Variationally optimized numerical orbitals for molecular calculations

The problem of variational optimization of the atomic orbitals used in molecular calculations is investigated. It is shown that the variational principle leads to an equation similar to the radial Schrodinger equation but containing an inhomogeneous term. As an example, the equations are solved for the minimum basis set orbitals for the methane molecule. The results show a substantial improvement over those of a previous calculation optimizing in a minimum basis of Slater orbitals.     

Optimum atomic orbitals for molecular calculations A review

This review is intended to give a broad outline of the many techniques used in the calculation of atomic structure and the methods of using the information gained from this work in molecular calculations. Consequently, no topic is considered in full depth and only selected examples from the literature are used to illustrate the main points. Extensive tabulatios of atomic and molecular properties are already available in the literature, and these serve as additional sources of examples. Only methods within the Hartree-Fock framework, where a single Slater determinant (or in some cases a linear combination of Slater determinants) and the variation principle form the basis of the model, are considered in detail. Extensions of the independent particle model to include correlation have been considered briefly and smaller corrections, such as magnetic and relativistic effects are omitted.

We describe, in the first part of the review, the partical requirements of the functional form of the basis set and consider examples of the types of functions available in the literature. These include exponential- and Gaussian type-functions and many others. For' chemical accuracy' the total energy of the electronic system should be estimated to within one kilocalorie or better, requiring at least Hartree-Fock accuracy for the isolated atoms and optimization or augmentation of the bases in the molecule. Smaller, less accurate basis sets for the atoms are still useful, however, in the prediction of certain atomic and molecular properties, and in supplying simple orbital pictures of interest to chemists, although producing poorer representations of the total wave function.

In order to produce good wave functions there are certain criteria that they may satisfy. These, when coupled with the independent particle model, produce many methods of obtaining wave functions of varying accuracy depending in the size and type of functions comprising the basis set. Some of the criteria considered include the minimal energy principle, the best approximation to operators other than the Hamiltonian and other less known, and perhaps less practical, methods.

The quality of the atomic wave functions, produced from Hartree-Fock equations, using different types of basis functions, may be investigated with the aid of many operators, and in particular the position operators, <rⁿ >, and tested in the prediction of such quantities as the electron-electron interaction operators. The atomic <rⁿ > values are extremely useful in choosing a basis for the calculation of a particular molecular property that depends heavily on the same region of space.

In order to allow for the polarization of an atom in a molecular environment, and hence achieve better molecular properties, one may either reoptimize or augment the existing basis. If large basis sets are used initially for the atom, then they may be contracted without appreciable loss of ‘chemical accuracy’ before being used in the molecular calculations. These points are illustrated, using different basis sets produced by several methods, for the molecules HF, H₂O, NH₃ and HCN. Rules for orbital exponents (non-linear parameters of the basis set) for atoms and molecules are also discussed.     

Simple approximate physical orbitals for GW quasiparticle calculations

Generating unoccupied orbitals within density functional theory (DFT) for use in GW calculations of quasiparticle energies becomes prohibitive for large systems. We show that, without any loss of accuracy, the unoccupied orbitals may be replaced by a set of simple approximate physical orbitals made from appropriately prepared plane waves and localized basis DFT orbitals that represent the continuum and resonant states of the system, respectively. This approach allows for accurate quasiparticle calculations using only a very small number of unoccupied DFT orbitals, resulting in an order of magnitude gain in speed.     

Atomic orbitals with angularly dependent Z eff to be used in molecular orbitals calculations

A new type of atomic orbital is proposed for use in molecular problems of quantum mechanics. This orbital is formally similar to Slater's orbitals but is characterized by an effective nuclear charge Z _eff which is an explicit function of the angles ? and φ. The fundamental state of the molecule H₂ ⁺ is studied using such an orbital.     

Semiempirical molecular orbital calculations of anisotropic 1H, 13C and 19F hyperfine coupling constants in hydrocarbon and fluorocarbon radicals

The anisotropic hyperfine coupling constants (AHCC) from the electron spin resonance (E.S.R.) spectra of a variety of atoms in organic radicals have been calculated by means of semiempirical molecular orbital wavefunctions in the INDO approximation. Hyperfine tensors involving ¹H, ¹³C and ¹⁹F nuclei are obtained for the ?H, ?H₃, CH₃?H₂, (CH₃)₃? hydrocarbon radicals, malonic acid radical, ?H₂F, ?F₂H, ?F₃ and CF₃?H₂ radicals. The calculated values are compared with available experimental, non-empirical and semiempirical values for these radicals. All integrals of the operator entering the electronic contributions have been evaluated over Slater type orbitals. The introduction of deorthogonalized wavefunctions gives generally better calculated results. In particular, the tensor components of the ¹⁹F AHCC are in good agreement with the experimental results without the necessity of readjusting the effective nuclear charges.     

Double perturbation calculations of spin-spin coupling constants using localized orbitals

The Fermi contact contribution to N.M.R. spin-spin coupling constants has been calculated to the fourth order by a double perturbation development starting from a fully localized determinant, according to the assumptions of the PCILO-CNDO method. The use of diagrammatic techniques greatly simplifies the evaluation. There is a cancellation of certain types of diagram. The coupling constant between bonded atoms appears in the second order through a contribution which only depends on the appropriate bond orbital. The next orders involve the other bonds and correlation effects. For nonbonded atoms, the first contribution appears in the fourth order and results from direct delocalization through space, involving only the bonds on the two atoms.

An analytical and numerical comparison with previous calculations is performed for H-H and C-H coupling constants on small organic molecules. The relative importance of the various processes is discussed for the J _HH vicinal coupling constants of ethylene.     

Comparisons of some molecular properties calculated with basis sets of Slater-type orbitals and floating spherical gaussian orbitals for BH3, BH4 -, B2H6, B4H4, C2H2, C2H4, C2H6, CH4, and C3H4

Some one-electron molecular properties are calculated for BH₃, BH₄ ^-, B₂H₆, B₄H₄, CH₄, C₂H₂, C₂H₄, C₂H₆, and C₃H₄. The wave functions used are constructed from minimal basis sets of STO's and FSGO's. The results obtained from the latter wave functions show that the good agreement with the STO values of the molecular energy is not always maintained with one-electron properties.     

Molecular orbitals of benzoxadiazole compounds with optical nonlinearities

Two benzoxadiazole compounds have been investigated. It is shown that in a derivative containing a nitro group, the effective electron-accepting moiety for second-order nonlinear optical characteristics is not the nitro group but the oxadiazole ring. The change in the dipole moment with excitation is perpendicular to the transition moment.     

Molecular pseudopotential calculations V

The equilibrium geometries, nuclear distances, wave functions and energies for the XY ²₊ , X₂Y⁺, Y₂H⁺ (X=Li, Na, K; Y=Rb, Cs), resp. the X₂H⁺, X₂Y⁺ (X, Y=Cu, Ag, Au) triatomic alkali ions, resp. noble metal ions, further the dissociation energies for the X₂Y⁺→X⁺+XY; XY ²₊ →Y⁺+XY and Y₂H⁺→Y⁺+YH processes are determined with the pseudopotential method. The calculations were performed using the Hellmann-type analytical potential with simple floating-type one-centre wave function.

     

Molecular pseudopotential calculations II

Acta physica Academiae Scientiarum Hungaricae - The ionization potentials and equilibrium internuclear distances of the diatomic homonuclear (Na2, K2, Rb2, Cs2) alkali metal and (Cu2, Ag2, Au2)...     

Ro-vibrational spectra of C2H2 based on variational nuclear motion calculations

A published ab initio-based potential energy surface and newly constructed dipole moment surface of acetylene have been used to compute vibrational band intensities. The line intensity calculations employed the variational nuclear motion code WAVR4 for computation of wave functions and energy levels, and a newly developed code DIPOLE4 for computation of dipole transitions. Owing to the high computational cost of J > 0 transitions using direct variational methods only J = 0 and J = 1 states and transitions have been computed variationally. The intensities of J > 1 transitions were extrapolated from J = 0 and J = 1 using Hönl–London coefficients. The resulting effective rotational constants B and transition intensities are compared with experimental data for the (3ν₄ + ν₅) combination band, the ν₃ and the ν₅ fundamental band. The prospects of using this procedure for extensive calculations of a hot line list, important for cool stars and extrasolar planets are discussed.     

Gauge-origin independent calculations of electric-field-induced second-harmonic generation circular intensity difference using London atomic orbitals

ABSTRACT

We present the first gauge-origin independent calculations of the circular intensity difference (CID) in electric-field-induced second-harmonic generation (EFISHG), including all contributions up to the electric-quadrupole–magnetic-dipole level. A recursive, open-ended response theory framework in combination with the use of London atomic orbitals allows us to ensure gauge-origin independent results. We apply this approach to study EFISHG-CID in a collection of chiral amino acids. We demonstrate that diffuse polarising basis functions are critical in order to obtain accurate CIDs, and that a basis set of at least aug-cc-pVTZ quality is needed in order to obtain results close to the basis-set limit. The use of London orbitals does not lead to significantly faster basis set convergence, although the improved basis set convergence allows the aug-cc-pVDZ basis set to be used with some confidence for larger molecules.     

Ab initio calculations for propyne and the hydrogen bonded complex NH H C C CH 3 3

The hydrogen-bonded cluster NH₃ …H—C≡C—CH₃ has been investigated by means of the coupled electron pair approximation, making use of a basis set of 198 contracted Gaussian-type orbitals. The calculated equilibrium structure is r _1^e (N—H) = 1?0127 Å, α_e(∠HN…H) = 112?32°, R _1^e (N…H) = 2?3593 Å, r _2^e (acetylenic C—H) = 1?0690 Å, R _2^e (C≡C) = 1?2078 Å, R _3^e (C—C) = 1?4711 Å, r _3^e (C—H) = 1?0894 Å and β_e(∠CCH) = 110?50°. The recommended equilibrium dissociation energy is D _e = 12?4±0?5 kJ mol^-1 and the calculated equilibrium dipole moment is μ_e = – 1?468 D, with the positive end of the dipole at the ammonia protons. Harmonic wavenumbers and absolute infrared intensities for the totally symmetric modes are calculated. Compared with free propyne the acetylenic CH stretching vibration experiences a bathochromic shift of 93 cm^-1 and an intensity enhancement by a factor of 5?5.     

H��C/Be��ϲ��໥���õķ��Ӷ���ѧģ��

利用分子动力学方法研究了H原子与C/Be样品的相互作用过程,当H原子轰击C/Be样品时,发现有一些H原子渗入样品中并且滞留在样品中,H原子的滞留率随H原子的初始入射能量的升高呈线性增长,有些沉积在样品中H原子与C原子相互作用形成H-C键。溅射产物以H原子和H2分子为主。H和H2的产额率随初始入射能量的变化趋势相反,分析了不同机制下产物H和H2的产额率随初始入射能量的关系,且通过分析H原子的入射能量和样品的原子密度的关系来研究轰击后的样品,发现样品中原子分布变化很小,同时分析了化合物中的化学键分布变化较小,只是其化学键的分布峰向样品表面移动。     

Molecular MCSCF calculations by direct minimization

An MCSCF method using single excitations is described. The wave-function is obtained by direct minimization. An illustrative calculation on LiH indicates that the method is appropriate for the calculation of one-electron properties, especially in bond-breaking geometries.