bluuebunny/crossref_metadata_2025_split huggingface dataset:
Application of graphical methods of spin algebras to limited CI approaches. II. A simple open shell case
Authors: Adams B. G. , Paldus J. , Čížek J. 
Published: December 2004

AbstractA time independent diagrammatic technique based on the Wick theorem and graphical methods of spin algebras, as outlined in Part I, is applied to a simple open shell case having one unpaired electron in addition to the pure singlet closed shell. Compact explicit expressions for the matrix elements of a spin independent Hamiltonian between conveniently chosen spin symmetry adapted states are given for the ground, mono‐ and bi‐excited configurations.
Lower bound molecular orbitals for H, HeH++, and H
Authors: Johnson J. W. , Poshusta R. D. 
Published: December 2004

AbstractGaussian orbitals are used to calculate Temple lower bounds for H, HeH++, and H. Molecular orbitals are constructed from individual Gaussian‐type orbitals (GTO) and from GTO contractions adapted for either upper or lower bounds of the hydrogen atoms. The MOS are optimized by minimizing either the upper bound, 〈H〉, or the variance, 〈(H – E)2〉. The best Temple lower bounds achieved by these methods are −0.60336 a.u. for , − 1.06224 a.u. for HeH++, and −0.13003 a.u. for H. Comparison is made with other types of molecular orbitals and with the exact wave functions for , HeH++. Analysis of the nuclear cusps is given. A prescription for constructing lower bound molecular orbitals is offered.
Coupled Hartree‐Fock calculation of static dipole polarizations of open‐shell ions
Authors: Roy H. P. , Gupta A. , Mukherjee P. K. 
Published: December 2004

AbstractIn this paper static dipole polarizabilities and shielding factors of 3p open‐shell atomic systems from A1 to C1 are presented using coupled Hartree‐Fock theory in the Roothaan scheme. The calculation was made for the ground as well as for some valence excited states of the ions. A variational approach was adopted to obtain the polarizability values and the results are compared with the existing data wherever possible. The shielding factor values are in good agreement with the theoretical N/Z ratio.
Formulas for evaluation of expectation values of monoelectric operators with modified gaussian functions
Authors: Biondi Franco , Salvetti Oriano , Gołebiewski A. 
Published: December 2004

AbstractFormulas are presented for the evaluation of the expectation values of various monoelectronic operators. The integrals are based on „Hermite‐Gausian”︁ or „Modified Gaussian Functions”︁ and are expressed in suitable form for a computer programming. It is pointed out that the final expresions are simpler than the analogou omes obtained from the usual Gausian functions and can be written as linear combinations of a few baic integrals.
Correlation energy contributions to reaction heats
Authors: George Philip , Trachtman Mendel , Brett Alistair M. , Bock Charles W. 
Published: December 2004

AbstractNew, more accurate, Hartree‐Fock limit energies (EHF) for ethane and ethylene are obtained from SCF total molecular energie using Ermler and Kern's procedure. These results, together with EHF values for other small closed shell molecules, are employed to calculate correlation energy (Ec) contributions to reaction heats. Cancellation to within 98% of the total Ec involved, and often to more than 99%, is found for a wide variety of chemical reactions, which strongly suggests that there are systematic regularities in the contribution to Ec from the different kinds of electron pairs in the valence shell. Assuming trictly localized pairs occupying orbitals having strongly directional character, Ec for the valence shell is evaluated in terms of Ec per lone pair, Ec per XH bond, and Ec per X/X shared pair for Ne and for molecules containing first row atoms, where X is C, N, O, and F.
Correlation effects to the expectation values of atomic systems
Authors: Brown Richard E. , Larsson S. 
Published: December 2004

AbstractThe Hartree‐Fock and first natural spin determinants were compared as reference determinants for calculating various one‐electron properties such as ρ(0), 〈½∇〉, 〈r−2〉,…, 〈r3〉, and r−112〉. Calculations were made on various small atoms and their positive and negative ions. For nearly all the expectation values studied, the first natural spin orbital determinant gave consistently superior results. In particular, the Hartree‐Fock functions gave markedly inferior results for some long range properties such as the magnentic susceptibilities of negative ions. The major correlation error in the expectation values is primarily an orbital effect which may be accounted for by including correlation terms in the one‐particle Hamiltonian. Such approximate Brueckner or best overlap orbitals should reproduce most one‐electron expectation values accurately.
Simplified methods for ab initio calculations. The valence states of CH2 and CH
Authors: Gervy D. , Verhaegen G. 
Published: December 2004

AbstractThree simplifying methodds are discussed and applied to the four lowest valence states of CH2(3B1, 1A1, 1B1 and 1Σ(1A)) and to the two lowest of CH(2A1 and 2∏u(2B1)). These methods concern: (1) the development of polarization functions for Gaussian‐lobe basis sets by least‐square fitting of numebrical multiconfigurational atomic fuinctions (this approach is tested also on (C2H2, (2) the use of intermediate Hamiltonians to calculate avoided crossings between potential hypersurfaces, and (3) thecalculation of correlation energies using an atoms‐in‐molecule approach.The calculated equilibrium geometries of the CH2 States are within 0.02 Å and 5° of available experimental data. The calculated term values and ionization potentials, Te(1A1 = 0.35 eV, Te (1B1) = 1.22 eV, Te (1Σ(1A)) 2.48 eV, I.P. (2A1) = 10.39 eV and I. P. (2∏u(2B1)) = 10.58 eV, are in agreement with some recent theoretical studies, and are very close to existing experimental information.
State vectors and propagators in many‐electron theory. A unified approach
Authors: Linderberg Jan , Öhrn Yngve 
Published: December 2004

AbstractA unitary group formulation of the many‐electron problem is employed to give explicit representations of state vectors which are convenient for the discussion of progerties derived from propagatorcalculations. New results are obtained concerning the nature of various random‐phase‐like approximations and ground state representatives are generated from consistency requirements for the spectral resolution of the polarization propagator. The explicit solution admits the calculation of ground state average values for arbitrary operators and a variational upper bound to the ground state energy.
A note on the importance of d orbitals in the calculation of effective interactions and the excitation spectra of atoms and molecules
Authors: Cherng Sharon , Westhaus Paul 
Published: December 2004

AbstractThe focal point of our discussion is the examination of truncated basis sets used in obtaining an accurate first principles clculation of the effective valence shell Hamiltonian by the canonical transformation‐cluster expansion approasch. Subsequent diagonalization of this effecitve valence shell hamiltonian yields the valence shell transition energies. A detailed analysis of numerical results obtained using a number of different basis sets of hydrogen‐like orbitals together with rigorous symmetry arguments celarly demonstrates the special role played by d orbitals in computing the 3P → 1D transition energy in carbon. The failure of early attempts to calculate the effective Hamiltonian for ethylene from first principles is examined in the light of recent ab initio calculations on ethylene involving d orbitals and the computations reported in this paper. We conclude that accurate calculations of the effective valence shell Hamiltonian for molecules must consider d orbitals in the excited orbital basis set.
SCF scheme for excited states and analysis of the orbital relaxation effect for H2O and FNO
Authors: Mrozek J. , Gołȩbiewski A. 
Published: December 2004

AbstractAn SCF scheme for excited states of closed‐shell systems based on the direct minimization technique is discussed. The utility of the scheme is tested for several excited states of H2O. The contribution of various tyeps of optimization of orbitals occupied in the excited state is discussed using the example of H2 O and FNO. It was found that relaxation of doubly occupied orbitals always gives a significnat contribution to the lowering of the excited state energy in the SCF process. Unexpectedly, on the other hand, optimization of the excited orbital in many cases gave negligible results.
Localized states in a simple cubic crystal via the next‐nearest neighbor approximation
Authors: Stȩślicka Maria , Stankiewicz B. 
Published: December 2004

AbstractThe energy spectrum of localized states in a simple cubic crystal is analysed, using the next‐nearest neighbor approximation. The main distinguishing feature between the nearest and next‐nearest neighbor approximation is the energy distribution of the localized states. Contrary to the tight‐binding approximation, a non‐symmetric distribution is found for clean surfaces, and split energy bands are found for surfaces completely covered by adsorbed atoms.
Test of an integral approximation scheme based on semiorthogonalized orbitals in LCAO SCF MO CI calculations of naphthalene
Authors: Kashiwagi Hiroshi , Takada Toshikazu 
Published: December 2004

AbstractAb initio LCAO SCF MO CI calculations of naphthalene are carried out with a minimal basis set to test an integral approximation scheme proposed in a previous paper. When 71.3 and 53.0% of the two‐electron integrals are neglected, the errors in the SCF total energy are only −0.0534 and −0.0006 a.u., respectively. In the latter case, the maximum absolute errors of the orbital energy and the gross AO population are 0.007 a.u. and 0.001, respectively. Even in the former case the errors of the excitation energies are less than 0.0004 a.u. Errors of oscillator strengths are also examined and are found to be tolerably small.
Ab initio valence bond calculations. VII. HF, HF+, and H2F+
Authors: Tantardini G. F. , Simonetta M. 
Published: December 2004

AbstractAb initio valence bond calculations for the ground and excited states of HF and HF+ are presented. Total energies, equilibrium geometries, dissociation energies, dipole moments, and spectroscopic constants for HF and HF+ have been calculated. The photoelectron spectrum of HF has been examined and interpreted by means of the valence bond formalism. The ground state of the protonated species H2F+ has been investigated.
A semi‐empirical MO theory for ionization potentials and electron affinities. II. Vertical and adiabatic values, benzenoid and nonbenzenoid aromatic hydrocarbons, and conjugated molecules with heteroatoms
Authors: Selsby R. G. , Grimison Alec 
Published: December 2004

AbstractFurther developments of a recent semiempirical, variable effective charge MO theory for calculation of ionization potentials (IP) and electron affinities (EA) as energy differences between separately minimized ground and ionized states are reported. The method is extended to adiabatic as well as vertical IPS and EAS by including core repulsion and σ bond compression energies in the total energy. The method is generalized to heteroatomic systems and is simplified by neglecting penetration integrals. As before, only two molecular parameters, the vertical IPS of benzene and naphthalene, are required to set the magnitude of the σ changes associated with the polarization of the core during loss or gain of a π charge. Twenty‐seven aromatic molecules are studied, including polyacenes, condensed ring compounds, nonbenzenoids with five and seven member rings, nonplanar molecules, and heteroatomics with N+, as in pyridine, N+2, as in pyrrole, and O+2, as in furan. The results are within 0.2 eV of the photoelectron spectroscopic vertical IPS and the predicted vertical‐adiabatic separation is consistent with the shape of the first band. The calculated EAS are within 0.2 eV of the observed values.The calculation is used to predict the IP and EA of the ionic photosensitizing cyanine dye, pinacyanol. The values obtained are consistent with the latest measured IP and EA of the adsorbed dye, corrected for surface and aggregation polarization effects.
Perturbation corrections to Koopmans' theorem. IV. Energy‐shifted perturbation theory
Authors: Chong Delano P. , Takahata Yuuzi 
Published: December 2004

AbstractEnergy‐shifted perturbation theory is studied in connection with corrections to Koopmans' theorem. The first three vertical Ionization potentials of N2, C2H2, and HCN are computed with basis sets of double‐zeta Gaussian‐type orbitals and double‐zeta GTO plus polarization functions. The average absolute deviation of calculation ionization potentials from the observed values is found to be 0.4 eV, whether one uses Brillouin‐Wigner or Rayleigh‐Schrödinger perturbation theory.
Removal of singularities in the numerical integrals for an STO basis set
Authors: Careless P. N. , Hyatt D. , Stanton L. 
Published: December 2004

AbstractAdvantages and difficulties of numerical integration in relation to a transcorrelated solution of the molecular Schrödinger equation are discussed. Because singularities in the two‐electron integrals can be completely removed in a transcorrelated calculation, the major difficulty remaining to be resolved is that of singularities in the one‐electron integrals. A general method of treating this problem is given which involves the derivation of some new polycentric expansion functions which are everywhere finite under the one‐electron part of the Hailtonian. The important improvements obtained are illustrated by some calculations on LiH.
The relationship between the unrestricted and projected Hartree–Fock methods in a simple three‐electron model system
Authors: Paldus J. , Čížk J. , Laforgue A. 
Published: December 2004

AbstractVarious forms of the unrestricted Hartree–Fock (UHF) scheme are studied for a simple three‐electron model system, represented by the PPP (Pariser–Parr–Pople) π‐electron model of the allyl radical. Both spin and space symmetry are violated in the UHF trial wave function, either individually or simultaneously. A comparison with the projected Hartree–Fock (PHF) schemes studied earlier is made and the effect of the order in which various symmetries are broken in both UHF and PHF schemes is studied. The effectiveness of various schemes follows from a comparison of the correlation energy and the wave function is obtained by various UHF (or projected UHF) and PHF schemes, in the whole range of the coupling constant, with the corresponding quantities given by the exact solution of the model. Finally, the implications of the stability of the restricted HF solutions for the behavior of various single‐ and multiparameter UHF and PHF schemes are briefly outlined and exemplified on the studied model.
Ab initioLCAO‐MO‐SCF calculation of the electrostatic molecular potential of chlorpromazine and promazine
Authors: Petrongolo Carlo , Preston Harry J. T. , Kaufman Joyce J. 
Published: December 2004

AbstractThe electrostatic potential V(r) arising from the ab initio LCAO‐MO‐SCF wave functions of chlorpromazine (CPZ) and promazine (PZ) has been calculated and discussed. In this approximation, the most probable sites of attack and reaction paths of electrophilic reagents are pointed out and compared. The analysis of V(r) shows that the phenothiazine group has strong nucleophilic properties which are influenced by the phenothiazine substituent and that the electrostatic reactivity of CPZ and PZ is decidedly different near the phenothiazine substituent and similar near the side chain N atom. The dependence of V(r) on the accuracy of the wave function has also been discussed by comparing some ab initio results on pyrrole, pyrazole, and imidazole obtained with a large basis set with an ab initio minimum basis set and with CNDO calculations.
Dynamics of molecules in contact with an external medium at equilibrium
Authors: Simons Jack 
Published: December 2004

AbstractWhen considering the dynamical properties of a molecule in contact with an external medium whose degrees of freedom are at equilibrium, one can adopt either of two approaches to the problem. The equations of motion which govern the coupled molecule‐medium system can be solved (or approximately solved), after which the initial values of the medium's coordinates are averaged over (with an equilibrium distribution function as weighting factor) to obtain the desired property of the molecule. In the second approach, which is the subject of the present work, the effects of the medium on the molecule of interest are incorporated into a time‐dependent effective potential which contains the equilibrium average molecule‐medium interaction as well as terms arising from fluctuations in the medium's coordinates about their equilibrium values. By introducing such an effective potential via the cumulant expansion technique, the problem of studying dynamical properties of the molecule is reduced to the study of a molecule which is in the presence of a time varying external field which no longer depends explicitly upon the coordinates of the medium. In addition to developing the basic method for treating such problems, applications of the method to interesting problems are briefly discussed.
Bond length alternation in cyclic polyenes. I. Restricted Hartree–Fock method
Authors: Paldus J. , Chin E. 
Published: December 2004

AbstractThe problem of bond length alternation in cyclic polyene models as described by the Pariser–Parr–Pople π‐electron Hamiltonian and its relationship to the singlet stability problem for symmetry adapted Hartree–Fock solutions for these systems is investigated using the restricted Hartree–Fock method. The σ‐energy contribution is approximated by a quasiharmonic empirical potential. It is shown that the restricted Hartree–Fock energies favor the cyclic polyene distortion and an estimate of the distortion and of the stabilization energy for infinite linear polyenes is obtained.
SCF and CI Studies of Hund's rules for the effects of electronic correlation and delocalization. I
Authors: Brown Richard E. , Colpa Johannes Pieter 
Published: December 2004

AbstractIn connection with the reinterpretation of Hund's multiplicity rules for molecules, a detailed study has been made of the energy differences in the total energy and its components for the triplet and singlet Πu states of the hydrogen molecule and the analogous states of the four‐ and six‐membered hydrogen atom rings. For the hydrogen molecule, both SCF and CI studies indicated that the outer electron is considerably more contracted in the triplet than in the singlet state. In both approximations, the energy difference is dominated for all bond distances of chemical and physical significance by the electron‐nuclear attraction component and not by the electron repulsion component as predicted by simple first‐order perturbation theory. Although the correlation energy for each of the states is of the same magnitude as the energy differences considered here, the difference of the correlation energies is much smaller. It had little effect on the qualitative differences between these states of the hydrogen molecule. For the four‐ and six‐membered rings, SCF studies were made on the lowest singlet and triplet states where one electron was promoted from the σg to a Πu orbital. Even though the coupled electrons were more delocalized in these cases, the electron repulsion became relatively more important. However in all cases, the lower state had the highest electron repulsion energy and lower electron‐nuclear attraction. The triplet state continued to have the more contracted outer open‐shell orbital.
Ab initio calculation of the heptamer (NH3)7 as a reasonable starting point for a description of the ammonia crystal
Authors: Bridet Jacques , Fliszár Sándor , Odiot Simone , Pick Robert 
Published: December 2004

AbstractQuasi‐Wannier functions for the ammonia crystal have been determined from optimized ab initio calculations of the heptamer (NH3)7, thus accounting for all the first neighbor interactions. The calculated geometry and binding energy are in good agreement with their experimental counterparts.
On the Sanibel coefficients in the expansion of spin‐projected slater determinants
Authors: Löwdin Per‐Olov 
Published: December 2004

AbstractEvery Slater determinant D may be uniquely analyzed in terms of spin components Dl = OlD which are pure spin eigenfunctions, so that S2Dl = l(l+1)D. Every component Dl = OlD may in turn be written as a sum of symmetric combinations of Slater determinants, Tk = [αμ−kβk‖αkβν−k], and the coefficients c in the expansion OlD = ∑k c Tk are known as the “Sanibel coefficients.” By using the relation S2Dl = l(l+1)D, a recursion formula for the coefficients c is derived, which is then explicitly solved in the special case when Sz has the pure quantum number m = 0.
Ab initio molecular fragment calculations with pseudopotentials: Model peptide studies
Authors: Gáspár R. , Gáspár R. 
Published: December 2004

AbstractThe energetics of rotation about the NC′(ω); NCα(φ), and CαC′(ϕ) bonds of the peptide unit have been investigated in the pseudo‐FSGO fragment scheme on model compounds formamide and N‐methylacetamide. The results indicated that the position of the minimum in ω is in the near vicinity of 0°, i.e., the planar arrangement of the peptide unit. The minimum in φ (C′NCαH) has been found to be 180° and in ψ(HCαC′N) to be 60°, in good agreement with PCILO and Gaussian‐70 results.
Vibrational–rotational levels of diatomic RKR potentials
Authors: Requena A. , Zuñiga J. , Peña R. 
Published: December 2004

AbstractThe vibration–rotation levels for the diatomic RKR potential curve are solved using both perturbational and variational approaches. To obtain any‐order correction of the energy from unperturbed parameters, an iterative scheme is formulated in the hypervirial framework. Variational calculations are carried out upon a rotationless Morse oscillator basis set and using a transformation technique to treat the effective potential energy function. Numerical results for the RbH X 1Σ+ state are obtained. The accuracy of the energy levels is tested by solving the Schrödinger equation by a numerical procedure.
Vibronic coupling of electronic states. IV. Harmonic CBO potentials with equal minima positions—the influence of different vibronic coupling strengths on the electronic absorption and emission spectra containing a longest‐wavelength electronically forbidden transition
Authors: Gustav Klaus , Colditz Roland 
Published: December 2004

AbstractThe influence of vibronic coupling between two harmonic CBO potentials with equal minima positions on the electronic absorption and emission spectra is investigated in the framework of our model using the variational procedure. The numerical results, being identical with those obtained through the vibronic coupling model of Fulton, Gouterman, and Brickmann, are discussed with regard to the longest‐wavelength electronically forbidden transition, its vibrational structure, and the Stokes loss.
Quantum‐chemical study of electrophilic addition reaction of iodine to ethylene
Authors: Suqian (S. Q. Jin) Jin , Ruozhuang (R. Z. Liu) Liu 
Published: December 2004

AbstractThe relative stability of and barrier to interconversion of the two possible intermediates in the electrophilic addition of iodine to ethylene have been studied by means of ab initio molecular calculations with pseudopotential approximations. The geometries of the 2‐iodoethyl and ethylene iodonium cations have been optimized by the energy gradient technique with pseudopotential approximations. From the results of the calculations, it is found that the only possible intermediate is the cyclic ethylene iodonium ion, as shown by experiments.