bluuebunny/crossref_metadata_2025_split huggingface dataset:
Perturbative ab initio calculations of intermolecular energies. III. The water dimer
Authors: Daudey J. P. 
Published: December 2004

AbstractThe interaction energy between two water molecules A and B is calculated by the method described in Paper I [1], previously applied for the interaction between two helium atoms (Paper II) [2]. This interaction energy is obtained as the difference between the energies of the complex (A + B) and the monomers (A) and (B), obtained by a perturbation method. The results obtained with the perturbation developed up to the second order in a minimal atomic basis set are decomposed into classical contributions and contributions linked to the exchange possibility. Charge transfer contributions are important and the localized character of the hydrogen bond is examined. It is pointed out that the definition of the set of excited configurations for the calculation of the energies of the isolated monomers is important, especially when one tries to use a small atomic basis set. A similar effect in SCF‐type calculations is evaluated. The contribution of higher orders is evaluated by the CIPSI method.
Matrix formulation of the generalized Hartree‐Fock methods
Authors: Mestechkin M. M. , Whyman G. E. 
Published: December 2004

AbstractSpin‐projected one‐particle density and spin density matrices are presented as polynomials of suitable unprojected quantities with generalized Sasaki‐Ohno coefficients. Thus an explicit form of Harriman's theorems is given. For the two‐particle spatial density matrix an expansion in direct products of powers of unprojected residual electron and spin density matrices is given. For these basic matrices of the scheme the variational spin‐extended equations are formulated.
Configuration interaction calculations on the nitrogen molecule
Authors: Langhoff Stephen R. , Davidson Ernest R. 
Published: December 2004

AbstractA contracted Gaussian basis set capable of describing about 63% of the correlation energy of N2 has been used in a detailed configuration‐interaction calculation. Second‐order perturbation theory overestimated the correlation energy by 23–50% depending on how H0 was chosen. Pair‐pair interaction affects the correlation energy by about 20% while quadruple excitations have an 8% effect.
Accurate analytical self‐consistent field wave functions for Tm2+ and Tm3+
Authors: Damommio A. , Synek M. 
Published: December 2004

AbstractThe analytical expansion self‐consistent field method was employed to perform ab initio calculations for the ground states of the rare‐earth ions, Tm2+, 4f13, 2F, and Tm3+, 4f12, 3H, (Z = 69). In each case the total number of basis functions used in the analytical expansions was 29, distributed as follows: 10, 8, 5, and 6, for the symmetries s, p, d, and f, respectively. All of the orbital exponents of the basis functions were optimized repeatedly, to the extent of the single‐precision computer representation. Values of 〈rn〉 for the 4f orbital of both ions are also presented, for the convenience of experimentalists.
More on molecular electronic structure of metal phthalocyanines
Authors: Mathur S. C. , Singh Jai 
Published: December 2004

AbstractMolecular orbitals of some of the 3d‐transition metal phthalocyanines have been calculated. π‐Electron charge densities over the atomic sites and the optical properties of the metal phthalocyanines have been calculated. The effect of the introduction of different metal atoms in the centre of the organic ring on the physical properties of the metal phthalocyanines has been discussed.
Variation of the polarizability of the hydrogen molecule ion and the hydrogen molecule with internuclear separation
Authors: Zeroka Daniel 
Published: December 2004

AbstractThe variation of the polarizability of H and H2 with internuclear separation R = 1.6 – R = 2.4 a.u. for H and R = 1.0 – R = 2.0 a.u. for H2 is determined using a variational method suggested by Das and Bersohn. From these data, values of 〈α〉0,J for which nuclear motion due to zero point vibration and centrifugal stretching is taken into account, are calculated at 300°K. The relative percent increases of the motion averaged values compared to the equilibrium values are as follows: 10.50% for H and 6.52% for H2.
Floating one‐center perturbation treatments for H‐like molecules based on screened hydrogen atom or molecular puff unperturbed problems
Authors: Ali M. K. , Meath William J. 
Published: December 2004

AbstractVarious floating one‐center perturbation schemes are developed for H‐like molecules. Previous work for the ‘1s’ hydrogen atom approach is extended through third order in the energy. In the molecular puff approach an exact ‘closed form’ solution is obtained for the zeroth‐order problem, which corresponds to a double layer molecular puff. Semianalytical results for the first‐order correction to the floating molecular puff wave function and for the energy through third order are developed which offer a convenient alternative to previous approaches. Explicit calculations for ground state H show that for R > 3aO the ‘1s’ and the more complicated ‘puff’ treatments are equivalent and that neither the ‘1s’nor the molecular puff function is an adequate zeroth‐order wave function for the important intermediate values of R. The usefulness of some of these methods in a variety of problems, where one‐center zeroth‐order wave functions do appear to be adequate, is discussed briefly.
Application of the distinguishable electron method
Authors: Chong Delano P. , Scott William R. , Yue Chee P. , Wang Pearl S. C. , Benston Margaret L. , Palke William E. 
Published: December 2004

AbstractIn order to make a better assessment of the distinguishable electron method developed by Kirtman and co‐workers, we have applied the method to some two‐electron atoms and to H2 and LiH. Our results lend support to the contention held by Kirtman and co‐workers that the distinguishable electron method is a practical way of calculating reasonably accurate physical properties.
Unified treatment of two‐electron integrals. II. One‐center, electron repulsion, spin‐spin and spin‐orbit integrals containing rij
Authors: Matcha Robert L. , Milleur Mac B. 
Published: December 2004

AbstractGeneral formulas are obtained for evaluating a basic type of one‐center two‐electron integral which arises in the computation of expectation values of spin‐spin and spin‐orbit operators over explicitly correlated wave functions. The correlation terms are assumed to be in the form of products of Slater functions and powers (not necessarily integer) of the interelectronic coordinate rij.
Hybridization by the maximum overlap method
Authors: Randić Milan 
Published: December 2004

AbstractA brief survey of the maximum overlap method is presented and some computational aspects of the approach are discussed. The hybrid compositions and bond overlaps are reported for some thirty small ring compounds and a list of characteristic hybrids for various structural environments is given. The table of characteristic hybrids is extended to acyclic hydrocarbons and the transferability of the maximum overlap hybrids is demonstrated. Those aspects of the method which depend on geometrical properties of molecules have been considered in some details and the discussion is extended to some structural features of cyclic systems. In particular the asymmetry of bonds of spiro carbon atom is examined and rationalization of puckering of large macrocyclic systems is presented. In the summary it is pointed to the method and its potential to discuss structural aspects of molecules at the particular level of accuracy expected to be of great use in organic and physical organic chemistry. Further development and improvement of the method is mentioned, but already in the present form it can produce hybrids which may constitute a useful basis for other more ambitious semiempirical calculations.
The hammerstein integral equation: a general technique for constructing a rapidly convergent padé‐type approximation to the logarithmic derivative
Authors: Pulfer J. D. , Whitehead M. A. 
Published: December 2004

AbstractThe radial one‐electron Schrödinger equation can be written as a nonlinear first‐order differential equation by making a suitable logarithmic transformation. The resulting Riccati equation has the equivalent Hammerstein integral representation [1],

where the kernel, N(r, r′) is

and H(r, r′) is the Heaviside unit step function. This kernel is a more general one than that developed in ref. [1]. Both kernels apply in cases where the Riccati equation corresponds to a Sturm–Liouville problem.It is shown that this integral equation can be integrated by parts so that, for any local potential, the integrand decreases as the cyclic folding procedure is applied. During this cyclic folding, the kernel generates an equation that contains only coefficients of β(r)0 and β(r)1. Consequently, after truncating at the end of the nth cycle, it is possible to write down a Padé‐type approximation to the logarithmic derivative as a known function of the independent variable. All coefficients in this approximation can be evaluated as simple algebraic formulations of P(r), R(r), and integrals over P(r).
Transformation properties of many‐electron wave functions with special attention to the relation between pair‐correlated DODS and configuration interaction
Authors: Wormer P. E. S. , Van der Avoird A. 
Published: December 2004

AbstractA method is presented that leads to a simple derivation of the explicit relation between pair‐correlated DODS schemes (e.g., the alternant molecular orbital method and the extended valence bond method) and configuration interaction.This result is based on a reduction formula for the representations of the general linear group, GL(m), carried by the N‐electron function space. Generally, this paper deals with the effect of “partitioned” orbital transformations on states with “local” permutation symmetry.
A general ab initio molecular multi‐configuration self‐consistent field algorithm
Authors: Hackmeyer M. 
Published: December 2004

AbstractThe ab initio multiconfiguration self‐consistent‐field (MC SCF) techniques and computer programs of Basch [1, 2] and the ab initio configuration interaction (CI) techniques and programs of Whitten and Hackmeyer [3] have been combined and generalized to form a general technique and program to yield optimized ab initio MC SCF wavefunctions for any set of Slater determinants. The Slater determinants are read in as input data to the program along with the spin parity that is being considered (optional) and the program successively does the CI calculation and one iteration of the SCF calculation, constructing the proper Fock–Hamiltonians by examining the set of Slater determinants and their CI coefficients. The Fock–Hamiltonian matrices are calculated and diagonalized in succession, a single two‐dimensional array being used to store these matrices. The basis function integrals are read from a tape only once during each MC SCF iteration (one MC SCF iteration = a CI calculation followed by one iteration of the SCF calculation).
Calculation of the magneto–optical activity of the hydrogen molecule
Authors: Svendsen E. Nørby , Hameka Hendrik F. 
Published: December 2004

AbstractWe calculated the Verdet constant of the hydrogen molecule. We found that the angle of rotation may be represented by ϕ0 = A0Hv2/(v − v2)2 where A0 is 3.23 × 10−33 microminutes sec2 per oersted‐cm‐atmosphere. This is in agreement with the experimental observations where ϕ0 is given by the same frequency dependence with the constant A0 × 2.72 = 10−33 in terms of the same units.
Method of complex molecular orbitals
Authors: Hendekoviá J. 
Published: December 2004

AbstractIn the spirit of Löwdin's extended HF scheme, an SCF method for the description of the molecular ground state, based on complex molecular orbitals, is developed. As a special case the method of parity mixing in orbitals is formulated. A calculational procedure for solving derived secular equations is described and numerical results, obtained in the minimal basis set, are reported for the N2 and CO molecule. Resulting ground state energies are close to the energies of the CI calculations with the same set of orbitals.
Coupled hartree–fock calculation of static and shielding factors for open shell atomic systems
Authors: Gupta A. , Roy H. P. , Mukherjee P. K. 
Published: December 2004

AbstractIn this paper a calculation of the static quadrupole polarizabilities and the shielding factors of the atoms and ions of the 2p open shell systems is presented. A fully coupled Hartree–Fock method using the Roothaan formalism is adopted. Calculations have been done for the ground as well as for some valence excited states. An antishielding effect is observed for all the atoms and ions under study.
All‐pair wave function and reduced variational equation for electronic systems
Authors: Náray‐Szabó G. 
Published: December 2004

AbstractA new type of wave function is proposed for atomic and molecular systems. This all‐pair function is constructed of N(N – 1)/2 identical geminals for N electrons. For systems with the highest multiplicity this is the full space part of the wave function. For closed shell systems it has to be multiplied by a Slater determinant according to the antisymmetry condition. In the case of maximal multiplicity a reduced variational equation is derived for the geminal. This equation is independent of the dimensionality of the system and contains the particle number as a multiplicative factor only. The method is extended to the closed shell case where a restriction has to be fulfilled. The reduction of the variational equation can be done only approximately. The use of identical geminals can be treated as a first approximation. An extension of the method, called the pair interdependent configuration interaction (PICI), is proposed. The special features of the method are discussed briefly.
Some remarks on the semiempirical one‐center electron repulsion integrals
Authors: Anno Tosinobu , Teruya Hirohide 
Published: December 2004

AbstractThe identification of the stage of ionization for various kinds of one‐center electron repulsion integrals, occurring when nonbonding or lone‐pair electrons are considered explicitly as well as π‐electrons, is discussed for conjugated organic molecules containing heteroatoms N. It is concluded that the value for the negative ions should be used for (πCπC | πCπC) in all the states but for (πNπN | πNπN) only in the π‐π states. In the n‐π states, the appropriate value of (πNπN | πNπN) is that of the neutral atom if the molecule contains only one N atom. If more than one N atom is involved in the molecule, some weighted mean of the values for the negative ion and for the neutral atom should be used. The value for the neutral atom is most adequate for one‐center repulsion integrals other than the (ππ | ππ) type in both the π‐π and the n‐π states. The method of determining these integrals is also discussed. It is concluded that they are to be determined from the consideration of appropriate electron‐transfer reactions except for exchange integrals. The exchange integrals are shown to have to be determined from the Slater–Condon parameters derived from the analysis of the experimental atomic energy levels. Illustrative calculations are given for the lower singlet levels of the formaldehyde, pyrazine, pyridine, and the p‐benzoquinone molecule. It is found that the calculated energies of the n‐π transitions become much too low unless the (ππ | ππ) values of the heteroatoms in the molecule are chosen differently in the n‐π states and in the π‐π states as pointed out theoretically in this article.
Singlet–triplet splittings as obtained from the Xα‐scattered wave method: A theoretical analysis
Authors: Bagus P. S. , Bennett B. I. 
Published: December 2004

AbstractThe theoretical determination of singlet–triplet splittings of the excited states of closed‐shell molecules is discussed with emphasis on the use of the Xα–scattered wave method. With this method, splittings can be computed in two independent ways. Both will have corrections due to orbital relaxation effects. The singlet–triplet splittings obtained with the Xα–scattered wave method for several large organic molecules are reviewed. It is seen that the results using the two splitting formulas differ by a large amount; in fact, they differ by the magnitude of the computed splitting. We provide a criterion for choosing the results obtained with one method over the other by showing that they both give upper bounds to the best result obtainable within the framework of the model. However, because of the large differences between the two methods, the quantitative value of the splitting should be viewed with caution.
Spin‐free quantum chemistry. XV Spin‐only neutron diffraction
Authors: Matsen F. A. , Picone J. M. , Welsher T. L. 
Published: December 2004

AbstractThe cross section for elastic neutron diffraction is analyzed for the spin‐only case, in which the orbital contributions to the magnetic moment density are negligible. For systems specified by spin‐free Hamiltonians, we show that the magnetic moment density is calculated from the unpaired electron density, a spin‐free quantity, which is equivalent to the spin density. The computation of the unpaired electron density is outlined and examples are discussed. The scattering cross section for an infinite interaction range Heisenberg model exhibits a temperature dependence which parallels that of the spontaneous magnetization. With a knowledge of the unpaired electron density one may determine the magnetic space group symmetry.
Spin‐free quantum chemistry. XVI. Spin correlation
Authors: Matsen F. A. , Welsher T. L. 
Published: December 2004

AbstractWe discuss the calculation of quasielastic critical neutron scattering for systems defined by a spin‐free Hamiltonian. The system dependent property which determines the critical scattering is the thermal average of a spin‐free operator called the general unpaired electron correlation operator. For localized models, we obtain the scattering as the Fourier transform of an unpaired site correlation function. The algebraic relationship between this correlation function and the usual spin correlation function is discussed as are its relationships to thermodynamic properties. Correlations in the infinite interaction range model, linear spin wave model, and infinite chain Heisenberg model are given. In the last case, an estimate of the low temperature correlation length is made.
SC Cellular multiple scattering in molecular electronic structure calculations
Authors: Keller Jaime 
Published: December 2004

AbstractRecent 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.
Electronic correlation studies. III. Self‐correlated field method. Application to 2S ground state and 2P excited state of three‐electron atomic systems
Authors: Lissillour R. , Guerillot C. R. 
Published: December 2004

AbstractThe self‐correlated field method is based on the insertion in the group product wave function of pair functions built upon a set of correlated “local” functions and of “nonlocal” functions. This work is an application to three‐electron systems. The effects of the outer electron on the inner pair are studied. The total electronic energy and some intermediary results such as pair energies, Coulomb and exchange “correlated” integrals, are given. The results are always better than those given by conventional SCF computations and reach the same level of accuracy as those given by more laborious methods used in correlation studies.
Perturbation theories and wave functions for calculation of electronic polarizabilities application to DNA bases
Authors: Adams Steven , Nir Shlomo , Rein Robert 
Published: December 2004

AbstractThree different forms of perturbation theories, variational perturbation, finite perturbation and second‐order, are evaluated regarding their value for calculation of electronic polarizabilities of small and intermediate size molecules. It is concluded that with the practical constraint of a small basis set the variational perturbation method is the most promising alternative for calculation of polarizabilities. For several small molecules, our calculated polarizabilities indicate that both IEHT and ab initio wave functions give values in close agreement with each other. Variational perturbation calculations of polarizabilities with IEHT wave functions also include the DNA bases.
Perturbation theory for degenerate states of atomic and molecular systems
Authors: Ivanov L. N. , Safronova U. I. 
Published: December 2004

AbstractThe first few terms of the perturbation expansions for the function and the energy shift of a degenerate state of an arbitrary quantum mechanical system are obtained using the adiabatic formula. It is shown how the expansion for the secular operator may be obtained from the expansion for the function. The results are used to calculate energies of the ground and some excited states and multiplet splittings of some beryllium‐like ions.
Coherent states and asymptotic behavior of the symmetric top wave functions
Authors: Doktorov E. V. , Malkin I. A. , Man'ko V. I. 
Published: December 2004

AbstractWave packets which may be considered as an analogue of the coherent states of the top are constructed. New integral representations are obtained for the D‐function; making use of those, various types of the asymptotic behaviour of the D‐function are obtained in the region of large quantum numbers.
Correlation effects in the PPP model of alternant π‐electronic systems: two‐point Padé approximant approach
Authors: ČÍŽek J. , Pellégatti A. , Paldus J. 
Published: December 2004

AbstractA general procedure, based on the two‐point Padé approximant technique, is formulated, enabling an interpolation of the low‐lying energy levels of the PPP (Pariser–Parr–Pople) Hamiltonian over the divergency gap separating the asymptotic perturbation expansions in both strongly and weakly correlated limits. The methods for the determination of the first few terms of the perturbation expansions in both limits are also briefly outlined. The procedure is applied to the five lowest singlet energy levels of the PPP model of the benzene molecule and the results are compared with the exact solutions for this model. The advantages as well as the shortcoming of this approach are pointed out and illustrated on the model calculation for benzene. The applicability of this technique to larger π‐electronic systems is discussed and a feasible procedure for its implementation is formulated.