bluuebunny/crossref_metadata_2025 huggingface dataset:
Ab initio calculations on sulfur‐containing compounds. II. One‐electron properties of H2S
Authors: Poirier Raymond A. , Daudel Raymond , Kari Roy E. , Csizmadia Imre G.
Published: December 2004

Closed‐shell RHF one‐electron properties are calculated for H2S using a total of 41 different s, p basis sets and two polarized basis sets (6–31G* and 6–31G**). Total energies and geometries alone are not a comprehensive criteria for selecting the best basis sets. It is shown here that the comparison of a number of one‐electron properties can serve as an excellent criteria for testing basis sets. The quality or reliability of a basis set is taken as being its agreement with a large uncontracted s, p basis set (s, p limit).
Theoretical studies on the interaction of proteins with base pairs. I. Ab initio calculation for the effect of H‐bonding interaction of proteins on the stability of adenine–uracil pair
Authors: Sarai Akinori , Saito Minoru
Published: December 2004

The hydrogen‐bonding interaction of protein with the adenine–uracil base pair was investigated by the ab initio MO method (STO‐3G level). We found that the stability of the base pair was greatly affected by the hydrogen‐bonding interaction of several residues of protein in different ways, depending on whether the interacting species is charged or neutral, whether the interaction is made from the major groove or minor groove side, and which of the two, adenine or uracil, is hydrogen bonded. These results were interpreted as the cooperative interaction between the base pair hydrogen bonds and external ones. The implications of the present results to biological functions were also discussed.
Numerical solution of Hartree–Fock equations for a polyatomic molecule: Linear H3 in momentum space
Authors: Defranceschi M. , Suard M. , Berthier G.
Published: December 2004

We give an example of multidimensional numerical solutions in momentum space, for the Hartree–Fock equations of the simplest molecule with more than two electrons and two nuclei.
Fitting electron densities of molecules
Authors: Hall G. G. , Smith C. M.
Published: December 2004

Compact, convenient expressions for the electron density are derived using a fitting functional. Results are given for H2O, CH4, HF, NH3, and PH3, and show the accuracy obtainable using differing numbers of functions on each center. The definition of an atomic charge using these expressions is discussed and it is shown that the Bader virial‐partitioning definition, in which the density is integrated over a volume around each nucleus, leads to convergent results.
Theory and computational methods for studies of nonlinear phenomena in laser spectroscopy. I. General formalism
Authors: Dmitriev Yuri Yu. , Roos Björn O.
Published: December 2004

A general formalism will be outlined, which uses steady‐state wave functions for the study of nonlinear phenomena occurring in molecular systems interacting with intense electromagnetic fields. The steady‐state approach has the advantage of being free from the secular divergencies and normalization terms which appear in a perturbation expansion of the time‐dependent wave function. A physical interpretation of the steady states will be given by considering the interaction between the molecule and the quantized electromagnetic field. The steady states appear as states of the combined system molecule plus electromagnetic field, with eigenvalues corresponding to the energy levels of the combined system in a semiclassical approximation. Evolution operators will be introduced and used to derive formulas for n‐photon transition probabilities between molecular states both in the ordinary configuration Hilbert space and in the composite Hilbert space spanned by the steadystate wave functions.
Theory and computational methods for studies of nonlinear phenomena in laser spectroscopy. II. Calculations of steady‐state wave functions
Authors: Roos Bjöurn O. , Dmitriev Yuri Yu. , Hotokka Matti
Published: December 2004

Methods will be developed for variational calculations of steady‐state wave functions and the corresponding quasienergies. These functions appear as solutions to the time‐dependent Schrödinger equation for a molecule interacting with an oscillating electromagnetic field. A variation principle is used to obtain coupled equations for each Fourier component (FC) of the steady‐state wave function. The FCs are expanded in configuration state functions using the structure of the complete active space (CAS) SCF approach. Two methods are outlined, one which is based on a common set of molecular orbitals for all FCs and one based on an individual optimization of both CI coefficients and molecular orbitals for each FC. The latter method leads to molecular orbital sets for the different FCs which are mutually nonorthogonal. Formulas are derived for the calculation of higher‐order dynamic susceptibilities for steady states. An application is made to the H2 molecule, and results are presented for the frequency‐dependent polarizability and hyperpolarizability along the molecular axis. The static values obtained are α = 6.413 (6.387) and γ = 676 (674) atomic units, with exact numbers within parentheses.
Direct MRCI method for the calculation of relativistic many‐electron wavefunctions. I. General formalism
Authors: Esser M.
Published: December 2004

The formalism of a quasi‐ or full‐relativistic multireference CI method has been developed and implemented. The scheme is appropriate for the calculation of molecular systems in which the relativistic effects are of the same order of magnitude as the correlation contributions. In this contribution some important symmetry aspects of a relativistic many‐electron wave function are discussed and the consequences for the CI matrix structure are shown. An efficient CI strategy in the form of a direct CI is presented, which avoids the construction of the whole CI matrix. Based on a determinantal expansion of molecular spinor products, the individual one‐ and two‐electron molecular integrals are processed, and the molecular symmetry is easily accounted for by a proper linear combination of Slater determinants in the CI starting vector. For an efficient CI organization some powerful techniques of the graphical unitary group approach have been transferred to the relativistic case.
The metric properties of the reduced nuclear configuration space
Authors: Mezey Paul G.
Published: December 2004

A proof is given for the triangle inequality of distance function d in the reduced nuclear configuration space M, used in the differentiable manifold model of potential‐energy hypersurfaces [P. G. Mezey, Int. J. Quantum Chem. Quantum Chem. Symp. 17, 137 (1983)]. This result completes the proof that M is indeed a metric space with metric d.
Conformation of p‐dimethylaminobenzylidene‐p‐nitroaniline, p‐nitrobenzylidene‐p‐dimethylaminoaniline, their stilbene and azobenzene derivatives
Authors: Patnaik Lalit N. , Das Sarojini
Published: December 2004

PCILO computations have been carried out on the conformation of p‐dimethylaminobenzylidene‐p‐nitroaniline [I(m)], p‐nitrobenzylidene‐p‐dimethylaminoaniline [I(n)] and the corresponding stilbene [II(a)] and azobenzene [II(b)] derivatives. The aniline rings in Im and In are found to be twisted out of the plane containing the central atoms by 60° and 30°, respectively. The two phenyl rings in case of II(a) are twisted out of plane in opposite directions by 30° each. II(b) was found to be planar. The results have been compared with the earlier experimental findings and used as a possible explanation for the visible absorption spectra of the four molecules.
An alternative computational strategy for direct space hartree–fock calculations on extended model chains
Authors: Delhalle Joseph , Harris Frank E.
Published: December 2004

Based on previous analyses of slowly convergent exchange lattice sums entering the configuration space restricted Hartree–Fock–Roothaan scheme for chain systems, an alternative computational strategy is developed. Within the present formalism, the traditionally used finite Fourier transform of k‐dependent LCAO density matrices are by‐passed and an advantageous computational organization is obtained.
The valence bond description of conjugated molecules i.SCFlevel
Authors: Hiberty P. C. , Ohanessian G.
Published: December 2004

Aiming at developing an approximate method to get good quality valence bond functions for any closed‐shell delocalized system, we analyze their SCF functions in terms of weighted bonding schemes, and investigate the general rules relating the weights of ionic structures to those of covalent ones. The butadiene case is treated in details, and the results are generalized to all closed shell singlet conjugated molecules. It is demonstrated that, contrary to what an intuitive generalization of the two‐electron‐two‐center model would predict, each bond is not described as a half‐covalent, half‐ionic entity, but that the ionic component is significantly preponderant. Some consequences on the behavior of conjugated systems under the influence of an electric field are discussed.
Kinetic energy functional in hyperspherical coordinates
Authors: Linderberg Jan , Öhrn Yngve
Published: December 2004

Hyperspherical coordinates and a generator coordinate representation are employed to find a simple form of the kinetic energy for a general three‐particle problem. An expression is developed for the determination of adiabatic hyperangular states in a local potential using the finite element method.
The hydrogen molecule for a two‐dimensional system
Authors: Silva A. Ferreira Da , Fabbri M.
Published: December 2004

The two‐dimensional (2D) energy of the hydrogen molecule is carried out by the Heitler‐London method. The 2D integrals (which are more localized compared to 3D ones) are performed in the light of the 3D Slater integrals. A discussion of such 2D systems is briefly outlined for doped semiconductors.
Local behavior of the kinetic energy in density functional theory
Authors: Zorita M. L. , Alonso J. A. , Balbas L. C.
Published: December 2004

The local behavior of several approximate kinetic energy functionals is analyzed, for the case of free atoms and ions, by comparison with the local kinetic energy of Hartree–Fock theory. The atomic electron densities used are, in all cases, Hartree–Fock electron densities. The kinetic energy functional obtained by the gradient expansion method (with a small number of terms) is, locally, not very accurate, but its integrated value is fortuitously accurate, due to a strong cancellation of errors. Functionals which have the Weizsäcker term tw = (Δ ρ)2/8ρ as a key ingredient are more accurate locally. The explicit incorporation of the shell structure and nonlocal density effects into the kinetic energy functional leads to the best results. The motivation for this work is that only a kinetic energy functional with an accurate local behavior will give good electron densities on solution of the Euler equation derived from it.
On the rotational invariance of the fock equations in indo methods using d functions
Authors: Schulz Joachim , Iffert Rüdiger , Jug Karl
Published: December 2004

The rotational invariance of the Fock equations is investigated. It is demonstrated that the inclusion of d functions requires additional hybrid integrals which do not occur in the original version of INDDO. Calculations are performed with SINDO1 on binding energies, ionization potentials, and dipole moments to show the differences between the various levels of approximation.
Two‐Dimensional, fully numerical molecular calculations. IV. hartree–fock–slater results on second‐row diatomic molecules
Authors: Laaksonen Leif , Sundholm Dage , Pyykkö Pekka
Published: December 2004

Fully numerical two‐dimensional Hartree–Fock–Slater calculations are reported for the diatomic molecules B2, C2, N2, CO, O2, F2, and BF. The model is identical to Becke's but the numerical method is different. Fully numerical ground‐state total and orbital energies are reported for the first time. The basis‐set truncation error in the LCAO calculations of Dunlap, Connolly, and Sabin influence the third and fourth decimals (in a.u.) of ET and ϵi respectively. Benchmarks of improved accuracy are provided for dissociation energies, bond lengths, and electronic multipole moments for future assessment of basis‐set errors.
Numerical method for the open‐shell restricted hartree–fock density‐matrix direct calculation
Authors: Mestechkin M. M.
Published: December 2004

A new computation procedure for direct calculation of the density matrix in the LCAO version of the restricted Hartree–Fock–Roothaan open‐shell theory is analyzed. It is proved that the procedure is quadratically convergent and stable to the round‐off errors independently of the Fock operator spectrum. The dependence of the limit matrix of the initial matrix is examined.
Ab initio calculations on H transfer in the HF trimer
Authors: Heidrich D. , Köhler H.‐J. , Volkmann D.
Published: December 2004

Systematic ab initio LCAO MO calculations with basis sets of increasing size have been performed to analyze the changes in relative stabilization energies of the two cyclic (D3h and C3h symmetry) and the noncyclic HF trimers. The results form the basis for a discussion of cyclic H‐transfer reactions.
Ab initioMODPOT/VRDDO/MERGE calculations on energetic compounds. IV. Nitrocubanes: Mononitro to octanitro quantum chemical calculations and electrostatic molecular potential contour maps
Authors: Hariharan P. C. , Kaufman Joyce J. , Lowrey Alfred H. , Miller Richard S.
Published: December 2004

Ab initio MODPOT/VRDDO/MERGE calculations have been carried out for all the different position isomers of nitrocubane from mononitrocubane through octanitrocubane for a perfect symmetrical cubic cubane skeleton and for mononitrocubane through septanitrocubane for the almost cubic experimentally determined cubane skeleton. These calculations were carried out with our own rapid efficient ab initio programs which also incorporate a number of desirable computational strategies for calculations on large molecules. The skeletal total overlap population of the cubane skeleton (a theoretical index we showed years ago to be sensitive and predictive of stability of energetic molecular frameworks) indicates that successive nitration seems to increase the stability of the cubane skeleton. Successive nitration also seems to increase the total overlap population of the CNO2 bond. There are subtle differences depending on the exact positional isomer for a constant number of nitro groups—but the overall trend is definite. We have also generated electrostatic molecular potential contour (EMPC) maps around these nitrocubanes. These maps are indicative of preferred positions of electrophilic and nucleophilic attack as a function of the number of nitro groups or their positions. These EMPC maps can also indicate, to a first approximation, a limit on how close these molecules may be able to approach each other in a crystal.
Consistent propagator approximations
Authors: Weiner Brian
Published: December 2004

A propagator approximation scheme is presented in the context of an abstract*‐algebra approach. The representation theory of such algebras is shown to play a crucial role in the definition of consistent approximations, i.e., approximate propagators based on model time evolutions and states. This procedure places superoperator methods of approximation on a sound Hilbert space footing. A generalization of the Fock vacuum property is introduced which leads to a simplification in the form of the model propagators. Finally a concrete example is considered that fulfills the conditions developed in this article showing that a consistent approximation to the electron propagator results in the Hartree–Fock–Boguliubov equations.
Energies of vibrating and rotating molecules by ladder operators
Authors: Huber Daniel
Published: December 2004

A method which is well suited for calculating numerically the energies of the bent vibrating and rotating polyatomic molecule is given. By an analytical method using ladder operators the work of calculating the matrix elements of the Watson Hamiltonian is reduced to mere bookkeeping. This results in fast computation and good control of the errors introduced. To demonstrate the practical usefulness of the method, three test calculations on H2O and SO2 are reported and compared with results from the literature. It is intended to distribute the computer program developed to interested workers in the field.
Effect of hubbard interaction on solitonic excitations in polyacetylene
Authors: Kulkarni Anil D. , Alexander S. A. , Matsen F. A.
Published: December 2004

We have studied the effect of Hubbard interaction on solitonic excitations in the polymer trans‐polyacetylene. These excitations are modeled using the Su, Schrieffer, and Heeger (SSH) Hamiltonian. Within this framework, we have calculated the full configuration interaction and restricted Hartree‐Fock energies of solitonic excitations in trans‐polyacetylene chains with 4–10 carbon atoms. These results are extrapolated to longer chains, and it is shown that the correlation energy for these chains approaches 3%. Thus, our calculations provide a justification, hitherto absent, of the accuracy of the Hartree‐Fock calculations reported in the literature.
Least‐squares numerical Rayleigh‐Ritz and minimum‐variance methods for molecular calculations
Authors: Thole B. T.
Published: December 2004

A general method is presented to find in a least‐squares sense a set of orthogonal eigenfunctions and their eigenvalues from local energy and numerical integration methods or by any other dissymmetric approach to solve the eigenvalue problem of a Hermitian operator. By this method a generalization of the minimum variance method to more than one eigenfunction is obtained, which is a variant of Scott's method. Also a new method is derived—called the minimum‐overlap method—that is a least‐squares numerical version of the standard Rayleigh‐Ritz method. Test calculations on the atoms Be and Tm and the molecules H2 and CO have been performed with both numerical Hartree‐Fock and Hartree‐Fock‐Slater methods. The least‐squares solutions are an improvement over other methods in the case of accurate basis sets. Numerical Hartree‐Fock calculations of moderate accuracy are found to be considerably faster than the analytic method.
Adiabatic SCF potential energy curves relevant to proton–oxygen molecular collisions
Authors: Staemmler V. , Gianturco F. A.
Published: December 2004

The large vibrational inelasticity observed in proton–O2 scattering at collision energies of ∼10.0 eV and for various angular distributions below the rainbow region is examined in terms of SCF adiabatic potential energy surfaces which exhibit strong O “character” within a specific range of relative distances between colliding partners. The possibility for this O2 distortion during encounters with protons to be responsible for the unusually large inelasticity is discussed and the time factors that are likely to play an important role during the dynamics are also considered and analyzed.
Effect of some factors on the energy band structure of proteins
Authors: Yi Xiao , Run‐Sheng Chen
Published: December 2004

The effects of four factors (different side chains, side‐chain disorder, conformational change, and ions and water) on the energy band structures of proteins have been investigated with the aid of the CNDO/2 crystal orbital method. The results indicate that these factors are very important. The consequences of these effects on the semiconductive properties of proteins are discussed.
A quality test for the Hartree‐Fock‐Roothaan SCF wave functions
Authors: Sordo J. A. , Pueyo L.
Published: December 2004

A quality test for the SCF wave function based on separate examination of the one‐ and two‐electron contributions to the total energy is proposed. The test is applied to 12 different STO basis sets for the ground state of the Ni atom and its predictions compared with those deduced for the minimization of the total energy. The new test allows for a reduction in the cancellation of errors detected in some applications of the standard SCF procedure. Some relations between the quality of the basis set and its size and structure are discussed.
Orbital correlation diagrams based on multiconfigurational variation of moments I. Theory
Authors: Müller‐Remmers Peter L. , Jug Karl
Published: December 2004

A multiconfigurational variation of moments (MCM) is presented to determine correlated orbital energies. Appropriate multiconfigurational one‐particle operators are introduced starting for closed‐shell systems from the restricted Hartree–Fock (RHF) scheme and for open‐shell system from the unrestricted Hartree–Fock (UHF) scheme. The advantage of these operators is the linear form of the correlation energy in the configuration interaction (CI) coefficients. They obey HF analogous pseudoeigenvalue equations and are therefore a generalization of the HF operator. In principle, the scheme can be extended to a multiconfiguration self‐consistent field (MCSCF) procedure for moments. In contrast to the SCF formalism they allow an orbital description of degeneracy and quasidegeneracy of the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbital. With these operators, funnels of thermally forbidden Woodward–Hoffman reactions, as well as dissociations, can be described in a physically meaningful fashion by orbitalcorrelation diagrams.
Orbital correlation diagrams based on multiconfigurational variation of moments II. Application
Authors: Müller‐Remmers Peter L. , Jug Karl
Published: December 2004

A formalism was developed in the multiconfigurational variation of moments (MCM) framework, which yields physically meaningful orbital energies for occupied and virtual orbitals starting from self‐consistent field (SCF) calculations. This is possible through a skillful distribution of the correlation energy on the orbital energies. The application of this method is demonstrated by SINDO1 calculations on the dissociation of H2 and the following symmetry‐forbidden reactions: (1) torsion of ethylene; (2) ring opening of (a) cyclobutene, and (b) cyclopropyl cation; (3) cycloreversion of 1, 1‐dicyano‐2‐methoxycyclobutane. The allowed reactions corresponding to 2a and 2b are investigated in the SCF scheme. The energy hypersurfaces are calculated for all reactions and the MO correlation diagrams are presented and discussed.
On the electronic structure of transition‐metal complexes II. Bonding characteristics in titanium chloride systems
Authors: Hilal Rifaat
Published: December 2004

The electronic structure of [TiCl4]n systems (n = 0, −1, −2, −3, and −4) has been investigated by the INDO method. Calculations show the stability of the tetrahedral structure over the square‐planar one, for any value of n, in accord with experimental observation. The occupation of the 4p orbitals of the titanium atom was found to increase regularly as the dihedral angle decreases and reaches a maximum at the square‐planar conformation. Energy partitioning analysis enabled much deeper understanding of bonding characteristics of the studied systems. It has been shown that the one‐atom energy component may be a very sensitive measure of the stability of the central metal atom in its various oxidation states.
Theoretical investigations of the electronic states of porphyrins. III. Low‐lying electronic states of porphinatoiron(II)
Authors: Rawlings Diane C. , Gouterman Martin , Davidson Ernest R. , Feller David
Published: December 2004

Ab initio configuration interaction calculations are reported on the lowest quintet, triplet, and singlet states of FeII(P). Due to the large number of states found, a catalog of the low‐lying states is presented. Novel triplet and quintet charge‐transfer states are reported as low as 1.3 eV. These states are d5 (S = 5/2) on the iron low‐spin‐coupled to the radical anion excited porphyrin ring (S = 1/2 or 3/2). Oscillator strengths originating from each of three low‐energy triplet states are reported.
Correlation contributions to the radical cation states of linear even polyenes: An open‐shell RHF‐CNDO/S(CI) analysis of the optical and photoelectron spectra
Authors: Bigelow Richard W.
Published: December 2004

Configuration interaction wave functions are calculated for the low‐lying radical cation states of trans‐butadiene, hexatriene, and octatetraene within the open‐shell RHF‐CNDO/S(CI) approach. The consequences of various one‐electron contributions to the interpretation of existing photoemission and radical cation optical spectra are emphasized. Electron correlation is shown to be essential to achieve adequate energy and intensity profiles assuming photoelectron or optical excitation. The excitation energies and transition amplitudes (optical and photoemission) are also found to be sensitive to the molecular geometry. The present results are consistent with previous interpretations that photoionization measurements probe the neutralmolecule alternating single‐double bond‐length structure, whereas optical excitation samples an ion‐state–state–induced “relaxed” reference configuration having a weakened bond‐length alternation. Calculated trends in the spectroscopic properties are extrapolated to extended members of the even‐polyene series.
Intermolecular interactions: Elaboration on an additive procedure including an explicit charge‐transfer contribution
Authors: Gresh N. , Claverie P. , Pullman A.
Published: December 2004

An additive procedure is derived for the computation of intermolecular interactions, in which an explicit expression for the charge‐transfer energy contribution ECT is implemented. In the total interaction energy,

the electrostatic terms EMTP and Epol are calculated as in our previous treatment. The dispersion contribution is calibrated by reference to variation‐perturbation computations on model systems and the repulsion contribution is computed as a sum of bond—bond, bond—lone pair, and lone pair—lone pair interactions. Tests of the procedure are given for representative hydrogen‐bonded systems.
Direct evaluation of spin representation matrices and ordering of permutation‐group elements
Authors: Rettrup Sten
Published: December 2004

A direct and general method is presented for constructing the orthogonal spin representation matrices (irreps) of the permutation group corresponding to the Yammanouchi‐Kotani coupling scheme. For arbitrary permutations the irreps are constructed directly from the Young tableaus by a process which is, in general, only quadratic in the number of spin eigenfunctions, but which in actual computations becomes linear on vector computers for moderate sizes of the matrices. We also introduce a graphical representation of the group elements and a universal lexical ordering of permutations. The methods have been implemented and computational examples are presented.
Comparison of theory and experiment for excited singlet states of the H2 molecule
Authors: Dressler K. , Wolniewicz L. , Quadrelli P.
Published: December 2004

This paper presents a survey of published and unpublished ab initio calculations of the vibrational structures of the ten lowest electronic singlet states of the hydrogen molecule up to the H(n = 1) + H(n = 2) dissociation limit. The data are based on adiabatic potential functions (clamped‐nuclei electronic energies and nuclear‐mass‐dependent diagonal corrections). Nonadiabatic coupling has been treated ab initio within the five states. of 1Λ symmetry (X,EF, GK, HH̄) and 1Σ I.1Πg. The accuracies of the theoretical energies are determined by comparisons with experimental data for H2, HD, and D2. The level shifts and predissociation probabilities of the excited 1Σ states, generated by nonadiabatic coupling with the discrete and continuous vibrational structure of the ground state, and radiative properties have also been calculated.
Use of coupled‐cluster based linear response theory and multireference hermitian MBPT to IP calculations of HF
Authors: Roy S. , Sengupta S. , Mukherjee D. , Mukherjee P. K.
Published: December 2004

We report in this paper the results of outer and inner valence IP calculations for the HF molecule using two different many‐body methods for the direct evaluation of energy differences. The first is the nonperturbative coupled‐cluster based linear response theory (LRT) and the second is the hermitian open‐shell many‐body perturbation theory (MBPT). A Huzinaga‐Dunning (9s5p→ 5s3p/3s) basis has been used. LRT uses an “ionization operator” S as in the equation of motion method (EOM) to generate the ionized states from a coupled‐cluster type of ground state. S is chosen to consist of single ionization and ionization‐cum‐shake‐up operators, thus treating the Koopmans as well as the shake‐up states on equal footing. LRT would thus be capable of computing both the outer and the inner valence regions with equal facility. This is borne out by the results. For the open‐shell MBPT, the model space is chosen to be spanned by the singly ionized determinants. The convergence of the results for the inner valence region is slow, and the results obtained from the [2, 1] Pade' approximants are presented. Unlike the LRT, the inner valence region is not reproduced with full complexity in MBPT, indicating that it is essential to modify the theory by way of expanding the model space to contain the shake‐up determinants also.
LCGTO‐LSD calculations for CH2
Authors: Radzio E. , Salahub D. R.
Published: December 2004

LCGTO‐LSD calculations for ground (3B1) and excited (1A1) states of methylene, CH2, have been performed. Various exchange‐correlation potentials and a variety of basis sets (including f functions) have been used. For both states the LSD optimized geometry agrees well with both experimental and the most advanced ab initio results. The correct ground state is found, and the 1A1‐3B1 energy separation was found to be ∼ 15 kcal/mol, using the “best” local exchange‐correlation potential (VWN), the experimental value being ∼ 9 kcal/mol. This result compares favorably with the Hartree‐Fock limit separation of 25 kcal/mol. The Kohn‐Sham exchange potential leads to a gap of ∼26 kcal/mol.
Charge distributions and chemical effects. XLII. Atomic charges and their role in energy calculations
Authors: Fliszár S.
Published: December 2004

A physically meaningful charge partitioning rooted in Mulliken's scheme meets with success, provided the usual equipartitioning of overlap populations involving dissimilar atoms is abandoned in favor of a constraint rendering all alkane carbons as similar as possible to one another. Charge analyses are to be carried out after configuration interaction involving reasonably large optimized basis sets. At this level, both the relative ordering and the magnitude of theoretical atomic charges in hydrocarbons are precisely those required for energy calculations of alkanes and alkenes featuring atomic charges in an explicit manner.
Invalidity of the ubiquitous mass‐velocity operator in quasirelativistic theories
Authors: Farazdel Abbas , Smith Vedene H.
Published: December 2004

The general problem of relativistic corrections to the kinetic energy in quasirelativistic theories, is discussed and related formulas are developed. It is shown that the well‐known mass‐velocity operator, Hmv = (−α2/8)p4, is incorrect and does not provide any proper relativistic corrections.
What do kinetic‐energy anisotropies tell us about chemical bonding? I. Diatomic hydrides
Authors: Sharma B. S. , Thakkar Ajit J.
Published: December 2004

The kinetic‐energy anisotropies of fifteen diatomic hydrides AH with A = H, Li, Be, B, C, N, O, F, Na, Mg, Al, Si, P, S, Cl are calculated from self‐consistent‐field wave functions constructed from extended basis sets of Slater‐type orbitals. It is found that there is no consistent ordering of the bond‐parallel and bond‐perpendicular components of the kinetic energy with respect to separated atom values. An analysis of the orbital contributions reveals that nonbonding π orbitals make large contributions to the total kinetic‐energy anisotropy. This makes it difficult, if not impossible, to deduce anything about the nature of the chemical bond from the total anisotropy. However, certain dimensionless orbital kinetic‐energy anisotropies are useful for interpretative studies because, in free atoms, these quantities have fixed values that depend only on the symmetry of the orbital.
Counterpoise corrections to the components of bimolecular energy interactions: An examination of three methods of decomposition
Authors: Bonaccorsi Rosanna , Cammi Roberto , Tomasi Jacopo
Published: December 2004

Counterpoise corrections for the basis set superposition error to the components of the bimolecular interaction energy are defined for three methods of decomposition. The results for the case of the NH3 + BH3 interaction are presented and discussed.
Study of photoelectron spectra of some XPY3 molecules (X = O, S and Y = Cl, Br) by the SCF‐Xα‐SW method
Authors: Pan Y. K. , Xin M. , Li D. , Chiu Lue‐Yung Chow
Published: December 2004

In this paper we extend our previous studies to investigate the ionization energies of some XPY3 molecules (X = O, S and Y = Cl, Br). The calculated orbital energies agree very well with reported experimental ionization energies. The molecular orbital orderings obtained coincide with recent experimental orbital assignments. The results are also compared with previous ab initio and semiempirical calculations for OPCl3, OPBr3, SPCl3, and SPBr3 molecules. The comparison indicates that the present results show improved agreement with experiment and clarify certain ambiguities in the earlier assignments.
Combining perturbation theory techniques with variational CI calculations to study molecular excited states
Authors: Buenker Robert J.
Published: December 2004

The accurate treatment of molecular excited states is based on a matrix solution of the electronic Schrödinger equation in a suitable AO basis which relies heavily on the existence of a good approximate description of a given eigenfunction prior to the solution of a secular equation. The manner in which one or more roots corresponding to excited states can be traced from a rather simple starting point to the final results obtained from a large‐scale CI treatment is outlined. In such calculations it is very useful to have a measure of the energy‐lowering capability of configurations which differ by at most a double excitation from a series of reference configurations which represent the dominant contributions to one or more electronic states. The efficient computation of the required Hamiltonian matrix elements for this purpose, as well as for the construction of the final secular equations, can be achieved through the use of the table CI method, which does not rely on any special relationship between configurations to complete its work. Employing CI expansions of length no greater than 10000‒20000 terms is very advantageous for the calculation of special properties of the resulting wavefunctions, especially those of spin‐dependent quantummechanical operators. With the help of perturbative corrections it is possible to obtain energy results with such methods which are accurate to within 0.01 hartree of the full CI limit [R. A. Phillips, R. J. Buenker, P. J. Bruna, and S. D. Peyerimhoff, Chem. Phys. 84, 11 (1984)], whose error is small compared to that inherent in the use of conventional double‐zeta‐plus‐polarization AO basis sets, therefore making further reduction of the CI errors almost inconsequential. Numerous examples for the calculation of the energy and properties of molecular excited states are surveyed.
Optimal spacing and weights in diffusion monte carlo
Authors: Vrbik Jan , Rothstein Stuart M.
Published: December 2004

We describe how to select optimal values of the time step τ and how to allocate computer time in order to minimize the error bar of the unbiased energy estimate (τ = 0 limit) in diffusion Monte Carlo simulations (DMC). Several polynomial models are considered, appropriate for both linearly biased and quadratically biased algorithms. An efficient nonoptimal design is also reported, which has the advantage of checking the model's adequacy. Further, we compare the efficiency of linearly biased and quadratically biased DMC, and we estimate the efficiency of DMC versus Green's function Monte Carlo.
Bond orders and valences from ab initio wave functions
Authors: Mayer I.
Published: December 2004

The definition and properties of the bond order and valence indices calculated from ab initio wave functions are summarized. Their physical interpretation relationships to the exchange effects in bonding and generalization to correlated wave functions are also discussed. Some examples with typical bond order and valence values are shown.
Quantum chemistry by quantum monte carlo: Beyond ground‐state energy calculations
Authors: Reynolds P. J. , Barnett R. N. , Hammond B. L. , Grimes R. M. , Lester W. A.
Published: December 2004

We present recent advances with the quantum Monte Carlo (QMC) method in its application to molecular systems. The QMC method is a procedure for solving the Schrödinger equation statistically, by the simulation of an appropriate random process. The formal similarity of the Schrödinger equation with a diffusion equation allows one to calculate quantum mechanical expectation values as Monte Carlo averages over an ensemble of random walks. We have previously obtained highly accurate correlation energies for a number of molecules, as well as the singlet‐triplet splitting in methylene and the barrier height for the H + H2 exchange reaction. Recently we have begun a program of extending the QMC approach to the calculation of analytic derivatives of the energy. A brief description of the approach is presented here, together with some preliminary results. In addition, we are now computing expectation values of properties other than the energy. We summarize how standard QMC must be modified, and present some results for H2 and N2. Finally, we describe preliminary work toward the goal of obtaining accurate molecular excited states through QMC.
Semiclassical time‐dependent theory of two‐photon spectroscopy. The effect of dephasing in the virtual level on the two‐photon excitation spectrum of isotachysterol
Authors: Birge Robert R. , Pierce Brian M.
Published: December 2004

It is commonly assumed that the nonlinear absorption of two photons is a process involving the simultaneous capture of two radiation quanta. The purpose of this paper is to evaluate semiclassically the spectroscopic consequences of relaxing this assumption by permitting dephasing in the virtual level. Semiclassical wave‐packet propagation theory is used to model the vibronic consequences of finite, virtual‐state population times. We demonstrate that extremely short virtual‐state lifetimes (1‒10 femtoseconds) can have a profound effect on two‐photon excitation line shapes and total vibronic envelopes. We provide experimental evidence suggesting that virtual state dephasing has an important influence on the two‐photon excitation spectrum of the polyene chromophore of isotachysterol. Our analysis suggests that dephasing in the virtual state is of poetntial importance in defining the vibronic development of two photon spectra of many polyatomic molecules in solution.
Basis‐Set dependence of exterior electron distributions of molecular orbitals
Authors: Ohno Koichi , Ishida Toshimasa
Published: December 2004

Interior electron densities are divided from exterior electron densities (EED), when an effective boundary is introduced. The EED concept was used to study the quality of wavefunction tails; the basis‐set dependence of ab initio MO for NH3 was studied from EED. The EED for the nonbonding orbital (3a1) increases dramatically with the size of basis sets, whereas that for the bonding orbital (1e) shows saturation even at the double zeta class. Although inclusion of polarization functions always gives the better total energy the EED (3a1) may either increase or decrease or decrease depending on the choice of the smaller or the larger exponents. The conventional choice of the polarization functions for 6‐311G* and 6‐311G* was found to yield worse wavefunction tails than the case of 6‐311G. Much better results were obtained with the more diffuse polarization functions. The (11s7p)/[5s4p] set designed for Rydberg states as well as the 6‐311 + G set proposed for negative ions gave excellent results comparable to the case of the near Hartree‐Fock calculation with 56 CGTO. Considerable improvements were also achieved for 4‐31G and 6‐311G sets, when the exponent for the outermost s‐type function was modified. The largest EED (3a1) gave the best agreement with the experimental ratio of EED's derived from Penning ionization electron spectroscopy.
Structural deformations of the DNA double helix in the first stages of DNA transcription studied with a simple model
Authors: Bonaccorsi R. , Scrocco E. , Tomasi J.
Published: December 2004

A very simple model of DNA in biological media, consisting of electric charges related to the phosphate groups and to counterions immersed in structured media of constant permittivity, is introduced and tested with the study of a model for the first stages of the DNA transcription.

This process is modeled into two steps involving three ‘states’: (1) the DNA system at the equilibrium, (2) the DNA with a small portion deprived of counterions, and (3) the DNA with a partial opening of the double helix in correspondence of the zone deprived of counterions.

An extensive investigation involving as variable parameters the length of the DNA specimen (from 31 to 1511 base pairs), the amount of condensed counterion charge (from complete compensation to zero), and the geometrical parameters identifying the local opening has shown that the proposed transcription mechanism is reasonable, and that the DNA model considered here may fill a gap between accurate models including all the interactions—and employed at present for small fragments—and unstructured models addressed to inspect the behavior at the limit of infinite DNA length.
Semidiffuse states of diatomic molecules: Configuration interaction studies of the lowest 2Σ+ and 2Δ states of NS, SiF, and CCl
Authors: Karna S. P. , Grein F.
Published: December 2004

It has been shown by ab initio configuration‐interaction methods that the lowest 2Σ+ states of NS and SiF are ‘semidiffuse’ states, like the B 2Σ+ state of PO. The lowest 2Σ+ state of CCl also appears to be semidiffuse, although here the situation is not so clear. Semidiffuse states require diffuse orbitals in the wavefunction, but they are not Rydberg states. The second 2Σ+ state of each molecule is shown to be the lowest ns Rydberg state, whereas the third 2Σ+ state is a valence state for NS and CCl, and a 4po Rydberg state for SiF. The lowest 2δ state of each molecule derives from the 7σ → 3π valence configuration. Comparison with available experimental information shows, in general, good agreement.
Chemisorption of O and O2 on Ag(110): An LCGTO‐LSD cluster study
Authors: Selmani A. , Andzelm J. , Salahub D. R.
Published: December 2004

As part of a study aimed at better understanding of molecular and dissociative chemisorption of oxygen on Ag(110), linear combinations of Gaussian type orbitals‐local spin density (LCGTO‐LSD) calculations have been performed for O, O−, O2, O−2, O2−2 and a variety of silver clusters interacting with O or O2.

For atomic O adsorption a very small cluster, Ag4, chosen to model the long‐bridge site already affords very good agreement with both recent EXAFS experiments and recent ab initio calculations. We calculate O to be 0.25 Å above the surface (exp. 0.2 Å). The Ag4O vibrational frequency is estimated to be 400 cm−1, in reasonable accord with the experimental EELS value of 325 cm−1.

Determination of the geometry for O2 (ads.) and, ultimately, of the dissociation path are far more difficult tasks. An extensive search for local minima in the vicinity of the LB site is being carried out. Results to date for small, Ag2 and Ag4, clusters have furnished insight into the factors influencing the structure. Overlap between the π* orbital of the O2 moiety and Ag s functions is a key factor; that is, there is an important covalent component of the binding. For geometries with O2 parallel to the surface, this is achieved by twisting the O2 fragment with respect to the [11¯0] grooves (geometries either parallel or perpendicular to the grooves yield zero π‖*−s overlap by symmetry). The structure with O2 perpendicular to the surface also achieves reasonable overlap and lies close in energy to the most stable ‘parallel’ geometry.
On the minimization of the global variance in the 1‐Reduced local‐energy matrix
Authors: Thomas Gerald F.
Published: December 2004

By minimizing the global variance in the 1‐reduced local‐energy matrix E1(X1; X1′), subject to the normalization of the 1‐reduced density matrix ρ1(X1;X1′), one derives an integral matrix equation for E1(X1;X1′) as a functional of ρ1(X1;X1′) at the location (X1;X1′) of an arbitrary member of an N (≥ 2)‐particle system. The implications for the possible local improvement in the accuracy of approximate wave functions through the imposition of global constraints are briefly discussed.
Electronic structure calculations for the molecules Si2 and Ge2 using all electron ab initio HF‐CI methods
Authors: Shim Irene , Nagarathna‐Naik H. M. , Gingerich Karl A.
Published: December 2004

Molecular orbitals for Si2 and Ge2 have been optimized in hyper‐HF calculations and utilized in valenxe CI treatments to describe the low‐lying states of the molecules. The calculational results reveal pronounced similarities between the electronic structures of Si2 and Ge2. Thus, for both molecules the two lowest‐lying electronic states, 3Σ(σΠu3) and 3πu(∑g1πu3), have crossing potential energy curves, and the two lowestlying states of 1∑g+ symmetry exhibit crossing of configurations. The Sequence of the low‐lying electronic states can be rationalized on basis of a simple molecular‐orbital picture in which the σg and the πu valence orbitals are almost degenerate. The spectroscopic constants derived from the present work compare favorably with the results of more elaborate calculations. It appears that transition energies derived in valence CI calculations between states of identical configurations are improved in large CI calculations, whereas this is not the case for transition energies between states of different configurations. The valence CI calculations based on the molecular orbitals optimized in hyper‐HF calculations appear to effer reliable descriptions of the chemical bonds as well as of the electronic structures of the molecules Si2 and Ge2.
Ab initio calculations on the barrier height for the hydrogen addition to ethylene and formaldehyde. The importance of spin projection
Authors: Sosa Carlos , Bernhard Schlegel H.
Published: December 2004

Heats of reaction and barrier heights have been computed for H + CH2CH2 → C2H5, H + CH2O → CH3O, and H + CH2O → CH2OH using unrestricted Hartree‐Fock and Møller–Plesset perturbation theory up to fourth order (with and without spin annihilation), using single‐reference configuration interaction, and using multiconfiguration self‐consistent field methods with 3‐21G, 6‐31G(d), 6‐31G(d,p), and 6‐311G(d,p) basis sets. The barrier height in all three reactions appears to be relatively insensitive to the basis sets, but the heats of reaction are affected by p‐type polarization functions on hydrogen. Computation of the harmonic vibrational frequencies and infrared intensities with two sets of polarization functions on heavy atoms [6‐31G(2d)] improves the agreement with experiment. The experimental barrier height for H + C2H4 (2.04 ± 0.08 kcal/mol) is overestimated by 7‒9 kcal/mol at the MP2, MP3, and MP4 levels. MCSCF and CISD calculations lower the barrier height by approximately 4 kcal/mol relative to the MP4 calculations but are still almost 4 kcal/mol too high compared to experiment. Annihilation of the largest spin contaminant lowers the MP4SDTQ computed barrier height by 8‒9 kcal/mol. For the hydrogen addition to formaldehyde, the same trends are observed. The overestimation of the barrier height with Møller‐Plesset perdicted barrier heights for H + C2H4 → C2H5, H + CH2O → CH3O, and H + CH2O → CH2OH at the MP4SDTQ/6‐31G(d) after spin annihilation are respectively 1.8, 4.6, and 10.5 kcal/mol.