Symmetry-adapted integrals over many-electron basis functions and operators

We consider integrals over symmetry-adapted basis functions that involve the coordinates of more than one electron. We focus on basis functions that can be written as products of one-electron functions and (say) a two-electron function. We show first that the two-electron parts of the basis functions can be absorbed into the operator, resulting in an integral over only one-electron basis functions, but a more complicated many-electron operator. We then prove a general formula for expressing such integrals in terms of symmetry-distinct integrals only. Received: 16 June 2000 / Accepted: 10 July 2000 / Published online: 19 January 2001     

A first principles study of Pd deposition on the TiO2(1 1 0) surface

 The adsorption of isolated Pd atoms on the (1 1 0) surface of rutile TiO₂ was investigated through ab initio embedded-cluster calculations performed at the Hartree–Fock, second-order M?ller–Plesset and Becke's three parameter hybrid method with the Lee–Yang–Parr correlation functional levels. The role played by the magnitude of the surrounding charges used in the embedding procedure was carefully analyzed. The most stable site for adsorption consisted of a fourfold hollow site in which the Pd atom was coordinated to a fivefold Ti atom, two basal oxygens, and a protruding oxygen atom. However, the adsorption energies computed after basis set superposition error corrections seemed to favor a bridge site in which the Pd atom binds two protruding oxygen atoms. A periodic slab calculation using gradient-corrected functionals and plane-wave basis sets confirmed that for full coverage, the hollow site was more stable, although Pd displacement along the fivefold Ti channels was almost free. These results agree with the experimental data obtained from scanning tunneling microscopy. Finally, the adsorption energy computed from the periodic calculations was found to be 1.88 eV. Received: 14 September 1999 / Accepted: 3 February 2000 / Published online: 19 April 2000     

The hierarchy of localization basins: a tool for the understanding of chemical bonding exemplified by the analysis of the VOx and VOx+ (x=1–4) systems

The hierarchy of the electron localization basins is a powerful tool of analysis of the bonding in molecules and solids within the “elfological” framework. It is a generalization of the molecular isodensity contour analysis originally proposed by Mezey. In this approach the basins are ordered with respect to the electron localization function values at the critical points which determine the reduction of the reducible localization domains. The procedure enabling the corresponding tree diagrams to be built is described and it is shown how the method can be used as a generator of mathematical definitions of chemical concepts. The possibility offered by this simple tool is illustrated by a study of the VO _x and VO _x ⁺ (x=1–4) oxides in their ground state and in some excited states. Received: 20 July 2000 / Accepted: 20 October 2000 / Published online: 23 January 2001     

Excitation energies, electron affinities and ionization potentials of the transition metals V, Cr and Mn

 Configuration interaction calculations were carried out for neutral ground and excited states and positively and negatively ionized states of the V, Cr and Mn atoms. Energy convergence with respect to systematic expansion of both the one-electron and configuration bases was investigated for valence correlation. Contributions from core electrons to the differential correlation energies and relativistic effects were evaluated separately. Assuming additivity of these contributions, excitation energies, electron affinities and ionization potentials of the atoms were obtained. All calculated values were in excellent agreement with the observed values within a deviation of 0.056 eV except for the electron affinity of the V atom, which had a calculated value 0.110 eV larger than the experimental value. Received: 9 August 2000 / Accepted: 26 October 2000 / Published online: 3 April 2001     

An ab initio multireference doubles excitation configuration interaction study of low-lying electronic states of Cd2 using Slater-type orbitals

Potential-energy curves for the ground state and lower excited states of the Cd₂ dimer have been calculated. They are obtained using a multireference doubles excitation configuration interaction procedure and employing Slater basis sets, previously optimized at the self-consistent-field level for excited states of the Cd atom. The spectroscopic constants and excitation energies for the bound states of Cd₂ have been compared with experimental as well as other theoretical results. The ground state of Cd₂ is essentially repulsive and presents a shallow van der Waals minimum. The computed adiabatic electronic transitions are in good agreement with the experimental ones. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Contracted basis sets for electrical property calculations derived from Second-order Møller–Plesset theory atomic natural orbitals

 Using established methods based on correlated atomic natural orbitals (ANOs), sets of contracted polarization functions are derived for use in calculations of atomic and molecular electrical properties (especially electric moments, dipole polarizabilities and related property hypersurfaces). Through test calculations on Ne, Ar, NH₃ and CO₂, these polarization functions are shown to reproduce the accuracy of larger basis sets, to incorporate dynamical electron correlation effects and are economical to use in conjunction with sophisticated electron-correlation treatments. We also show how triple-zeta polarized ANO and double-zeta polarized ANO basis sets are constructed from these contracted polarization functions for use in the calculation of reliable zero-point vibrational averages of electrical properties. Received: 20 December 1999 / Accepted: 15 February 2000 / Published online: 12 May 2000     

An improved iterative solution to solve the electrostatic problem in the polarizable continuum model

 We present a discrete iterative interpolation scheme (DIIS) to improve the convergence rate of electrostatic calculations in the polarizable continuum model (PCM) to describe solvent effects on molecular solutes. The electrostatic calculations may easily become the bottleneck of the calculation when the solute size is large. For large molecules iterative procedures turn out to be computationally more convenient than matrix inversion or closure methods. The DIIS scheme is compared here to another iterative procedure (DAMP) and to the biconjugate gradient (BCG) method. The comparisons show that DIIS leads to a sizeable saving of computational time for the C-PCM and IEF-PCM methods (average 40%) compared to DAMP, and more than 50% with respect to the BCG method. Received: 5 October 2000 / Accepted: 13 November 2000 / Published online: 19 January 2001     

Domain-averaged Fermi holes – a new means of visualization of chemical bonds. Bonding in hypervalent molecules

The nature of bonding in several hypervalent molecules was analyzed at the ab initio SCF level using the recently proposed methodology based on the analysis of domain-averaged Fermi holes. The results of the analysis demonstrate that, for sufficiently flexible basis sets, the expansion of the valence shell does indeed take place for second row central atoms in PF₅, SF₄, and SF₆. On the other hand, no such expansion was observed for the first row N atom in NF₅. Received: 1 June 2000 / Accepted: 11 October 2000 / Published online: 23 January 2001     

Theoretical study of silicon–sulfur clusters (SiS2)n (n = 1–6)

 The possible geometrical structures and relative stability of (SiS₂) _n (n=1–6) silicon–sulfur clusters are explored by means of density functional theory quantum chemical calculations. The effects of polarization functions and electron correlation are included in these calculations. The electronic structures and vibrational spectra of the most stable geometrical structures of (SiS₂) _n are analyzed by the same method. As a result, the regularity of the (SiS₂) _n cluster growth is obtained, and the calculation may used for predicting the formation mechanism of the (SiS₂) _n cluster. Received: 17 November 1999 / Accepted: 3 November 2000 / Published online: 3 May 2001     

The Born closure approximation for the scattering amplitude of an electron-molecule collision

When the fixed-nuclei (FN) approximation is applied to the calculation of electron scattering from a polar molecule, the resulting cross section diverges in the forward direction of scattering. This is due to the long-range nature of the interaction between the electron and the molecular dipole. To avoid this difficulty, a hybrid method is proposed for the calculation of the scattering amplitude. This method is based on the FN approximation for a close collision and the Born approximation for a distant collision. The present paper describes the detailed formulation of the method for practical applications. Furthermore the present approach is extended to other long-range interactions (due to quadrupole moment and/or polarization effect) and to a dipole-allowed vibrational excitation. In these cases, while no divergence occurs, it is often difficult to confirm the convergence of the partial-wave expansion. With the employment of the present approach, it is much easier to confirm the convergence and hence to obtain reliable cross sections. The formulas are given for diatomic molecules as well as for polyatomic ones. Received: 12 June 2000 / Accepted: 6 July 2000 / Published online: 24 October 2000     

Study of association of 2-methoxyethanol in the aqueous phase

 Monte Carlo simulations have been carried out for 2-methoxyethanol in an isothermal–isobaric ensemble (NPT) at 298.15 K and 1 atm pressure. The optimized potential for liquid simulation force field parameters has been used for modeling 2-methoxyethanol and the TIP4P model for water. Intramolecular rotations are described by an analytical potential function fitted to ab initio energies. It has been shown that the water molecules can form hydrogen bonds between adjacent O atoms of CH₃OCH₂CH₂OH in aqueous media. The self-association of 2-methoxyethanol in aqueous media has been studied by statistical perturbation theory. Received: 9 October 2000 / Accepted: 5 January 2001 / Published online: 3 May 2001     

Electron affinities, excitation energies and ionization potentials of the transition metals (I) Sc and Ti

The electron affinities of the Sc and Ti atoms have been obtained by configuration interaction calculations. Energy convergence with respect to the systematic expansion of both the one-electron basis set and the configuration space was investigated for valence electrons, and the inclusion of correlation contributions from core electrons and relativistic effects gave the electron affinities of 0.181 eV and 0.163 eV for Sc and Ti, respectively. These are in excellent agreement with the observed values of 0.189 ± 0.020 eV and 0.080 eV. The same approach was applied for the first excited states and positive ions of both atoms. Excellent agreement with the experimental results was also obtained for these states. Received: 16 February 1998 / Accepted: 2 April 1998 / Published online: 23 June 1998     

Analysis of the RGD sequence in protein structures: comparison to the conformations of the RGDW and DRGDW peptides determined by molecular dynamics simulations

Geometric properties of the RGD sequence in a data set of protein crystal and NMR structures deposited in the Protein Data Bank were examined to identify structural characteristics that are related to cell adhesion activity. Interatomic distances and dihedral angles are examined. These geometric measures are then used in an analysis of the conformations of the RGDW and _DRGDW peptides obtained from molecular dynamics simulations (Stote RH, et al. (2000) J Phys ChemB 104:1624). This analysis leads to the suggestion that differences in the accessible conformations contribute to the difference in biological activity between the RGDW and the _DRGDW peptides. Received: 15 August 2000 / Accepted: 4 October 2000 / Published online: 21 March 2001     

Electric and magnetic multipole integrals in STO basis sets: an analytical approach

A new method for the evaluation of one- and two-centre magnetic and electric multipole integrals for Slater-type functions is presented. The method is strictly analytical in that no approximations of any kind are involved. Two simple functions, ℐ₁ ^aug and ℐ₂ ^aug, are introduced, which employ only functions that are well known in electronic structure theory. With the use of augmentation exponents these functions apply to multipole integrals as well as other one-electron integrals, such as nuclear attraction integrals. The proposed method includes the analytic determination of derivatives of the integrals with respect to atomic displacements. Some illustrative test calculations are presented and compared to results from the literature. Received: 20 April 1998 / Accepted: 13 October 1998 / Published online: 1 February 1999     

Prediction of DNA far-IR absorption spectra based on normal mode analysis

 We present a computational method which couples normal mode analysis in internal coordinates of a molecule with very far IR spectroscopy. The analytical expression for the dependence of IR absorption on frequency incorporates frequencies and optical activities of each normal mode. In order to predict far-IR spectra of a molecule we evaluate the optical activity of each normal mode. This optical activity is determined by the vibration amplitude of the dipole moment produced by a normal mode. We calculated normal modes of DNA double-helical fragments (dA)₁₂ · (dT)₁₂ and (dA-dT)₆ · (dA-dT)₆ and evaluated their optical activities. These were found to be very sensitive to the DNA base-pair sequence. The positions of the resonance peaks in the calculated absorption spectrum of (dA)₁₂ · (dT)₁₂ are in a good agreement with those obtained by Fourier transform IR spectroscopy (Powell JW et al. 1987 Phys Rev A 35: 3929–3939). Received: 20 June 2000 / Accepted: 5 January 2001/ Published online: 3 May 2001     

A computational model of the 5-HT3 receptor extracellular domain: search for ligand binding sites

A three-dimensional model of the 5-HT₃ receptor extarcellular domain has been derived on the basis of the nicotinic acetylcholine receptor model recently published by Tsigelny et al. Maximum complementarity between the position and characteristics of mutated residues putatively involved in ligand interaction and the pharmacophoric elements derived by the indirect approach applied on several series of 5-HT₃ ligands have been exploited to gain insights into the ligand binding modalities and to speculate on the mechanistic role of the structural components. The analysis of the three-dimensional model allows one to distinguish among amino acids that exert key roles in ligand interactions, subunit architecture, receptor assembly and receptor dynamics. For some of these, alternative roles with respect to the ones hypothesized by experimentalists are assigned. Different binding modalities for agonists and antagonists are highlighted, and residues which probably play a role in the transduction of binding into a change in conformational state of the receptor are suggested. Received: 27 July 2000 / Accepted: 15 September 2000 / Published online: 21 December 2000     

Intramolecular coupling study on nonlinear optical signals

 In this contribution, we have introduced intramolecular coupling in order to study possible modifications in the topology of the resonances associated with the four-wave mixing signal emerging as a consequence of incorporating the permanent dipole moments when the rotating-wave approximation is not included. Received: 17 September 1999 / Accepted: 9 March 2000 / Published online: 21 June 2000     

Spin-projected coupled-cluster theory with single and double excitations

Coupled-cluster (CC) theory including single (S) and double (D) excitations and carried out with a spin-unrestricted Hartree–Fock (UHF) reference wave function is free from S + 1 spin contamination as can be confirmed by an analysis of the expectation value of the spin operator, Ŝ ². Contamination by the S + 2 contaminant can be projected out by an approximate procedure (APCCSD) with a projection operator, P^, represented by the product of the spin annihilation operators ? _{s+ 1} and ?_s+2. The computational cost of such a projection scales with O(M ⁶) (M is the number of basis functions). The APCCSD energy obtained after annihilation of the S + 2 contaminant can be improved by adding triple (T) excitations in a perturbative way, thus leading to APCCSD(T) energies. For the 17 examples studied, the deviation of the UHF-CCSD(T) energies from the corresponding full configuaration interaction values is reduced from 4.0 to 2.3 mhartree on the average as a result of annihilating the S + 2 contaminant in an approximate way. In the case of single-bond cleavage, APCSSD leads to a significant improvement of the energy in the region where the bonding electrons recouple from a closed shell to an open shell singlet electron pair. Received: 13 April 2000 / Accepted: 12 July 2000 / Published online: 24 October 2000     

Inexpensive and accurate predictions of optical excitations in transition-metal complexes: the TDDFT/PBE0 route

Time-dependent density functional theory (TDDFT) is applied to calculate vertical excitation energies of three representative transition metal complexes. The computational model (PBE0) is obtained by combining the Perdew-Burke-Erzenrhof (PBE) generalized gradient functional with a predetermined amount of exact exchange. Our results show that the TDDFT/PBE0 model represents a cheap and reliable tool for the computation of optical excitations for transition metal complexes. Received: 8 August 2000 / Accepted: 7 September 2000 / Published online: 23 November 2000     

Electric response properties of a confined gas of independent particles acted upon by a direct current electric field

Exact results for linear and nonlinear electric response properties of a non-interacting ensemble of charged particles, confined within an impenetrable box and subjected to a static, homogeneous electric field, are derived and discussed. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 5 June 2000