariser-Parr-Pople approximation

The Pariser-Parr-Pople approximation is used to calculate the electronic structure, electronic absorption spectrum, and polarizability for biphenyl, terphenyl, and quaterphenyl. The self-consistent MO are taken as basis functions for the multiconfiguration approximation. The minimum number of singly excited configurations is included. Bond orders, bond lengths, transition energies, oscillator strengths, and wave functions of the excited states are given in that approximation. The results are compared with published data and, where possible, with experiment. Calculation of the -electron polarizability with allowance for configuration interaction is discussed. The agreement with experiment is satisfactory for all the characteristics calculated.     

Electronic structure of the pyrimidine and purine components of nucleic acids in their ground and lower excited singlet and triplet states

Quantum-chemical calculation of the energies of the electronic transitions and the electronic structures of the neutral and ionic species of the nucleic acids components in their ground and lower excited singlet and triplet ππ* and nπ* states has been carried out in the all-valence-electron approximation CNDO /S . The results of the calculation allow one to identify the most photoreactive sites of the molecules and to consider the dependence of the location of these sites on the ionic state of the molecules. The calculated data are compared with our previous results obtained in a π-electron approximation. The individual absorption spectra of various ionic and tautomeric species of the nucleic acids components obtained by us earlier have been decomposed into bands corresponding to separate electronic transitions. As a rule, there is a good agreement between the calculated data in the two approximations and the experimental results.