bluuebunny/crossref_metadata_2025 huggingface dataset:
The lower valence states of linear polyenes: Locations and identifications
Authors: Mc Diarmid Ruth
Published: December 2004

The experimental transition energy to the valence Ag state of butadiene is used to validate a subset of the theoretical calculations that have been carried out on this molecule. The validated calculated Ag transition energies of these calculations are then compared with the experimental Bu transition energies to determine the relative state ordering in isolated, unsubstituted butadiene, hexatriene, and octatetraene. The Ag origins are concluded to lie below the Bu origins for all polyenes except butadiene. Experimental confirmation of this conclusion is presented. The extreme breadth of the Ag transition, 1.0 eV, is noted. Some possible implications of this breadth are discussed.
Adiabatic coordinate separation and large N‐dimensional limit in two‐electron ions
Authors: Goscinski Osvaldo , Mujica Vladimiro
Published: December 2004

The 1/N expansion is used to generate semiclassical effective potentials for two‐electron ions. These potentials can be considered an improvement over the conventional ones computed by Lin and Fano for the full two‐electron coulomb potential insofar as they incorporate some of the quantum mechanical effects. No falling into the nucleus is allowed. Furthermore, the minima of these effective potentials are in surprising agreement with those computed by Fano, Macek, and Lin. This would indicate that the collective variable R, associated with N = 6, leads to a much smaller expansion parameter N, making the adiabatic separation more justified. The role and significance of these broken symmetry solutions with geometric localization are discussed as well as generalizations. The procedure is semiclassical in the sense that the kinetic energy becomes negligible by having a large effective mass.
Bond critical points in the electronic structures of binary hydrides
Authors: Edgecombe K. E. , Boyd R. J.
Published: December 2004

The bond critical points of the binary hydrides formed by the elements of the first two rows of the periodic table have been calculated. Particular attention has been paid to the basis‐set dependence of the bond critical points at the experimental equilibrium geometries, or where necessary at model geometries. With the exception of H2S, stepwise extension of the basis set leads to a smooth convergence of the bond critical points to a set of values which appear to converge to the Hartree–Fock limit. For H2S it is shownb that the position of the bodn critical point is not only more sensitive to the presence of polarization functions in the basis set, but depends strongly on the orbital exponents of the polarization functions. Extensive optimizations of the exponents of the polarization functions have been carried out with the (12s9p/5s) basis set for second‐row hydrides. The effects of contracting the Huzinaga basis sets have been examined.
Electronic structure and chemical bonding of the dimer of bis(η5‐cyclopentadienyl)ytterbium methyl
Authors: Xu(K. H.Hsu) Guang‐Xian , Ren Jingqing
Published: December 2004

The electronic structure, charge distribution, and chemical bonding of the dimer of bis‐(η5‐cyclopentadienyl)ytterbium methyl have been studied by an unrestricted INDO program made applicable for the lanthanoid compounds [1]. The bond order, composition, and the nature of the bridge bonds have been discussed. The existence of weak interaction between two ytterbium atoms was shown.
A finite expansion method for the calculation and interpretation of molecular electrostatic potentials
Authors: Rabinowitz James R. , Namboodiri Krishnan , Weinstein Harel
Published: December 2004

Because it is useful to have the molecular electrostatic potential as an element in a complex scheme to assess the toxicity of large molecules, efficient and reliable methods are needed for the calculation and characterization of these potentials. A multicenter multipole expansion of the molecular electron charge density calculated with a limited Gaussian basis set is shown here to have only a finite number of nonzero terms from which the molecular electrostatic potential can be calculated. The discrete contributions to the electrostatic potentials from the terms of this expansion provide a physically meaningful decomposition of the potential and a means for its characterization. With pyrrole as an example, the electrostatic potential calculated from this finite expansion of the electron density is compared to that obtained from exact calculations from the same wave function. Good agreement is obtained at distances greater than 1.5 A from any atom in the molecule. In contrast, rearrangement of the terms into an expansion corresponding only to Mulliken atomic charges and dipoles yields a decomposition that produces electrostatic potentials which agree less well with the exact potential. This discrepancy is attributable to the neglect of terms due to higher moments.
On optimization procedures based upon the atomic thomas‐fermi energy
Authors: Ten Hoor Marten J.
Published: December 2004

For the total atomic Thomas‐Fermi (TF) energy many expressions in terms of the kinetic and potential energy contributions can be given. Thirty of these expressions exhibit either a maximum or a minimum if some variational approximation to the TF function is used. Three of these expressions, to note E, G, and J (see text) have been used in an optimization procedure, in which four two‐parameter and two three‐parameter approximate TF functions have been considered. One‐parameter functions cannot be optimized, as the one parameter must be fixed to ensure proper normalization. It is found that optimization of E and G give reasonable and similar results, whereas the results of optimization of J are generally not very impressive. Where possible, expectation values of the type 〈rn〉 (with n = −1, 1, 2, and 3) have been calculated from ten approximate TF functions. A new estimate of the exact atomic TF energy, as well as of the derivative of the TF function at the origin, has been obtained.
Model universal coulomb hole function for many‐electron systems
Authors: Gritsenko O. V. , Bagaturjants A. A. , Kazansky V. B.
Published: December 2004

In the framework of the homogeneous electron gas theory we give a model function Gc of the Coulomb hole that can be considered as an approximate universal correlation function for many‐electron systems. The function Gc reflects the right asymptotic behavior of the correlation function of an electron gas in high and low density limits and enables one to reproduce experimental correlation energies of a number of atoms of the first and second periods in a local density approximation with the relative error 0.3–4.2%. The estimate of contributions of electrons with parallel or antiparallel spins into correlation energy shows that in the domain of densities typical for atoms of the first and second periods, the Coulomb correlation of electrons with parallel spins is in high extent suppressed by the Fermi correlation.
An MNDO study of the reaction of methanol with fulminic acid and acetonitrile oxide
Authors: Sharma Krishan K. , Aggarwal Anil K.
Published: December 2004

The reaction pathway of fulminic acid (HCNO) and acetonitrile oxide (CH3CNO) with methanol as a nucleophile (RCNO + CH3OH → RC(OCH3)NOH) and the formation of H‐bonded complex with methanol have been studied using the MNDO method. MNDO‐SCF calculations were performed with complete geometry optimization using the Davidon–Fletcher–Powell method. The reaction pathways were studied by varying all the bond lengths, the bond angles and the twist angles, using the distance C3O2(R) between the carbon of the 1,3‐dipoles and the oxygen of the methanol molecule as the reaction coordinate. The reaction is exothermic and proceeds in two steps. The first step is the formation of a five‐centered hydrogen‐bonded complex (INT) and is the rate‐determining step of the reaction. The second step involves the rearrangement of the H‐bonded complex to the product, and this step requires a very small amount of activation energy. Thus, there is an intermediate on the reaction pathway, and therefore, the reaction is stepwise. Acetonitrile oxide is less reactive (activation energy 34.59 kcal/mol) relative to fulminic acid (activation energy 28.91 kcal/mol).
Tautomerism of uracil, cytosine, isocytosine, and some of their thio‐derivatives
Authors: Leś Andrzej , Ortega‐Blake Iván
Published: December 2004

We present an ab initio study of tautomerism in uracil, cytosine, isocytosine, and some of their derivatives, mainly those due to thio substitution. We advance gas phase enthalpies for the tautomerization processes. We observe that the substitution of atoms not directly involved in the tautomerism has no appreciable effect on the enthalpy values. On the other hand, thio substitution of the oxygen involved in the tautomerism produces a general and small shift favoring the thiol isomer in aromatic complexes. We compare the theoretical predictions with the experimental evidence available and find them to agree.
Application of cholesky‐like matrix decomposition methods to the evaluation of atomic orbital integrals and integral derivatives
Authors: O'neal Douglas W. , Simons Jack
Published: December 2004

When viewed as a square two‐indexed matrix, the array of atomic orbital‐based, two‐electron integrals (ij|kl) is a positive semidefinite array. Beebe and Linderberg showed, in 1977, that actual or near linear dependencies often exist within the types of atomic orbital basis sets employed in conventional quantum chemical calculations. In fact, large (i.e., higher quality) bases were shown to be substantially more redundant than smaller or more spatially separated bases. In situations where there exists significant basis near redundancy, the rank (r) of the (ij|kl) ≡ Vl,J matrix of integrals will be significantly smaller than the matrix dimension M. When this occurs, it proves computationally tractable to decompose the M‐dimensional matrix V into components L (V = LLT) which contain all of the information needed to form the full V matrix. The Cholesky algorithm allow such a decomposition to be carried out and forms the basis of the work described here. The method is found to be highly successful in reducing the number of integrals and integral derivatives that must actually be calculated. In particular, results on the C2 molecule indicate that the algorithm can be superior to traditional methods of integral derivative generation if the orbital basis is large enough to contain appreciable near redundancy. In contrast, results on benzene with a more spatially delocalized basis show that conventional methods are preferred whenever substantial basis (near) redundancy is not present.
Approximate density–external potential relation and the pauli potential for systems with coulombic interaction
Authors: Kozlowski P. M. , March N. H.
Published: December 2004

Earlier work on the Pauli potential VPauli, which allows the square root of the electron density to be calculated directly from a Schrödinger equation, is generalized from two‐level (radial) systems such as the Be atom to the n‐level case in one dimension. This is achieved using hyperspherical functions, in terms of which the first‐ and second‐order density matrices are expressed. It is confirmed that VPauli can be constructed from the ground‐state density ρ (x) and its first two derivatives, plus the functional derivative of the single‐particle kinetic energy with respect to ρ. Finally, contact is made with the Harriman construction, but now using approximate one‐body orbitals.
The effect of penetration on the multipole and multistreak expansions of molecular electrostatic potentials
Authors: Berrondo M. , Eggleston S. W. , Larson E. G.
Published: December 2004

We have separated the electrostatic potential of a molecule into two parts: an atomic‐like part, which is expanded in spherical harmonics around each nucleus, plus an overlap part, expanded in ellipsoidal harmonics around each pair of nuclei. Neglect of the penetration effect in these expansions yields a superposition of point and line multipoles. We have studied the penetration effect for the case of the hydrogen molecules and suggest an approximation for the elliptical penetration effect as a screening factor in the electrostatic potential.
Variational calculations of vibrational and vibration‐rotational properties of ozone
Authors: Anmin Tian , Ruifeng Liu , Zemin Sun , Xuefeng Zhou , Guosen Yan
Published: December 2004

Vibrational and vibration‐rotational energy levels of ozone and its isotopic substitutes have been calculated variationally by the ladder operator method. Thirty vibrational band origins and rotational energies of vibrational ground states for these molecules have been given. The good agreement between the calculated results and the observed values shows that the calculation method is a promising one for variational studies of vibrational and vibration‐rotational properties of nonlinear polyatomic molecules.
Evaluation of two‐center, two‐ and three‐electron integrals involving correlation factors over Slater‐type orbitals. II. Kinetic and potential energy integrals and examples of numerical results
Authors: Budziński Jan , Firszt Mirosława , Woźnicki Wiesław
Published: December 2004

This article is concerned with the construction of the general algorithm for evaluating two‐center, two‐ and three‐electron integrals occurring in matrix elements of one‐electron operators in the basis of variational correlated functions. This problem has been solved here in prolate spherical coordinates, using the modified and extended form of the Neumann expansion of the interelectronic distance function rkij derived in Part I of this series for k = −1, 0, 1, 2. This work expands the method proposed by one of us in the preceding paper for integrals of the types mentioned above. The results of numerical calculations for different types of the two‐ and three‐electron integrals are presented. The problem of convergence of the proposed procedures used is also discussed.
Ab initio studies of parts of the potential surface for the system C3H6 + HO2
Authors: Skancke Per N.
Published: December 2004

The addition reactions between HO2 and propene leading to the radical intermediates CH3CHCH2OOH and CH3CHOHCH2 have been studied by ab initio molecular orbital calculations using a 6‐31G* basis set and including electron correlation through fourth‐order Møller–Plesset calculations. The intermediates are predicted to have energies of about 5 kcal/mol below the total reactant energies, the complex resulting from the HO2 attack on the central carbon of propene being slightly preferred. The activation energies for the addition to the terminal carbon and the central carbon are predicted to be 8.5 and 8.0 kcal/mol, respectively, at the highest level of calculation [MP4(SDTQ)] with corrections for spin contamination. Spin contamination corrections are found to be very important in the calculation of these values. Referring to previous calculations at the same level for the addition of HO2 to ethylene [12], we assume that the addition step is the rate‐determining one in the reaction leading to HO and propene oxide. The observed activation energy for this reaction, 14.2 kcal/mol [2], is significantly higher than the predicted one for the addition step. The discrepancy found, 6.2 kcal/mol, is virtually the same as the one encountered in the ethylene case, 6.6 kcal/mol [12]. The barrier to intramolecular hydrogen migration leading to the intermediate radical CH2CH2CH2OOH is found to be 42.6 kcal/mol at the highest level of calculation. Spin contaminiation corrections are not important for this energy.
Exact and approximate Hartree–Fock calculations for extended metallic systems
Authors: Calais Jean‐Louis , Delhalle Joseph
Published: December 2004

Starting out with the electron gas, we make a survey of the reasons for the singularity in the derivative of the orbital energy with respect to the wave number at the Fermi level for a realistic extended metallic system. Some properties of the occupation function are reviewed and it is pointed out that the direct reason for the singularity resides in a divergent lattice sum originating in the exchange part of the orbital energy. Numerical aspects are discussed, in particular with reference to the difficulty in detecting this singularity in actual computations.
Strategies for electron correlation calculations on large molecular systems
Authors: Saebø Svein
Published: December 2004

The two main problems in applying common methods for electron correlation to large systems are (1) the steep dependency of the computational task with the size of the system and (2) the large and often prohibitive number of two‐electron integrals that must be stored and retrieved during the calculation. The direct local correlation method eliminates both these problems. This method is a combination of the local correlation method that eliminates the steep computational dependency with the size of the system and extension of the direct SCF approach to electron correlation methods. The latter method eliminates external storage of the electron repulsion integrals. In this review, the direct local correlation approach and its computer implementation will be described in detail, including computational examples and comparisons to similar methods developed in other groups. The feasibility of future applications to extended systems is discussed.
Theoretical study of the hydrogen chemisorption on a ZnO surface
Authors: Nakatsuji H. , Fukunishi Y.
Published: December 2004

Reactions of a hydrogen molecule with a ZnO surface are studied by an ab initio method. For simulating the ZnO (10 1 0) surface, one ZnO molecule both with and without a Madelung potential is used. Since the electrostatic potential due to the ionic layer decreases exponentially, the effect of the layers deeper than the second one can be neglected. The Madelung potential is, therefore, expressed by the 32 point charges of ±0.5 situated on the first and second layers. Several low‐lying states of ZnO and the ZnO + H2 system have been calculated by the symmetry‐adapted cluster (SAC) and SAC–CI methods. It is found that the 1Σ+ state of ZnO is the ground state and catalytic active and the other states are inactive. ZnO (1Σ+) reacts with H2 and dissociatively adsorbs it with making ZnH and OH bonds. This occurs both with and without the Madelung potential. Without the Madelung potential, the heat of reaction is 81.3 kcal/mol and the reaction barrier is 14.0 kcal/mol. With the Madelung potential, the heat of reaction decreases to 73.5 kcal/mol and the barrier decreases to 11.5 kcal/mol. The mechanism of this reaction is the electron donation from the 2pπ orbital of O to the antibonding σu MO of H2 and the back‐donation from the bonding σg MO of H2 to the LUMO of ZnO. In the intermediate stage of the reaction, the dipole of ZnO works to increase the overlap of the active MOS to make the reaction easier. Throughout the reaction, the in‐plane 2pπ orbital of O and the HOMO of ZnO are inactive and work to keep the ZnO bond stable during the catalytic process.
A molecular dynamics study of large‐scale reversible aggregation of anisotropic particles
Authors: Brugè F. , Martorana V. , Fornili S. L. , Palma‐Vittorelli M. B.
Published: December 2004

We report findings of 1000 ps molecular dynamics simulations of a bidimensional system of 4050 Lennard–Jones particles with electric dipoles, undergoing spinodal separation. This simple system is used to model the reversible aggregation of building blocks bearing specific and fixed adhesion sites at their surface. Aggregation regions so obtained resemble images of self‐assembled biological structures. Statistical analyses of these regions evidence the interplay of thermodynamic instability and of interaction range between the attachment sites. They also illustrate some basic aspects of the morphogenesis of extended biomolecular/cellular structures, self‐organized from initially homogeneous solutions.
Comments on the carbon cluster C60 and on its complexes with alkaline elements
Authors: Corongiu G. , Clementi E.
Published: December 2004

We have analyzed in the Hartree–Fock approximation the carbon cluster C60 with a single‐zeta [(9,5)/(2,1)] basis set and a double‐zeta [(9,5)/(4,2)] basis set, the latter with and without 3d polarization functions. Estimates of the correlation energy correction were obained either using Becke's density functional theory or the Clementi–Chakravorty's electron–pair density approximation. The cluster's positive ion and singly and doubly charged negative ions have also been studied (doublets for C and C and singlet and triplet for C) and computed both with a doublezeta basis set and defferent geometries or a double‐zeta plus polarization basis set. The geometries considered include the one obtained by quantum molecular dynamics using the Car–Parrinello approximation and two additional near this minimum. The computed ionization potential and electron affinity are in reasonable agreement with the experiments considering the basis sets adopted. A lithium, a sodium, or a potassium atom or the corresponding positive ions have been placed at the center of the cluster and have been shown to form stable complexes: C60Li+, C60Li, C60Na+, C60Na, C60K+, and C60K. In addition, preliminary data with a calcium atom are reported. Computations on model cluster C5, C6, and C9 are also reported to show that one needs large basis sets, extended use of polarization functions, and correlation corrections for quantitative results, more accurate than ∼5 kcal/mol per carbon atom, in the total energy, as in this work.
Ab initio SCF molecular dynamics: Exploring the potential energy surface of small silicon clusters
Authors: Maluendes S. A. , Dupuis M.
Published: December 2004

A few classical nuclear trajectories at finite temperature have been calculated from ab initio SCF energy gradients. They have been used as an alternative means to search for local minimum energy structures on the Born–Oppenheimer surfaces for some elemental silicon clusters. The approach is found to be beneficial in yielding different structures of silicon clusters. In other cases, the trajectories stay trapped in only one region of the phase space.
Monte Carlo simulation of liquid hydroxylamine using ab initio intermolecular potential functions
Authors: Michopoulos Yanos , Rode Bernd M.
Published: December 2004

A potential model for intermolecular interactions between hydroxylamine (NH2OH) molecules based on ab initio quantum mechanical calculations is reviewed and critically assessed by analyzing results from a Monte Carlo simulation of liquid hydroxylamine. The liquid structure is studied in detail using radial, energy, and angular distribution functions, coordination numbers, and their distribution. Results indicate a large first solvation shell (5.3 Å), which contains 13 molecules, out of which only 4 are truly bonded by nonlinear, low‐energy hydrogen bonds. These are of either the OH…O or the OH…N type, as NH…O and NH…N linear bonds are considerably suppressed, and no cyclic dimers are found. The dependence of the structural and physical properties on the simulation characteristics has also been investigated.
Cobalt spectroscopy and the structure of the active site of carbonic anhydrase
Authors: Garmer D. R. , Krauss M.
Published: December 2004

Theoretical models of divalent cobalt bound to the active site of the enzyme, carbonic anhydrase, are constructed to study the effect of the first‐shell geometry and coordination number on the experimentally observed visible spectra. Favorable comparisons of the ab initio calculations of the hexa‐aquo complex of Co(II) with experimental results provides a test of the method. The d–d spectra variation with pH in the enzyme is found to be determined by the first‐shell complex geometry as obtained from energy optimization. The low pH complex is predicted to be predominantly five‐coordinate with two waters in the first‐shell, whereas the high pH complex is predominantly four‐coordinate. Equilibria between the four‐ and five‐coordinate structures at low pH is not indicated by the calculation.
Inter‐ and intramolecular motions in proteins
Authors: Parak Fritz
Published: December 2004

The use of 57Fe Mössbauer radiation allows the study of protein crystal dynamics by a time‐resolved analysis of X‐ray scattering. In myoglobin cystals, the main source of the root mean squared amplitude of motions comes from intramolecular protein dynamics. Segments of the size of an α‐helix move collectively. Long‐range correlated motions give only a minor contribution. Comparison with Mössbauer absorption spectroscopy shows that protein‐specific dynamics is frozen out below 200 K and the lattice dynamics is mainly responsible for the low‐temperature behavior.
Studies of protein hydration in aqueous solution by high‐resolution nuclear magnetic resonance spectroscopy
Authors: Wüthrich Kurt , Otting Gottfried
Published: December 2004

Individual hydration water molecules in aqueous protein solutions have been observed using experimental schemes for homonuclear two‐dimensional and heteronuclear three‐dimensional NMR experiments in H2O solution, which do not require suppression of the solvent line by presaturation. In these experiments, the location of the hydration waters is determined from their nuclear Overhauser effects (NOEs) with individual hydrogen atoms of distinct amino acid residues. In the basic pancreatic trypsin inhibitor (BPTI), four internal water molecules that had been reported in three different crystal forms were also found to be in the same locations in the solution structure, with lifetimes with respect to exchange of the water protons in excess of 0.3 ns. Additional NOEs with polypeptide protons located on the protein surface may involve either hydration water molecules or hydroxyl protons of amino acid side chains. Their total number is small compared to the number of NOEs expected from the hydration water molecules identified in the crystal structures of BPTI.
Saddle‐point expansion in molecular‐orbital theory
Authors: Marañón Julio
Published: December 2004

We propose a novel method for calculation of the electronic correlation energy of molecular systems in the path integral formalism. The procedure consists of saddle‐point expansion of the path integral around the Hartree–Fock energy. By one loop‐expansion of the molecular path integral into the generalized space phase of the molecular orbitals, the shift energy is obtained.
Algorithmic tools in the study of semiempirical potential surfaces
Authors: Liotard Daniel A.
Published: December 2004

The most efficient optimization methods implemented in the semiempirical package AMPAC are presented. They concern the minimization of the energy or of the gradient norm by either pseudo‐Newton or quadratic procedures, the search for transition states, and the intrinsic reaction coordinate in conjunction with variational transition‐state theories. Nonlocal methods such as simulated annealing are also introduced. © 1992 John Wiley & Sons, Inc.
On the implications of the structure of 3′‐azido‐3′‐deoxythymidine and related compounds to antiviral activity
Authors: Da Motta Neto Joaquim Delphino , Zerner Michael C. , De Alencastro Ricardo Bicca
Published: December 2004

We report structure–activity relation studies on 3′‐azido‐3′‐deoxythymidine (AZT) and the implications to the biological activity of this class of compounds. The adiabatic potential surface (APS) of the title compound has been examined with the LCAO–MO–SCF method within the AMI approximation. This study has shown at least 13 minima, all separated by small energy differences and barriers. We have found that the equilibrium favors the anti,gg conformations, in variance to previous studies that predicted the syn,gg conformers to be the most stable forms. The most stable conformation (A) is favored by about 0.5 kcal/mol. However, calculations simulating a bulk‐water environment suggest that the three lowest energy conformations (A, B, and C) become almost degenerate in solution. We suggest that the crystallographic conformation (L), characterized by a high dipole moment, and analogous to C, undergoes a strong stabilization upon rotation of the 3′‐azido group and that these two conformers, C and L, are the only ones in which the hydroxyl proton is free of steric hindrance. This last point has some relevance from the biological point of view since it is generally accepted that this site must be phosphorylated in order for AZT to achieve its therapeutic effects. The above results suggest that, once in solution, conformer L isomerizes to C, which is the bioactive form of AZT. © 1992 John Wiley & Sons, Inc.
A combined quantum chemical/molecular mechanical study of hydrogen‐bonded systems
Authors: Vasilyev V. V. , Bliznyuk A. A. , Voityuk A. A.
Published: December 2004

A computational approach, which involves the combination of the OPLS force field and molecular orbital MNDO, AM1, and PM3 methods, has been developed to describe the effects of a large, molecular mechanically simulated environment on the Hamiltonian of a quantum chemical system. To test the validity of the combined quantum mechanical/molecular mechanical (QM/MM) potential, a systematic study of the structures and energies of neutral and charged hydrogen‐bonded complexes has been carried out, including comparisons with pure semiempirical calculations and available experimental and ab initio data. It is shown that, in many cases, the hybrid QM/MM potential behaves better than do related MNDO/M, AM1, and PM3 methods. As a case in point, the draw‐back of AM1 favoring bifurcated H‐bonded structures over single ones is not presented in the combined AM1/OPLS scheme. Possible ways of improvement of the combined QM/MM potential are discussed. © 1992 John Wiley & Sons, Inc.
The C2‐DIIS convergence acceleration algorithm
Authors: Sellers Harrell
Published: December 2004

We present a theoretical and numerical comparison between two DIIS algorithms to which we refer herein as C1‐DIIS and C2‐DIIS. The C2‐DIIS algorithm is shown to be equivalent to the traditional C1‐DIIS algorithm near convergence and more stable numerically as regards the accumulation of round‐off error when the C1‐DIIS equations become (nearly) singular. The C2‐DIIS algorithm also offers alternative solutions to the DIIS equations when anharmonicities or numerical difficulties are problematic. These properties of the C2‐DIIS algorithm allow the use of much larger DIIS spaces, obviating the need for truncation of the DIIS space, which, when done, usually results in a loss of information contained in the iterated subspace. The C2‐DIIS method can be considered to be a variant of the singular value decomposition method. © 1993 John Wiley & Sons, Inc.
Multiple time scale Hartree–Fock molecular dynamics
Authors: Hartke Bernd , Gibson Douglas A. , Carter Emily A.
Published: December 2004

This is the first application of a rigorous, established multiple time‐step method to ab initio molecular dynamics. The resulting algorithm is conceptually simple and easy to implement, but very effective. It translates the large mass differences present in ab initio molecular dynamics into substantial savings in computer time while retaining high accuracy. This transforms ab initio molecular dynamics from a desirable but prohibitively expensive possibility into a viable method, at least for short‐time phenomena in small systems or for otherwise inaccessibly complicated potential energy surfaces. © 1993 John Wiley & Sons, Inc.
Spatially confined simple quantum mechanical systems
Authors: Zicovich‐Wilson C. , Planelles J. H. , Jaskóalski W.
Published: December 2004

A study of two simple quantum mechanical system, i.e., harmonic oscillator (HO) and hydrogen atom (H) trapped inside the wells is performed. The influence of the spatial confinement on the energy spectra of both systems is investigated. An analytically solvable model of the well potential is presented in the case of the HO. A central and noncentral localization of HO in the well is discussed. The results are used to explain some reported anomalous experimental data on the porphine IR spectrum. The case of hydrogen atom is studied by solving the problem of the electron in the potential V = Z/R cot r/R. An exact formula for the energy is derived for s states. For others, analytically nonsolvable symmetries, a formula with correct asymptotic behavior is proposed. The results are compared with some numerical calculations for spherical rectangular well and an extension to many‐electron atoms is also presented. The effect of breaking degeneracy and of ordering energies of H in a different way than in the case of many‐electron systems is broadly discussed. © 1994 John Wiley & Sons, Inc.
A comparative study on the structure of M2Se and M2I+ (M = Ag, Au) using pseudopotentials and full Ab initio methods
Authors: Alemany Pere , Novoa Juan J. , Bengtsson Lars
Published: December 2004

The molecules of M2Se and M2I+ (M = Ag, Au) are used as test models to study the quality of the pseudopotential methodology when using the Hartree–Fock and second‐order Møller‐Plesset methods. We have used two implementations of the Wadt and Hay pseudopotentials: the new large‐ and small‐core pseudopotentials (known as LANL 1DZ and LANL2DZ in GAUSSIAN‐92) and the traditional one used for a long time. It is found that the optimum geometry depends on the type of pseudopotential selected. A comparison with the results computed when all the electrons are taken explicitly into account shows that the new LANL1DZ and LANL2DZ give the right answer. Using these potentials, the geometry and potential energy surface of the M2Se and M2I+ systems is explored and its optimum geometry found. © 1994 John Wiley & Sons, Inc.
Dynamics of photochemical reactions: Simulation by quantum calculations for transition metal hydrides
Authors: Daniel C. , Heitz M. C. , Lehr L. , Schröder T. , Warmuth B.
Published: December 2004

The photodissociation dynamics of some organometallic molecules in the lowest repulsive electronically states are reported for the following concurrent primary reactions: (i) the homolysis of a metal–hydrogen bond vs. the heterolytic loss of a carbonyl ligand in HCo(CO)4; (ii) the photoinduced elimination of molecular hydrogen vs. the loss of a carbonyl ligand in H2Fe(CO)4; and (iii) the photoinduced elimination of molecular hydrogen vs. the loss of a mesithylene ligand in H2Os(CO)Mes (Mes = C6H3(CH3))3. The dynamics are simulated quantum mechanically using a time‐dependent wavepacket propagation technique on potential energy surfaces obtained from CASSCF/CCI calculations for HCo(CO)4 and H2Fe(CO)4 and from SCF‐INO/MRCI calculations for H2Os(CO)Mes. This approach gives a rather detailed view of some important elementary processes that contribute to the photochemistry of these complexes. The nature of the photoactive excited states is determined without ambiguity, as well as the time scales, the branching ratio of the different primary dissociation pathways, and some features of the absorption spectra. © 1994 John Wiley & Sons, Inc.
Application of many‐body perturbation theory in the localized representation for the all‐trans conjugated polyenes
Authors: Kapuy E. , Bogár F. , Tfirst E.
Published: December 2004

Ab initio self‐consistent field (SCF) calculations are performed with the standard 6‐31G* basis set for all‐trans conjugated oligomers C2n+2H2n+4. The canonical occupied and virtual molecular orbitals (MOs) are separately localized by unitary transformations. Due to the localization, the perturbation operator is partitioned into two‐particle and into single‐particle terms; the MBPT is, therefore, a double‐perturbation expansion in this case. By using the localized representation of the MBPT, the correlation energy contributions can be partitioned into local and nonlocal effects. It can be shown that the local effects are very important and well transferable, which makes possible the calculation of the correlation energy of larger molecules if the localized molecular orbitals (occupied and virtual) of smaller related molecules are known. © 1994 John Wiley & Sons, Inc.
On the accuracy of molecular properties by coupled‐cluster methods for some difficult examples: Oxygen atom, iron atom, and cyano radical
Authors: Urban Miroslav , Watts John D. , Bartlett Rodney J.
Published: December 2004

Coupled‐cluster (CC) methods at the level of CCSD, CCSD+T(CCSD), CCSD(T), CCSDT‐1, and CCSDT‐3 are applied to calculations of the dipole moment and polarizability of the CN molecule, ionization potentials and electron affinities of the oxygen and iron atoms and CN molecule, and the energy splitting of the 5D and 5F states of the iron atom. Both UHF and ROHF references are applied. Extended basis sets are used in some comparison of CC data to experiment. All calculated atomic and molecular properties are known as challenging problems, suitable for a careful analysis of the performance of sophisticated versions of the CC approach. Attention is paid to energy terms distinguishing CCSD(T) from CCSD+T(CCSD). We exploit results from various iterative and noniterative high‐level CC methods in the assessment of error bars in calculations of atomic and molecular properties. © 1994 John Wiley & Sons, Inc.
Extrapolation of real‐space quantum chemical calculations from finite‐size super cells to the ideal infinite system. II. Application to one‐dimensional polymers
Authors: Nolting V. , Verwoerd W. S.
Published: December 2004

Calculations of finite atomic clusters based on the Hartree–Fock self‐consistent field theory are modified to model more closely the ideal behavior of the infinite system. The density matrix of the standard finite supercell calculation is extrapolated to an infinite supercell so that it contains information from a continuum of k points in the first Brillouin zone. This modification is incorporated into the self‐consistency loop of the MOPAC quantum chemistry program and leads to improved results compared to a standard finite supercell calculation. Heats of formation, bond lenghts, and electronic properties converge more quickly to the correct ground‐state values. For polyacetylene, we obtain a reduced bond‐length alternation of Δr = 0.084 Å, which is in agreement with more sophisticated calculations containing electron correlation effects. © 1994 John Wiley & Sons, Inc.
On a generalized Kepler–Coulomb system: Interbasis expansions
Authors: Kibler M. , Mardoyan L. G. , Pogosyan G. S.
Published: December 2004

This article deals with a dynamical system that generalizes the Kepler–Coulomb system and the Hartmann system. It is shown that the Schrödinger equation for this generalized Kepler–Coulomb system can be separated in prolate spheroidal coordinates. The coefficients of the interbasis expansions between three bases (spherical, parabolic, and spheroidal) are studied in detail. It is found that the coefficients for the expansion of the parabolic basis in terms of the spherical basis, and vica versa, can be expressed through the Clebsch–Gorden coefficients for the group SU(2) analytically continued to real values of their arguments. The coefficients for the expansions of the spheroidal basis in terms of the spherical and parabolic bases are proved to satisfy three‐term recursion relations. © 1994 John Wiley & Sons, Inc.
Role of tunneling of hydrogen in photoenolization of a ketone
Authors: Sengupta Debasis , Chandra A. K.
Published: December 2004

Photoenolization of a ketone in its lowest triplet state was examined using the AM1 semiempirical molecular orbital method with complete geometry optimization at the configuration interaction level in the restricted Hartree–Fock frame. The theoretical barrier fits with a polynomial given by Eq. (1) and the probability of tunneling of hydrogen was calculated by the WKB method. The density of states above the zero‐point level was estimated by the Whitten–Rabinovitch approximation. Rate constants for the hydrogen and deuterium‐abstraction processes via tunneling were then computed at different temperatures. © 1994 John Wiley & Sons, Inc.
A semiclassical density functional evaluation of the smoothly varying part of the Hartree–Fock binding energy in atoms
Authors: Delchev Ya. I. , Pavlov R. L. , Pavlova A. , Marinova L. P. , Maruani Jean
Published: December 2004

A semiclassical density functional approach is used to evaluate the smooth part of the variation of the Hartree–Fock (HF) binding energy in atoms, from helium through xenon. The energy density functional is chosen with an improved form for the kinetic energy functional (KEF). The variation of the HF binding energy is split into smooth and oscillating (shell‐structure) parts, in accordance with Strutinskyøs self‐consistent averaging procedure, which is equivalent to a semiclassical ħ‐expansion of the KEF. This enables a well‐grounded evaluation of the oscillating part of the HF binding energy, which displays a quasi‐periodic behavior expressing clearly the shell structure of atoms. © 1994 John Wiley & Sons, Inc.
Stationary response with exponential transformation: A perturbative analysis for molecular static properties
Authors: Ghose Keya Basu
Published: December 2004

We present here a perturbative analysis of the coupled cluster response method for molecular static properties with Euler and extended coupled cluster functionals under cubic truncation. Comparative analysis is meant to cater to both pedagogical and practical interests. Comprehensive tables for energy‐derivative expressions and equations at the stationary point are presented. © 1995 John Wiley & Sons, Inc.
The interaction of chemical bonds. IV. Interbond charge transfer by a coupled‐cluster‐type formalism
Authors: Surján Péter R.
Published: December 2004

A fully linearized coupled‐cluster technique is used to improve a multiconfigurational wave function. The reference function is constructed as the antisymmetrized product of strictly localized geminals. The matrix elements appearing in the formalism are trivial to evaluate. The form of the cluster operator is chosen to produce one‐electron transfer from one geminal to another. The method is tested on the He ⃛ He potential curve. It is found that the importance of such charge‐transfer contributions is the same as that of dispersion. Clusters of three He atoms are also examined and some illustrative calculations on small molecules are presented. © 1995 John Wiley & Sons, Inc.
A formulation of multiple‐reference CI with terms linear in the interelectronic distances. II. An alternative ansatz
Authors: Gdanitz Robert J. , Röhse Robert
Published: December 2004

An alternative ansatz for r12‐MR‐CI is given. The final formulas are much more easily obtained than was possible previously. The numerical performance is demonstrated with a model calculation of the ground state of helium using three different Gaussian basis sets (5s, 10s, 16s). With the two largest basis sets, the energies obtained with the new formulas, the formulas of Part I of this series of articles, and the formulas of the original formulation agree within 2 μEH. Since the new ansatz is much easier to handle mathematically, we recommend its usage for future work. © 1995 John Wiley & Sons, Inc.
Evaluating the performance of correlated methods in molecular property calculations: Pattern recognition and clustering in spaces of theoretical descriptions
Authors: Maroulis George
Published: December 2004

A rigorous approach to the evaluation of the performance of correlated methods in molecular property calculations is proposed. Theoretical descriptions of molecules are identified as collections of molecular property values. Distance functions are then defined in the space of theoretical descriptions and the metric properties are used to define proximity and similarity between theoretical descriptions. Graph theoretic arguments and pattern recognition techniques are used to study ordering, classification, self‐organization, and clustering in the space of theoretical descriptions. © 1995 John Wiley & Sons, Inc.
Performance of valence‐universal multireference coupled‐cluster theory for quasi‐degenerate states: The H8 and DZPH4 models
Authors: Jankowski K. , Grabowski I.
Published: December 2004

Valence‐universal coupled‐cluster (VU–CC) methods corresponding to the approximations S ≃ S1 + S2 (VU–CCSD) and S ≃ S1 + S2 + S3 (VU–CCSDT) for the cluster operator S have been applied to two model systems for which the degree of quasi‐degeneracy of the two lowest, totally symmetric, singlet states may be varied over a wide range by changing their geometry. The performance of the VU–CC methods is investigated with the aim of verifying the findings of recent extensive reliability studies of these methods [Jankowski et al., J. Chem. Phys. 97, 7600 (1992); Ibid. 101, 3085 (1994)] based on calculations for the less complex minimum basis set H4 model. The present results confirm these findings. In particular, the VU–CCSD energies are less accurate than those obtained with other single‐ and multireference methods including up two‐body amplitudes. It is also confirmed that the impact of the S3 clusters is significant and the accuracy of description is rather insensitive to the kind of molecular orbitals employed. © 1995 John Wiley & Sons, Inc.
Coordinate scaling and adiabatic connection formula for ensembles of fractionally occupied excited states
Authors: Nagy Á.
Published: December 2004

The coordinate scaling for the density matrix of ensembles of fractional occupied states of the density functional theory is explored. The ground‐state adiabatic connection formula is extended to the ensemble exchange‐correlation energy. © 1995 John Wiley & Sons, Inc.
Chemistry and the near‐sighted nature of the one‐electron density matrix
Authors: Bader Richard F. W.
Published: December 2004

Two different macrospopic pieces of copper have different external potentials and, because of the unique functional relationship between the electron density and the external potential as demanded by density functional theory, should possess different electron density distributions. Experimentally, however, an atom in the bulk exhibits the same electron density in both samples and they possess identical sets of intensive properties. Density functional theory does not account for the fundamental observation underlying the theory of atoms in molecules: that what are apparently identical distributions of charge can be observed for an atom or a grouping of atoms in systems with different external potentials and that these atoms contribute essentially identical amounts to the energies and all other properties of the systems in which they occur. It is shown that, unlike the external potential, the kinetic energy density and the potential energy density, defined by the virial of the Ehrenfest force acting on electron density, are short‐range functions. As recorded in the first article on atoms in molecules, they exhibit a local dependence on the electron density that causes them to faithfully mimic the transferability of the atomic charge distributions from one system to another. The electron, the kinetic energy, and the virial densities are all determined directly by the one‐electron density matrix, a function termed near‐sighted by Professor Kohn. It is this near‐sighted property of the one‐matrix that underlies the working hypothesis of chemistry—that of a functional group exhibiting a characteristic set of properties. The observations obtained from the theory of atoms in molecules and the atomic theorems it determines demonstrate the existence of a local relationship between the electron density and all properties of a system. © 1995 John Wiley & Sons, Inc.