bluuebunny/crossref_metadata_2025 huggingface dataset:
Matrix elements in all valence electron models
Authors: Linderberg Jan , Seamans Lloyd
Published: December 2004

Model Hamiltonians for all valence electron calculations are examined with regard to the possibility of obtaining consistent sets of matrix elements for the description of electromagnetic processes such as photon absorption, optical activity, and magneto‐optical activity. Linear and angular momentum and position operator matrix elements are related to Hamiltonian matrix elements through symmetry relations and equations of motions. The possibility of elimination of empirical interatomic matrix elements is studied.
Error analysis of variationally optimized upper‐ and lower‐bound wave functions for H
Authors: Ley Barbara E. , Thorpe Tony , Rothstein Stuart M.
Published: December 2004

Wave functions which are a linear combination of H‐type elliptical orbitals are optimized to provide either an upper bound or a lower bound to the H ground state. For the latter, Temple's formula is used. Three criteria are considered to determine the relative accuracy of these wave functions: (i) energy (calculated versus exact eigenvalue); (ii) average error; and (iii) local energy. Although the lower‐bound optimized wave functions obtained are the most accurate available for H from approximate wave functions, they are still inferior to the corresponding upper‐bound wave functions by criteria (i) and (ii). In particular, using criterion (ii), it is shown numerically that the upper‐bound functions are “correct to second order,” while the lower‐bound functions are almost, but not quite, “correct to second order.” Despite this, the local energy analysis, criterion (iii), reveals that the lower‐bound wave functions can be more accurate than the upper‐bound functions in some regions of space, and hence give more accurate values for physical properties sensitive to these regions. Examples considered are the dipole–dipole and Fermi contact interactions.
Variational bounds on transition probabilities
Authors: Barnsley Michael F. , Robinson Peter D.
Published: December 2004

Complementary variational functionals are derived which impose upper and lower bounds on transition probabilities. These functionals are used to yield bounds in terms of sets of sum rules, and illustrative calculations are presented for hydrogen, helium and krypton atoms.
Orthogonalization of overlapping orbitals by optimal polynomials. I. Polynomials constructed from spectral radii
Authors: Ra Øystein
Published: December 2004

Inverses and inverse square roots of overlap matrices are approximated by polynomials constructed on the basis of an integral transform of the metric resolvent and Kublanovskaya's conformal mapping technique. Given reasonable upper and lower bounds for the support of the overlap matrix spectral distribution, the described expansions have significantly better convergence properties than the well known power series methods, yet retain the simplicity of these schemes.
Convergence behavior of some multiconfiguration methods
Authors: Banerjee A. , Grein F.
Published: December 2004

The optimization scheme of the “multiconfiguration method based on the generalized Brillouin theorem” (MCGBT) has been analysed and found to converge quadratically. Its rate of convergence has been compared with that of other optimization methods such as the first‐order Rayleigh‐Schrödinger perturbation, the steepest descent, the single vector diagonalization, the Newton‐Raphson, and the conventional SCF method. The convergence of the MCGBT scheme has been found to be superior to the convergence of the above mentioned schemes.
Group theoretical classification of states of a molecular system at definite states of its constituent parts
Authors: Kaplan I. G. , Rodimova O. B.
Published: December 2004

A method is developed for determining the allowed states of a many‐particle system at definite states of the subsystems (impurity ion complexes in crystals, nucleon clusters in nuclei, polyatomic molecules). The advantage of the method proposed here over those previously developed is that the present one is independent of the number of particles in the subsystems. Depending on the value of spin Sa the subsystems are considered either as bosons or fermions. The representation character expression whose expansion gives all the terms 2s+1Γ(α) with a definite value of total spin of the system is written as the product of permutation and orbital factors. The orbital factor is defined in terms of characters of the local point group representations. Some alternative ways of calculating the permutation factor are discussed: a) with the use of tables of reduction of the unitary transformation group U2Sa+1 in a three‐dimensional rotation group; b) through the plethysm coefficients; and c) in terms of 3nj‐symbols of three‐dimensional rotation group. Some examples of application of the method to various systems are presented.
On Löwdin's projection operators for angular momentum. I
Authors: Crossley Richard J. S.
Published: December 2004

Löwdin has presented his angular momentum projection operators in two forms, the sum form deduced from the product form. A direct proof of the sum form is presented here, together with a brief account of application of the technique to the pd configuration.
A survey of some theoretical studies of negative ions
Authors: Simons Jack
Published: December 2004

The quantum chemical methods employed by us to investigate the stabilities, charge densities, and bonding characteristics of atomic and molecular anions are briefly reviewed. The results of our work on chemically interesting species are surveyed, as are our initial results on the treatment of solvation effects in anionic systems. Finally, a simple‐minded approach to the problem of finding shape resonances for electron–atom scattering processes is outlined.
Absorption line shape of two coupled oscillators decaying in two different mediums
Authors: Hardisson A. , Mauricio F. , Velasco S.
Published: December 2004

The linear response theory is used to study the line shape of two coupled oscillators, decaying in two different baths, when one of the oscillators is coupled to the radiation field. The baths are considered to be thermally excited. The analysis is based on the computation of the correlation functions 〈a (t)ai (0)〉 and 〈ai (t)a(0)〉 of each oscillator, taking the coefficients associated with the operators a and ai in the Heisenbemg representation as the starting point of the calculation. The line shape in different cases is also discussed.
Exact eigenvalues for the Coulomb potential with cut‐off
Authors: Linz Peter , Chen Tien Chi
Published: December 2004

The solution of the quantum‐mechanical one‐particle problem involving a Coulomb potential with a cut‐off contains Whittaker functions, difficult to evaluate individually. However, the energy expression involves a ratio of two contiguous Whittaker functions, and the entire ratio is easily expressed as a convergent continued fraction. Representative energy eigenvalues are calculated, correcting the errors due to an earlier Bessel function approximation by Wannier.
Dynamic potential barrier and tunneling
Authors: Chojnacki Henryk , Laskowski Zbigniew
Published: December 2004

The tunneling transfer probability has been considered within the framework of the time dependent perturbation theory. It has been found that the probability of proton transfer may be enhanced by several orders when a dynamic potential barrier is assumed.
Electronic structure of SiH2, PH2, and their positive and negative ions
Authors: Ball John R. , Thomson Colin
Published: December 2004

Ab initio LCAO‐MO‐SCF calculations on SiH2 and PH2 and their positive and negative ions are reported, using a variety of Gaussian basis sets. The charge distribution, bonding, and molecular properties of these ions are compared with the available experimental data.
Symmetry of nonrigid molecules and isomerization processes
Authors: Gilles J. M. F. , Philippot J.
Published: December 2004

Starting from the concept of a totally flexible molecule, rigidity is introduced by restricting progressively the allowed permutations. Each nonrigid isomer is then characterized by its Longuet‐Higgins group ℒ of allowed permutation inversions. For a given ℒ all nonrigidity types correspond to all possible choices of the symmetry subgroup ℒ of the skeleton. The structure of ℒ also allows a characterization of the isomerization processes studied in chemical kinetics. In both situations, isomerization mechanisms may be associated with generators and are, in the simplest situations, represented by Cayley graphs.
Metric‐constrained variation method for atoms and molecules
Authors: Morikawa Tetsuo
Published: December 2004

A new method is presented for the variational calculation of a set of vectors under the condition that the metric of the vectors remains unchanged through the process of variation. Application of this method to typical measures (energy, overlap, distance, etc.) in quantum chemistry gives rise to new variational equations, for which the solution yields the Löwdin symmetric orthonormalization, the Kashiwagi–Sasaki generalization, the symmetric deorthogonalization, and the Adams localization, etc.
Many‐body perturbation theory, coupled‐pair many‐electron theory, and the importance of quadruple excitations for the correlation problem
Authors: Bartlett Rodney J. , Purvis George D.
Published: December 2004

Many‐body (diagrammatic) perturbation theory (MBPT), coupled‐pair many‐electron theory (CPMET), and configuration interaction (CI) are investigated with particular emphasis on the importance of quadruple excitations in correlation theories. These different methods are used to obtain single, double, and quadruple excitation contributions to the correlation energy for a series of molecules including CO2, HCN, N2, CO, BH3, and NH3. It is demonstrated that the sum of double and quadruple excitation diagrams through fourth‐order perturbation theory is usually quite close to the CPMET result for these molecules at equilibrium geometries. The superior reliability of the CPMET model as a function of internuclear separation is illustrated by studying the 1∑ potential curve of Be2. This molecule violates the assumption common to nondegenerate perturbation theory that only a single reference function is important and this causes improper behavior of the potential curve as a function of R. This is resolved once the quadruple excitation terms are fully included by CPMET.
Beryllium dimer, a critical test case of MBPT and CI methods
Authors: Blomberg Margareta R. A. , Siegbahn Per E. M.
Published: December 2004

The ground‐state potential curve for the beryllium dimer is calculated as a critical test case for methods based on many‐body perturbation theory (MBPT) and configuration interaction (CI). In particular, the recently proposed double excitation (DE) MBPT method is compared to the standard SCF‐CI method including single and double excitations from a single reference determinant. The SCF‐CI method is shown to give surprisingly accurate results compared to more complete CI calculations including a larger configuration space, whereas the DE‐MBPT method breaks down more or less completely, particularly for larger basis sets. The results thus demonstrate the importance of including the renormalization terms in this case. Finally, Davidson's correction and related methods lead to an even more severe breakdown than the DE‐MBPT method.
Universal basis sets and transferability of integrals
Authors: Silver David M. , Wilson Stephen , Nieuwpoort W. C.
Published: December 2004

The concept of a universal basis set for electronic structure calculation is illustrated by presenting results obtained when basis sets are transferred from one atom to another. A single Slater‐orbital basis set, consisting of nine 1s and six 2p functions, produces Hartree‐Fock total energies and orbital energies in good agreement with the most accurate calculations of these energies obtained using different basis sets individually optimized for each atom. Transferability of integrals is a natural consequence of the use of the same basis set for each atom in a molecule.
Theoretical study on the vertical electronic spectrum of carbonyl fluoride, F2CO
Authors: Vasudevan K. , Grein F.
Published: December 2004

Ab initio self‐consistent‐field (SCF) and configuration interaction (CI) calculations on the ground and excited states of carbonyl fluoride (F2CO) were carried out at its experimental ground‐state equilibrium geometry. Vertical transition energies deduced from the CI results provide assignments for the electronic systems I–IV, experimentally observed by Workman and Duncan. The singlet excited state, 1A1 (π→π*), is found to be a mixed valence–Rydberg state and to he 1 to 1.2 eV above the suggested experimental value, irrespective of the choice of the basis used for the CI calculations.
Preliminary attempt to follow the enthalpy of an enzymatic reaction by ab initio computations: Catalytic action of papain
Authors: Bolis G. , Clementi E. , Ragazzi M. , Salvaderi D. , Ferro D. R.
Published: December 2004

A new theoretical approach to study the enthalpy variations occurring during an enzymatic reaction is presented. The structural modifications of the enzyme–substrate complex along the reaction path are distinguished as macro‐ and microdeformations. Macrodeformations, which concern primarily the approach of the substrate to the enzyme and the release of the reaction products and arise from nonbonded interactions, are treated with an empirical method for computing the energy of a macromolecule. Microdeformations, which are local displacements driven by variations of the electronic structure and its energy and involve only a limited portion of the complex, are treated with the ab initio SCF‐LCAO‐MO method. The reaction path is idealized as a sequence of major steps: at each step, first the empirical program REFINE is used to calculate the geometry of the system for that step, then the energy of an appropriate subsystem is computed ab initio with the program IBMOL, using the geometry provided by REFINE and applying small concerted atomic displacements. Thus along the entire reaction path one can obtain an energy profile computed with the ab initio method and compatible with the structure of the whole complex. This approach was applied here to the first steps of the reaction of proteolysis catalyzed by papain. The formation of an ion pair ImH+ …S− between the side chains of residues His‐159 and Cys‐25 was examined in detail. The results show that the instability of the ion pair decreases by ˜ 11.5 kcal/mol when the interactions with residues Asn‐175 and Ala‐ 160 are taken into account; the instability is further decreased by ˜2 kcal/mol after a partial geometry optimization. The energies of the noncovalent enzyme–substrate complex and of the tetrahedral intermediate were computed, considering N‐methyl acetamide (NMA) as model substrate and representing papain with the residues Cys‐25, His‐159, Gln‐19, and Ala‐160. The interaction energy of the noncovalent complex is ‐3.8 kcal/mol, compared to the value of +7.4 kcal/mol for the CH3S− ‐NMA complex. The tetrahedral intermediate is found to be less stable than the noncovalent complex by 27 and 38.5 kcal/mol, respectively, for the papain–NMA and the CH3S− ‐NMA systems. While these rather large energy differences are possibly due to the incorrect geometry of the tetrahedral intermediate and optimization of the structure is required, it appears that the interactions with the various protein residues represent a very important stabilization factor, which lowers the onthalpy variations during the reaction.
Energy migration in one‐dimensional structures with resonance interaction
Authors: Fedyanin V. K. , Yakushevich L. V.
Published: December 2004

A new approach is proposed to derive the equation of elementary excitation motion along chains and it is used to obtain an important correction of the equation.
Excited electronic states of a hydrogen bond: Bifluoride ion
Authors: Lozes Richard , Sabin John R.
Published: December 2004

We report here a summary of a limited CI calculation carried out on the C∞v and D∞h electronically excited states of bifluoride ion. This species is interesting as the prototype of a hydrogen‐bonded system. It is determined that the lowest‐lying excited states of the system are dissociative and/or autoionizing.
Heme proteins and metalloporphyrins: Redox chemistry and oxygen binding
Authors: Dolphin David , Addison Anthony W. , Cairns Max , Dinello Robert K. , Farrell Nicholas P. , James Brian R. , Paulson Donald R. , Welborn Curtis
Published: December 2004

Metalloporphyrins perform a variety of functions in nature from the storage and transport of electrons and molecular oxygen to the decomposition of hydrogen peroxide and the activation of oxygen. The chemistry of both the centrally coordinated metal and the porphyrin macrocycle play important roles in these reactions. The use of model systems and metalloporphyrins, other than iron porphyrins, is described for the elucidation of the mechanism of action of the natural systems.
Assessment of reaction center special‐pair chlorophyll models
Authors: Maggiora Gerald M.
Published: December 2004

A discussion of the experimental evidence for the existence of special‐pair chlorophyll in the reaction centers of plants and photosynthetic bacteria is presented, and an assessment of the adequacy of various in vitro chemical model systems designed to mimic the properties of these reaction centers is given. For plant systems it appears that the in vitro models successfully mimic almost all measured in vivo properties, whereas in bacterial systems a similar situation does not obtain. Possible structural models of special‐pair chlorophyll derived primarily from in vitro model studies are described. Their suitability as models of the photooxidizable pigment in plant and bacterial reaction centers is analyzed, and alternative structures for the bacterial case, which is the least well characterized structurally, are considered.
Molecular electrostatic potential of the B‐DNA helix. I. Region of the guanine–cytosine base pair
Authors: Pullman Alberte , Zakrzewska Chrystyna , Perahia David
Published: December 2004

The electrostatic molecular potential minima around the guanine–cytosine base pair within a B‐DNA minihelix are computed, taking into account the contributions of the sugar‐phosphate backbone and of the adjacent base‐pairs. The calculations are based on ab initio SCF wave functions of the different constituents of the nucleic acid. The results point to significant differences in the potential between the isolated nucleic acid bases or base‐pairs and those within the DNA. Altogether the minima in the G–C regions are strongly enhanced in the minihelix. They benefit from the field created by the neighboring phosphates. From the purely electrostatic viewpoint an ambiguity remains as concerns the relative affinity of N7 and N3 of guanine for electrophiles. On the other hand, guanine should altogether be more susceptible than cytosine to such reagents, this ordering concerning also its NH2 group compared to that of cytosine.
Subduction coefficients for 〈2N/2–S, 12S〉 ↓ 〈2, 1〉 ⊗ 〈2, 1〉 of U(n) ↓ U(n1) ⊗ U(n2)
Authors: Sarma C. R. , Dinesha K. V.
Published: December 2004

The determination of the subduction coefficients for states of the unitary group U(n) under the restrictions U(n) ↓ U(n1) ⊗ U(n2) have been considered for the spin free states of many electron systems. Using the transformation properties of the tensor basis spanning the irreducible representation 〈2N/2–S, 12S〉 of U(n) under the permutations of electron coordinates, a simple programmable procedure has been developed for the determination of these coefficients. The procedure has been illustrated using a simple example.
Two useful identities involving spherical harmonics
Authors: Liberato De Brito Adelsindo , Eggarter Tomas P.
Published: December 2004

We present two identities that permit a simplification of some lengthy derivations with spherical harmonics. Examples of their use are given.
Polarization effects in photosynthetic membranes
Authors: Rubin A. B. , Kononenko A. A. , Venediktov P. S. , Borisevitch Galina P. , Knox P. P. , Lukashev E. P.
Published: December 2004

This paper investigates the polarization effects associated with functional processes in photosynthetic membranes.
Theoretical description of fluidity in biological membranes: Rotational motion in lipid hydrocarbon chains
Authors: Hosur Ramakrishna V. , Joshipura Anjan S.
Published: December 2004

A mathematical model to relate order and rotational motion in lipid hydrocarbon chains in biological membranes is proposed. Schrödinger equations with suitable potential functions for CC rotations in lipid hydrocarbons chains have been solved to obtain wave functions characterizing these motions. For a free chain a threefold potential function has been assumed. The effect of collisions between neighboring chains in a membrane is considered by including another term (δ function) in the potential function.
Improvement of an integral approximation scheme based on semiorthogonalized orbitals
Authors: Osanai You , Kashiwagi Hiroshi
Published: December 2004

In a previous paper, a scheme of integral approximation was proposed, in which a large number of two‐electron integrals containing a certain kind of orbital pairs, i.e., weakly related pairs, can be neglected. A new criterion for partitioning orbital pairs into two groups, i.e., strongly and weakly related pairs, is introduced in order to allow for neglect of more integrals without sacrificing the accuracy of a computation. Test calculations on the BH3C2H4 complex show that by the use of the new version, results of roughly the same accuracy as was obtained by the old version is obtained by retaining 80% of the integrals used in the old version. This kind of saving is more significant for larger molecules. For example, in a calculation on Cu‐porphine with 203 CGTO'S, the revised version will require about 2.0 × 106 integrals, while the original version will require about 4.5 × 106. And these two approximate calculations are expected to give the results of roughly the same accuracy.
Projected surface energy bands, Shockley surface states, and bonding in transition‐metal monocompounds with rock‐salt structure: Example of NbC
Authors: Tomášek Mojmír , Pick Štěpán
Published: December 2004

The qualitative theory of Shockley surface states is used to discuss the existence of surface states on three faces of niobium carbide: (001), (011), and (111). The results obtained for NbC are generalized to include other simple transition metal compounds MX, X = C, N, O. Surface states of these and related materials are of interest in chemisorption and catalysis. The qualitative theory of Shockley states appears to be useful tool in detecting strong covalency effects in solids.
Quantum model for transport through membranes
Authors: Ibáñtez‐Mengual J. A. , Tejerina‐García A. F.
Published: December 2004

In the present paper a new model for the transport through membranes, introduced previously by Hosur, is considered. In this model, the membrane is assimilated to a potential barrier, and the material flow through the membrane is determined from the transmission coefficient of the barrier, assuming the existence of an energy difference among the molecules placed at both sides of the membrane. An equation for the transport, in the case of small energy differences, is obtained, which is particularized to the cases that the energy difference is caused by a temperature gradient, a concentration gradient, and both gradients acting together. In all cases, under certain limitations, formally identical equations to those of the thermodynamics of irreversible processes are obtained.
Shellwise virial scaling: Approximation for atomic hole states
Authors: Katriel J. , Davidson E. R.
Published: December 2004

A partitioning of the kinetic and potential energies of atoms within the SCF framework into shell components is proposed. It is demonstrated that this partitioning nearly satisfies a shellwise viral theorem for SCF wave functions. This property is used in order to generate approximate relaxed wave functions for atomic hole states by scaling each shell of the frozen description of the hole in terms of the neutral‐atom ground‐state orbitals. Very good estimates of ΔSCF relaxation energies and reasonable estimates of the overlap integrals between the frozen and relaxed hole wave functions are obtained.
Reduced hamiltonian orbitals. III. Unitarily invariant decomposition of hermitian operators
Authors: Coleman A. J. , Absar I.
Published: December 2004

A decomposition of an N‐particle operator as a sum of N + 1 components is defined such that, in the case of a model system employing a finite one‐particle basis set, the decomposition is invariant under unitary transformations of the basis set. Applied to a two‐particle Hamiltonian, this decomposition gives rise to the distinction between the independent‐particle energy and the coupling energy defined in previous papers. Applied to the reduced density operator for a quantum state, the decomposition corresponds to partitioning the density into irreducible components. This partitioning is illustrated by graphs of electron density for the water molecule.
The coupled‐cluster method with a multiconfiguration reference state
Authors: Banerjee Ajit , Simons Jack
Published: December 2004

The coupled‐cluster approach to obtaining the bond‐state wave functions of many‐electron systems is extended, with a set of physically reasonable approximations, to admit a multiconfiguration reference state. This extension permits electronic structure calculations to be performed on correlated closed‐ or open‐shell systems with potentially uniform precision for all molecular geometries. Explicit coupled cluster working equations are derived using a multiconfiguration reference state for the case in which the so‐called cluster operator is approximated by its one‐ and two‐particle components. The evaluation of the requisite matrix elements is facilitated by use of the unitary group generators which have recently received wide attention and use in the quantum chemistry community.
The kernel of DWBA transition amplitude in atom–diatom reactive scattering
Authors: Suck Sung Ho
Published: December 2004

The kernel of the distorted‐wave Born approximation (DWBA) transition amplitude will be explored with attention to the atom–diatomic molecule reactive scattering process of A + BC → AB + C. Our study of the kernel reveals valuable intrinsic properties regarding the state‐to‐state reactive scattering process. In particular, such a study will help us to better understand (i) the favored geometric configuration during collision, (ii) the spatial domain of contribution to the differential and total cross sections, and (iii) the structural dependence of the kernel distribution on the mass ratio of the reactant molecule BC and the departing atom C, particularly in the case of colinear rearrangement collisions. In this study we choose the FH2 system as an illustration.
Magnesium and calcium cation–ligand interactions within the pseudopotential approach. II. Cation–GABA interactions
Authors: Blake I. Ortega , Leś A.
Published: December 2004

We performed ab initio pseudopotential and CNDO calculations on γ‐aminobutyric acid (GABA) and its Ca2+ and Mg2+ clathrates. We were particularly interested in the rotational barrier existing between two extreme conformers of GABA and its modification upon metal complexing. We found that the pseudopotential method predicts a coordination of the ions to GABA and that this coordination inverts the rotational barrier observed for the isolated molecule. We also looked into the adequacy of CNDO for the study of this type of coordination and found several shortcomings in its predictions. The biological implications of these findings are discussed and a hypothesis on the role of a GABA–Ca2+ complex is presented.
Algebraic structure of fermion density matrices. II
Authors: Dyadyusha G. G. , Kryachko Eugene S.
Published: December 2004

The properties of the algebraic structure of fermion density matrices are studied. The algebraic structure of a density matrix leads to a more varied and detailed classification scheme than that offered by the usual shell structure approach. Investigation of the algebraic structure of fermion density matrices by the methods of algebraic topology leads to a classification scheme based on Betti numbers.
Self‐Consistent methods in Hückel and extended Hückel theories
Authors: Mukhopadhyay A. K. , Mukherjee N. G.
Published: December 2004

A self‐consistent procedure for the Hückel theory, first indicated by Harris [J. Chem. Phys. 48, 4027 (1968)] has been fully developed. To avoid time consuming repeated orthogonal‐nonorthogonal transformations and diagonalization of large matrices, a steepest descent technique has been suggested.
Basis set generation for the SCF calculation
Authors: Adamowicz Ludwik
Published: December 2004

A method for basis set generation for SCF calculations is proposed. Using SCF orbitals and orbital energies obtained in the extended basis set the Fock operator can be expressed as its spectral resolution. The sum of differences between occupied orbital energies and corresponding eigenvalues obtained by the diagonalization of this operator in the new smaller basis set is a criterion of the quality of this new set. The present method consists of the minimization of this sum by changing the parameters that determine the new basis functions. An example of the optimization of the different Gaussian basis sets for the LiH molecule is described.
Exact formulas for overlap integrals of Slater‐type orbitals with equal screening constants
Authors: Jones Herbert W.
Published: December 2004

Exact formulas for 147 overlap integrals between Slater‐type orbitals with equal screening constants are presented in the most simplified form. This represents all combinations of orbitals with quantum numbers: 1 ≤ N ≤ 5, 0 ≤ L ≤ 3, and M ≤ L. The formulas are automatically generated by computer using the “C‐matrix” single‐center expansion method. There are no limitations to the applicability of this method to orbitals of higher quantum numbers.
Extension of EWMO model to particle‐hole excitations
Authors: Deshmukh Pranawa , Linderberg Jan
Published: December 2004

Examination of the random phase approximation in relation to the energy weighted maximum overlap model suggests a way of accounting for singlet–triplet splittings in particle–hole spectra. Calculations for the first row hydride molecules are used to illustrate applications.
Automatic geometry optimization for molecules with d orbitals. III. The EHT method with electrostatic corrections
Authors: Beran S. , Slanina Z. , Zidarov D. C.
Published: December 2004

A procedure has been developed for automatic optimization of molecular structures in the EHT method with possible inclusion of electrostatic correction terms, operating with analytical formulas for the first derivative of the total energy in Cartesian coordinates in the s, p, d basis of Slater orbitals. Illustrative examples are given of optimization of the structural parameters of FeCl3, Fe2Cl6, FeCl4, FeCl4−, FeCl2, and FeCl and of optimization of the reaction pathways of the dissociation of Fe2Cl6 yielding the other species of the above set. The values are in good argreement with the available experimental data; this agreement is discussed briefly in connection with the general applicability of the EHT method combined with automatic geometry optimization to theoretical study of compounds containing transition metal atoms.
Information theory interpretation of the Pauli principle and Hund rule
Authors: Bonchev D.
Published: December 2004

Making use of different information measures, the Pauli exclusion principle and the first Hund rule were found to be related to a trend toward acquiring a maximum information content of the atoms and molecules, and more generally, for any fermion system. The bosons conversely always have a minimum (zero) information content with respect to the permutation symmetry of their wave functions. Some new interpretations of the Pauli principle are presented.
Interactions between nucleic acid bases in hydrogen bonded and stacked configurations: The role of the molecular charge distribution
Authors: Langlet J. , Claverie P. , Caron F. , Boeuve J. C.
Published: December 2004

Some aspects of the use of simplified formulas for the evaluation the interaction energy between two molecules is discussed. This energy is obtained as the sum of four terms: electrostatic, polarization, dispersion, and short‐range (exponentially decreasing) repulsion. The effect of using several approximations is considered (i) for representing the charge distributions of the isolated molecules (which determine the electrostatic and polarization terms), and (ii) for evaluating the short‐range repulsion term. The various charge distributions considered are semiempirical atomic net charges (Del Re + Pariser‐Parr), atomic charges and dipoles (CNDO) and corresponding “effective” atomic charges, and many‐centered multipole distributions obtained from ab initio SCF calculations (charges, dipoles, and quadrupoles located on the atoms and the middles of segments joining pairs of atoms, whether chemically bonded or not). As concerns the short‐range repulsion, the various procedures considered are a sum of atom‐atom terms, a sum of bond‐bond terms, and the use of anisotropic van der Waals radii for heteroatoms (oxygen and nitrogen). In all cases, the dispersion energy is obtained as a sum of atom‐atom terms (of the R−6 type). These various procedures are checked in the case of the interactions between nucleic acid bases, for two rather different kinds of configurations, namely, hydrogen bonded and stacked. This comparison reveals a rather complicated picture, namely the results got from the various levels of approximation of the molecular charge distribution lead to different degrees of agreement according to different situations, e.g., for guanine‐cytosine interactions, qualitative agreement is found between the various methods as concerns the relative order of stacked and hydrogen bonded situations, while agreement is much less satisfactory for adenine‐uracile interactions. One of the main conclusions is that a sufficiently sophisticated representation of the molecular charge distribution is required in order to get reliable results for all possible configurations of a complex. Such comparative studies should bring significant help as concerns the development of the reliable simplified procedures for evaluating intermolecular interaction energies.
Potential energy curves in complementary base pairs and in model hydrogen bonded systems
Authors: Chojnacki Henryk , Lipiński J´zef , Sokalski W. Andrzej
Published: December 2004

The potential energy curves for the intermolecular proton transfer in complementary base pairs and respective hydrogen bonded model systems have been studied at the semiempirical all‐valence and ab initio STO‐3G level. The proton transfer probability was found to be markedly greater in excited electronic states than that of the ground state. Substantial lowering of the potential barrier height for the coupled double proton transfer in model (HCOOH)2 system has been observed when the dynamics of zero‐point vibrational deformations of the heavy atom skeleton and the environmental effects were taken into account in nonempirical STO‐3G calculations. The results of quantum‐chemical calculations indicate on the possibility of the double proton transfer in complementary base pairs corroborating the submolecular Löwdin hypothesis on the mechanism of spontaneous mutations.
Comparative studies on drug‐receptor binding of phenylethylamine derivatives using calculated group contribution constants
Authors: Lukovits I.
Published: December 2004

Group contribution constants of phenylethylamine derivatives were calculated using a modified version of the Free‐Wilson approach and data published on group contributions were also collected. The biological activity indices used to extract these contributions are the inhibition of phenylethanolamine N‐methyl transferase, inhibition of norepinephrine uptake, dopamine β‐hydroxylase substrate activity, phenylethanolamine N‐methyl transferase substrate activity, and antagonism to the pressor activity of epinephrine. The different sets of calculated group contributions were compared. Correlation could be demonstrated between sets of group contributions, except those extracted from the antipressor activity data. It is concluded that the interaction mechanism between the receptor site and the aromatic ring might be similar in the systems considered. Methylation of the nitrogen atom appearently does not cause any change in specificity at the molecular level.
Interaction of tylophorinidine with lysozyme
Authors: Gurnani S. , Datta G. , Mulchandani N. B. , Sen G. , Mehta S. K. , Sengupta S.
Published: December 2004

The interaction of tylophorinidine (TPD) with lysozyme—a model protein—with biological activity, was investigated by determining its fluorescence and by assessing its activity under various conditions. The results indicated that TPD associated with lysozyme at pH 9.2 efficiently with an association constant Ka of 3.3 X 104 M–1 at 26°C. Ka increased with the increasing temperature in the range 26 to 55°C; the calculated enthalpy change ΔH was found to be 2.3 kcal/mol. Under the same conditions as above TPD also associated with the free amino acid tryptophan with a Ka of 1.7 X 104 M–1 indicating half the efficiency of its association with protein lysozyme. TPD associated lysozyme was less active than the uncomplexed enzyme in the above temperature range although beyond 45°C the inhibition was more significant. The results imply that TPD binds lysozyme outside the cleft region in the temperature range studied here. However, with increasing temperature the cleft region is gradually widened and/or the whole molecule is expanded such that the accommodation of whole or part of the TPD molecule is facilitated leading to the blockage of lytic activity.
Ab initio molecular orbital calculation of fe‐porphine with a double zeta basis set
Authors: Kashiwagi Hiroshi , Obara Shigeru
Published: December 2004

An ab initio LCAO SCF MO calculation was performed on planar Fe‐porphine with a double zeta basis set consisting of 300 CGTO's. SCF wave functions of several states of Fe‐porphine and its cation were obtained. The net charge of Fe is in the range of 1.39 to 1.53. The highest occupied orbital is ascertained to be a pure porphine π‐MO, 1a1u. The calculated ionization potentials of the two highest occupied orbitals, 1a1u and 5a2u are 5.98 and 6.43 eV, respectively. They are in good agreement with experiments. The role of the porphine macrocycle on the oxidation of Fe is discussed in terms of gross atomic populations and with contour maps of the density difference.
Methods of composite molecular wave functions. I. Variational principle and multiconfiguration SCF theory
Authors: Matsuoka Osamu
Published: December 2004

The Silverstone–Stuebing variational principle for the discontinuous wave functions of one‐electron systems is generalized for many‐electron systems. The variational functional of energy takes real or complex value. The condition that it is real is given. Using the generalized variational principle, a multiconfiguration SCF theory for the composite molecular wave function is formulated. According to the theory, we may divide the whole space into space‐filling cells, solve the SCF equations in each cell and build up the wave functions of the system by gathering the wave functions obtained in the cells. For use in the basis‐set expansion method, the SCF equations are rewritten as matrix forms in which only one‐ and two‐center integrals appear if an expansion center is located in each cell.
Monte‐Carlo simulation of water solvent with biomolecules: Serines with reaction‐field correction
Authors: Romano Silvano
Published: December 2004

Along the lines of previous work [S. Romano and E. Clementi, Gazz. Chim. Ital. 108, 319 (1978); Int. J. Quantum Chem. 14, 839 (1978); 17, 1007 (1980)], we carried out Monte Carlo simulation on serine–water clusters (the neutral molecule and two conformers of the zwitterion) surrounded by an appropriate dielectric continuum simulating the bulk solvent. Results for clusters in vacuo and in the dielectric continuum were compared; similarities and differences could be qualitatively interpreted as produced by competition among different factors.
A hybrid technique of orthonormality constrained orbital optimization in SCF calculations
Authors: PrasadBhattacharyya Sankar , Mukherjee Debashis
Published: December 2004

A recently proposed orthonormality constrained orbital optimization technique is operationally modified further by coupling it to a gradient biased method, namely the steepest descent procedure of McWeeny. The hybrid technique developed in this way is shown to have better convergence properties in closed and unrestricted open‐shell calculations. The technique can be adapted to MCSCF procedures as well. The important role played by "orbital symmetries" in the operation of the method is analysed. Similarities and differences of the present method with the orthogonal gradient method are pointed out. Possible avenues of circumventing convergence difficulty that one may encounter in pathological cases, particularly in ab initio calculations involving extended basis set, are suggested.
Structure and spin‐purity conditions for reduced density matrices of arbitrary order
Authors: Luzanov A. V. , Whyman G. E.
Published: December 2004

For arbitrary k, the separation of spin variables is performed in the reduced density matrix of the kth order (RDM‐k) on the basis of the Fock coordinate function method. The independent spatial components of RDM‐k are analyzed. For RDM‐k of the total spin eigenstate, their number is proved never to exceed its spin multiplicity 2s + 1. Integral and other nontrivial interrelations between spatial components are established which turn out to be the necessary and sufficient conditions of spin purity of a wavefunction corresponding to a given RDM‐k. It is shown that the r‐rank k‐particle spin distribution matrix F, defined as a spatial coefficient at the spin‐tensorial operator of rank r in the RDM‐k expansion, can be obtained by reduction of the (k + r)‐particle charge density matrix F. In particular, all spatial components of RDM‐2 are explicitly expressed in terms of the four‐electron charge density matrix only. This allows us to purpose some approximative formulas for the McWeeny‐Mizuno spin–orbit and spin–spin coupling functions in the case of the weak spin contamination.
Partitioning technique, perturbation theory, and rational approximations
Authors: Löwdin Per‐Olov
Published: December 2004

Instead of the Schródinger equation ℋ︁Ψ = EΨ subject to the boundary condition 〈φ|Ψ〉 = 1, where φ is a normalized reference function in the Hilbert space, one studies the inhomogeneous equation (ℋ︁ − ℰ)Ψℰ = aφ, where ℰ is a complex variable, with the same boundary condition, which gives a = 〈φ|ℋ︁|Ψℰ〉 − ℰ = ℰ1 − ℰ. Introducing the projector P = 1 − |φ〉〈φ| for the complement to O = |φ〉〈φ|, one finds easily the explicit solution Ψℰ = (1 − Pℋ︁/ℰ)−1φ = (1 + Tℰℋ︁)φ, where Tℰ = (ℰ − Pℋ︁)−1P = P(ℰ − Pℋ︁P)−1P is the reduced resolvent associated with the auxiliary Hamiltonian H̄ = Pℋ︁P. The existence of these operators is discussed. It is shown that, if the parameter ℰ is real in the “discrete part” of the spectrum to ℋ︁, then ℰ and ℰ1 = 〈φ|ℋ︁|Ψℰ〉 = 〈φ|ℋ︁ + ℋ︁Tℰℋ︁|Φ〉 ≡f(ℰ) bracket a true eigenvalue E satisfying the relation E = f(E). The Newton‐Raphson solution to the equation F(ℰ) = ℰ − f(ℰ) = 0 is related to the variation principle. Putting ℋ︁ = ℋ︁0 + V and expanding the inverse (ℰ − Pℋ︁0 − PV)−1 in terms of powers of V or (V − α), one gets various expansions relating to finite‐order perturbation theory. Exact expressions for the ordinary wave and reaction operators are obtained. If A is an arbitrary nonsingular operator and h = {h1,h2,…,hn} is a linearly independent set, the inner projection Án = |h〉 〈h|A−1|h〉−1〈h| is a “rational approximation” to the operator A which converges toward A when n→∞ and the set h becomes complete. If A is positive (or has a finite negative part) the convergence is from below. Applying this principle to the partitioning technique, one gets rational perturbation approximations instead of the standard power series, similar to the Padé approximants but derived in a different way with the remainder term under control. The method has been used to calculate lower bounds to eigenvalues.
Failure of strong asymptotic conditions in four‐dimensional field theories
Authors: Khuri N. N.
Published: December 2004

It is shown that the renormalization group imposes severe restrictions on analytic continuation in coupling constant in the case of field theories in four dimensions.
Estimating tunneling phenomena
Authors: Harrell Evans M.
Published: December 2004

Several tunneling phenomena are surveyed. A unified, rigorous treatment of them can be based on a simple technique of integration by parts coupled with growth estimates of eigenfunctions, using, for example, WKB approximations. In particular, the analysis of Harrell and Simon of the resonance widths in the hydrogen Stark effect can be simplified.
Towards a molecular theory of phase transitions in fatty acid monolayers
Authors: Dunne Lawrence J. , Combs Leon
Published: December 2004

A molecular theory of phase transitions in fatty acid monolayers at the air/water interface is proposed based on rotational ordering of molecules about their longitudinal axes. The first order statistical mechanical lattice model of Bell, Mingins, and Taylor (BMT) which is an equilibrium diluted Ising model is used to describe the monolayer behavior of some simple aliphatic carboxylic acids. The interaction energy parameters in the BMT model are adjusted to give reasonable agreement with the experimentally observed chain length dependence, and the energies thus obtained are compared with those calculated for interacting aliphatic carboxylic acid dimers by the technique of perturbative configuration interaction using localized orbitals (PCILO). It is concluded that intermolecular rotational ordering due to the anisotropy of the intermolecular potential plays a significant role in simple fatty acid monolayer phase behavior. A possible experimental test of the model is briefly described.
Electronic structure of beryllium
Authors: Oriade Joseph
Published: December 2004

The electronic energy bands in beryllium have been recalculated. The earlier work of Terrell [1] was found to contain a systematic error in the form of overlapping muffin tins. The new band structures give a density of states with the Fermi surface lying in the hole like portion, consistent with Hall measurements. All existing calculations misplaced the Fermi surface. As a further check on the new bands, the Hall coefficient AH was calculated. We obtained AH = (7.6 ± 0.8) × 10−24 cgs units for the easy axis or c direction, in excellent agreement with the experimental value of AH = 8.56 × 1024 cgs units.
Structural factors affecting Aryl Hydrocarbon Hydroxylase induction by Dibenzo‐p‐dioxins and Dibenzofurans
Authors: Cheney B. Vernon
Published: December 2004

Quantitative structure‐activity relationships have been developed to rationalize the experimental data obtained with a series of dibenzo‐p‐dioxins and dibenzofurans in the assays for receptor binding and aryl hydrocarbon hydroxylase (AHH) induction. Lateral substituents (in positions 2, 3, 7, and 8 of the tricyclic system) do not affect receptor binding and AHH induction in the same manner. Various hypotheses are suggested to explain this finding. Of special interest is the possibility that the lateral substituents are directly involved in the mechanism which transforms the receptor to the active state. The implications of this possibility are considered with regard to the design of an antidote for poisoning caused by the chlorinated congeners which occur as contaminants in certain commercial products.