Radial electron-pair densities in momentum space and shell structure of atoms

 The radial electron-pair intracule (relative motion) H(u) and extracule (center-of-mass motion) D(R) densities in position space were known to reveal four types of maxima which are related to the four inner electron shells, K, L, M, and N, of atoms. The corresponding radial electron-pair intracule Hˉ(v) and extracule Dˉ(P) densities in momentum space are studied for the 102 atoms from He (atomic number Z=2) to Lr (Z=103). The densities Hˉ(v) and Dˉ(P) are found to have either one maximum or two maxima, and the numbers of maxima in Hˉ(v) and Dˉ(P) are the same for 98 atoms. For these atoms, the locations υ _max and P _max and the heights Hˉ _max and Dˉ _max of the corresponding maxima satisfy the approximate relations υ _max ≅ 2P _max and Hˉ _max ≅Dˉ _max /2. On the basis of their Z-dependence, the maxima in Hˉ(v) and Dˉ(P) of the 102 atoms are classified into five types. Shell-pair decompositions of the radial densities show that these maxima reflect five outer electron shells of atoms. Received: 24 January 2001 / Accepted: 12 March 2001 / Published online: 13 June 2001     

Influence of diffuse and polarization functions on the second-order Møller–Plesset optimized dihedral angle of biphenyl

 Using 6-31G and 6-311G basis sets to which diffuse and polarization functions were added in a stepwise fashion (a total of 16 basis sets), Hartree–Fock (HF), MP2 and B3LYP geometry optimizations were performed on biphenyl. With the MP2 method, diffuse functions raise the dihedral angle φ, for example, from 46.3° for 6-31G to 54.1° for 6-311++G, while polarization functions lower it, for example, from 54.1° for 6-311++G to 42.1° for 6-311++G(2d,2p). For a single set of polarization functions, φ(MP2) lies close to or above φ(HF) (44–47°), but for a double set it is below φ(HF) and is close to B3LYP values (38–42°) which show little basis set dependence. The most reliable value for φ, 42.1° [MP2/6-311++G(2d,2p)], is expected to increase slightly by adding more diffuse functions. The corresponding best calculated energy barrier at 0° (coplanar conformation) is 2.83 kcal/mol, much higher than the experimental estimate (1.4 ± 0.5 kcal/mol). The barrier at 90° is 1.82 kcal/mol, in line with the experimental estimate (1.6 ± 0.5 kcal/mol) and with previous theoretical results. Received: 9 September 2002 / Accepted: 15 November 2002 / Published online: 1 April 2003 Correspondence to: Friedrich Grein e-mail: fritz@unb.ca Acknowledgement. The author would like to thank NSERC (Canada) for financial support.     

Atomic electron-pair distances and subshell radii in position and momentum space

For the 53 neutral atoms from He to Xe in their ground states, the average distances < u> _{n l , n ′ l ′} in position space and < v> _{n l , n ′ l ′} in momentum space between an electron in a subshell nl and another electron in a subshell n ^′ l ^′ are studied, where n and l are the principal and azimuthal quantum numbers of an atomic subshell, respectively. Analysis of 1700 subshell pairs shows that the electron-pair distances < u> _{n l , n ′ l ′} in position space have an empirical but very accurate linear correlation with a one-electron quantity U _{n l , n ′ l ′}≡L _r +S _r ²/(3L _r ), where L _r and S _r are the larger and smaller of subshell radii < r> _{n l} and < r> _{n ′ l ′}, respectively. The correlation coefficients are never smaller than 0.999 for the 66 different combinations of two subshells appearing in the 53 atoms. The same is also true in momentum space, and the electron-pair momentum distances < > _{n l , n ′ l ′} have an accurate linear correlation with a one-electron momentum quantity V _{n l , n ′ l ′}≡L _p +S _p ²/(3L _p ), where L _p and S _p are the larger and smaller of average subshell momenta < p> _{n l} and < p> _{n ′ l ′}, respectively. Trends in the proportionality constants between < u> _{n l , n ′ l ′} and U _{n l , n ′ l ′} and between < > _{n l , n ′ l ′} and V _{n l , n ′ l ′} are discussed based on a hydrogenic model for the subshell radial functions. Received: 8 April 1998 / Accepted: 6 July 1998 / Published online: 18 September 1998     

Correlated electron-pair properties of the Li atom in momentum space

On the basis of multiconfiguration Hartree–Fock calculations, correlated electron-pair intracule (relative motion) and extracule (center-of-mass motion) properties are reported for the Li atom in momentum space. The present results are more accurate and consistent than those in the literature. Received: 10 September 2001 / Accepted: 11 December 2001 / Published online: 22 March 2002     

Quantum mechanics and mixed quantum mechanics/molecular mechanics simulations of model nerve agents with acetylcholinesterase

 The accurate modeling of biological processes presents major computational difficulties owing to the inherent complexity of the macromolecular systems of interest. Simulations of biochemical reactivity tend to require highly computationally intensive quantum mechanical methods, but localized chemical effects tend to depend significantly on properties of the extended biological environment – a regime far more readily examined with lower-level classical empirical models. Mixed quantum/classical techniques are gaining in popularity as a means of bridging these competing requirements. Here we present results comparing two quantum mechanics/molecular mechanics implementations (the SIMOMM technique of Gordon et al. as implemented in GAMESS, and the ONIOM technique of Morokuma et al. found in Gaussian 98) as performed on the enzyme acetylcholinesterase and model nerve agents. This work represents part of the initial phase of a DoD HPCMP Challenge project in which we are attempting to reliably characterize the biochemical processes responsible for nerve agent activity and inhibition, thereby allowing predictions on compounds unrelated to those already studied. Received: 10 October 2001 / Accepted: 13 November 2002 / Published online: 1 April 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: M. M. Hurley e-mail: hurley@arl.army.mil     

Density functional theory gas- and solution-phase study of nucleophilic substitution at di- and trisulfides

 Density functional calculations indicate that nucleophilic substitution in the thiolate–disulfide and thiolate–trisulfide exchange reactions proceeds by an addition–elimination pathway. Solution calculations were performed using B3LYP/6-31+G* and the polarized continuum method. These solution-phase calculations indicate that for the reactions where the sulfur under attack bears a hydrogen atom, the substitution proceeds via an addition–elimination mechanism; however, when a methyl group is attached to the sulfur under attack, the S_N2 mechanism is predicted. Received: 12 October 2001 / Accepted: 28 November 2001 / Published online: 8 April 2002     

A DFT study of pyramidalized alkenes: 7-oxasesquinorbornenes and 7,7′-dioxasesquinorbornenes

  DFT calculations of 7′–oxasesquinorbornenes and 7,7′-dioxasesquinorbornenes using the B3LYP/6–31G* method are reported. All the investigated structures (syn- and anti- derivatives) showed significant non-planarity of the central double bond, with the exception of those anti-derivatives possessing symmetrical structures. The influence of the replacement of the methylene groups at position 7- of the norbornene fragment with oxygen and the introduction of second and third (peripheral) double bonds and benzene rings on the molecular and electronic structures of these molecules have also been investigated. Received: 11 November 2002 / Accepted: 6 June 2002 / Published online: 29 April 2003     

Chemical reactivity and selectivity using Fukui functions: basis set and population scheme dependence in the framework of B3LYP theory

The use of Fukui functions for the site selectivity of the formaldehyde molecule for nucleophilic, electrophilic and radical attacks has been made with special emphasis to the dependence of Fukui values on the basis sets as well as population schemes in the framework of B3LYP theory. Out of the five population schemes selected viz., Mulliken population analysis, natural population analysis, CHELP, CHELPG and atoms in molecules (AIM), it is found that the CHELPG and AIM schemes predict precise reactive site with less dependency on the basis sets. Charges derived from Hirshfeld partitioning, calculated using the BLYP/dnd method (implemented in the DMOL³ package), provide non-negative Fukui values for all the molecular systems considered in this study. Supporting results have been obtained for acetaldehyde and acetone molecules at the 6-31+G** basis set level. These results support the fact that high Fukui values correspond to soft–soft interaction sites. On the other hand, the correlation of the low Fukui value to the hard–hard interaction site merits further investigation. Received: 10 November 2001 / Accepted: 6 March 2002 / Published online: 13 June 2002     

Orbital-band interactions and the reactivity of molecules on oxide surfaces: from explanations to predictions

 The surface chemistry of oxides is relevant for many technological applications: catalysis, photoelectrolysis, electronic-device fabrication, prevention of corrosion, sensor development, etc. This article reviews recent theoretical works that deal with the surface chemistry of oxides. The account begins with a discussion of results for the adsorption of CO and NO on oxides, systems which have been extensively studied in the literature and constitute an ideal benchmark for testing the quality of different levels of theory. Then, systematic studies concerned with the behavior of adsorbied alkali metals and sulfur-containing molecules are presented. Finally, a correlation between the electronic and chemical properties of mixed-metal oxides is analyzed and basic principles for designing chemically active oxides are introduced. Advances in theoretical methods and computer capabilities have made possible a fundamental understanding of many phenomena associated with the chemistry of molecules on oxide surfaces. Still many problems in this area remain as a challenge, and the approximate nature of most theoretical methods makes necessary a close coupling between theory and experiment. Following this multidisciplinary approach, the importance of band-orbital interactions for the reactivity of oxide surfaces has become clear. Simple models based on band-orbital mixing can explain trends found for the interaction of many adsorbates with oxide surfaces. These simple models provide a conceptual framework for modifying or controlling the chemical activity of pure oxides and for engineering mixed-metal oxides. In this respect, theoretical calculations can be very useful for predicting the best ways for enhancing the reactivity of oxide systems and reducing the waste of time, energy and materials characteristic of an empirical design. Received: 21 June 2001 / Accepted: 8 October 2001 / Published online: 1 February 2002     

Digital erosion in the evaluation of molecular integrals

 In the course of checking our work on the symbolic calculation of molecular integrals over Slater orbitals, we obtained some results in substantial disagreement with two recent articles that describe numerical schemes. We believe that these schemes suffer from digital erosion, possibly because recurrence formulas were used outside their regions of stability. Our results were obtained using the ζ-function method, which expands the orbital on one atom onto the other, and integrates in polar coordinates. They were checked using elliptic coordinates. Both sets of calculations were performed symbolically. We summarize these calculations and discuss the impact of symbolic calculation on the accuracy of molecular computations. Received: 31 August 2001 / Accepted: 29 October 2001 / Published online: 8 April 2002     

Maxwell–Cartesian spherical harmonics in multipole potentials and atomic orbitals

 The nature of the Maxwell–Cartesian spherical harmonics S ⁽ⁿ⁾ _K and their relation to tesseral harmonics Y _nm is examined with the help of “tricorn arrays” that display the components of a totally symmetric Cartesian tensor of any rank in a systematic way. The arrays show the symmetries of the Maxwell–Cartesian harmonic tensors with respect to permutation of axes, the traceless properties of the tensors, the linearly independent subsets, the nonorthogonal subsets, and the subsets whose linear combinations produce the tesseral harmonics. The two families of harmonics are related by their connection with the gradients of 1/r, and explicit formulas for the transformation coefficients are derived. The rotational transformation of S ⁽ⁿ⁾ _K functions is described by a relatively simple Cartesian tensor method. The utility of the Maxwell–Cartesian harmonics in the theory of multipole potentials, where these functions originated in the work of Maxwell, is illustrated with some newer applications which employ a detracer exchange theorem and make use of the partial linear independence of the functions. The properties of atomic orbitals whose angular part is described by Maxwell–Cartesian harmonics are explored, including their angular momenta, adherence to an Uns?ld-type spherical symmetry relation, and potential for eliminating an angular momentum “contamination” problem in Cartesian Gaussian basis sets. Received: 9 July 2001 / Accepted: 7 September 2001 / Published online: 19 December 2001     

Transport properties of boron and aluminum

Transport cross sections and collision integrals are tabulated for a wide range of energies and temperatures for the interactions B–B and Al–Al. For aluminum, a semiclassical approximation was used to determine the scattering phase shifts from which the transport cross sections were calculated. For boron, the smaller reduced mass and the deep potential wells required the phase shifts at lower energies to be determined from a numerical solution of the time-independent Schroedinger equation; the semiclassical approximation was used at higher energies where the two methods agree. The variations of the collision integrals for viscosity and diffusion are presented graphically as a function of temperature. The results are applied to estimate the transport properties of gallium. Received: 9 July 1999 / Accepted: 18 August 1999 / Published online: 2 November 1999     

Band structure representations of the electronic structure of one-dimensional materials with helical symmetry

 The relationship between band structure and the topology of the orbital interactions between neighboring chemical units comprising several model one-dimensional polymers with helical (screw-axis) symmetry is analyzed. A perturbative model of orbital interactions based on a tight binding implementation of the extended Hückel method is developed. The model accounts for both the band topologies and the seemingly anomalous band extrema within the Brillouin zone constructed using the chemical repeat unit of the polymer. Received: 5 November 2001 / Accepted: 14 January 2002 / Published online: 3 May 2002     

Infrared spectra of CO in absorption and evaluation of radial functions for potential energy and electric dipolar moment

From quantum-chemical calculations of rotational g factor and new experimental measurements of strengths of lines in infrared spectra of vibration–rotational bands v′–0 in absorption, with 1≤v′≤4, of ¹²C¹⁶O, and from analysis of 16,947 frequencies and wave numbers assigned to pure rotational and vibration–rotational transitions within electronic ground state X ¹Σ⁺, including new measurements of band 4–0 of ¹²C¹⁶O, we evaluate radial functions for potential energy and electric dipolar moment, the latter both in polynomial form and as a rational function that has qualitatively correct behaviour under limiting conditions. Received: 8 November 2001 / Accepted: 5 February 2002 / Published online: 14 August 2002     

A thermodynamic and kinetic study of the formation of C<Subscript>20</Subscript> compounds encapsulating H,He and Ne atoms

 Binding energies of helium, neon and atomic hydrogen encapsulated inside a C₂₀ cage were calculated using an ab initio method at the B3LYP/6-31+G⋆ level of theory. The standard equilibrium constants for the reactions of noble-gas atoms going into the C₂₀ molecular cage have also been studied. The transition states for the reactions of C₂₀ with hydrogen and helium were further obtained with an ab initio method at the B3LYP/6-31+G⋆ level and the rate constants were estimated by using conventional transition-state theory. It was found that the hydrogen and helium atoms are extremely difficult to put into the C₂₀ cage. Once inside the cage, a helium atom can hardly get out, while a hydrogen atom can easily escape from the cage. The results are expected to enrich fullerene science and be helpful for fullerene applications such as storage. Received: 2 November 2002 / Accepted: 19 December 2002 / Published online: 30 April 2003 Correspondence to: R. Q. Zhang, e-mail: aprqz@cityu.edu.hk Acknowledgements. The work described in this paper was jointly supported by a grant from the City University of Hong Kong (project no. 7001222) and a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (project no. 9040633/CityU, 1011/01P].     

Some thoughts about the stability and reliability of commonly used exchange–correlation functionals – coverage of dynamic and nondynamic correlation effects

 The self-interaction error (SIE) of commonly used density functional theory (DFT) exchange functionals mimics long-range (nondynamic) pair correlation effects in an unspecified way. Slater exchange suffers from a larger SIE and, therefore, covers more nondynamic correlation effects than Becke exchange, which is the reason why exchange–correlation (XC) functionals based on Slater exchange lead to stabler restricted DFT solutions than those based on Becke exchange. However, the stability of an XC functional does not guarantee higher accuracy. On the contrary, if system-specific nondynamic correlation effects have to be introduced via the form of the wave function, these will be suppressed by nondynamic correlation effects already covered by the exchange functional. Hybrid functionals suffer less from the SIE and, therefore, cover a smaller number of nondynamic electron correlation effects. Accordingly, they are better suited when nondynamic electron correlation has to be introduced by the form of the wave function. It is shown that, for example, broken-symmetry unrestricted DFT calculations are more accurate when carried out with B3LYP than BLYP contrary to claims made in the literature. Received: 8 November 2001 / Accepted: 30 January 2002 / Published online: 8 April 2002     

Fully relativistic correlated benchmark results for uranyl and a critical look at relativistic effective core potentials for uranium

 A complete set of fully-relativistic benchmark results for the bond lengths and vibrational frequencies of uranyl at various levels of correlation treatment are presented. It is shown that the relativistic and correlation effects are of the same magnitude and should be treated on an equal footing. Results of uranyl calculations using various relativistic effective core potentials (RECP) are presented. Appropriate choices for RECPs for use in density functional theory (DFT) calculations in the local density approximation (LDA) and with the gradient-corrected B3LYP exchange-correlation functional are discussed. The conclusion is reached that small-core RECPs need to be used and that the best results as compared to the benchmark values are obtained by using a DFT functional that includes some fraction of Hartree-Fock Exchange. Received: 18 May 2001 / Accepted: 25 July 2001 / Published online: 30 October 2001     

Dressed coupled-electron-pair-approximation methods for periodic systems

 The techniques of matrix dressing for configuration-interaction (CI)-type or coupled-electron-pair-approximation (CEPA)-type correlation treatments are reviewed with respect to the application to periodic systems. All methods ranging from canonical second-order M?ller–Plesset perturbation theory over CI of single and double excitation, CEPA-0 or the averaged-coupled-pair-functional to self-consistent size-consistent CI can be formulated completely equivalently as an eigenvalue problem or as a solution to a system of linear equations. The size consistency of each method is obtained in a natural way, and invariance under orbital rotations is clearly assessible. A remark on the size consistency of the Davidson correction is presented. Additionally, the direct generation of localized Hartree–Fock orbitals as basic ingredients for the correlation calculations are addressed, as well as selected results on ring molecules, polymers, and 3D cubic beryllium as a model crystal. Received: 28 August 1999 / Accepted: 5 March 2000 / Published online: 21 June 2000     

Deadwood in configuration spaces. II. Singles + doubles and singles + doubles + triples + quadruples spaces

The effect of truncating singles + doubles configuration interaction (CISD) and singles + doubles + triples + quadruples (CISDTQ) spaces on the energies of the systems Ne, H₂O, CO and C₂ is investigated through the use of a previously described, general, selected CI program. CI expansions generated by Hartree–Fock orbitals as well as by natural orbitals are examined and the latter typically exhibit faster convergence as regards the energy. For the CISD wavefunctions of Ne, H₂O, CO and C₂, chemical accuracy is reached by using, respectively, 34, 47, 53 and 55% of the full sets. For the triples + quadruples parts of the wavefunctions on the other hand, chemical accuracy is already reached by using only 1, 4, 6 and 9% of the respective full sets. Received: 14 August 2001 / Accepted: 6 December 2001 / Published online: 8 April 2002