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.     

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].     

Contracted Gaussian-type basis functions revisited. IV. Atoms Rb to Xe

We report minimal-type contracted Gaussian-type function (GTF) sets, #n=(n3333/n33/n3) with n=5 and 6, #7= (74333/743/74), and #8= (84333/843/75), for the fourth-row atoms from Rb to Xe. Test calculations are performed on the Ag₂ molecule. Spectroscopic constants given by split valence sets derived from #5 and #6 are a little contaminated by basis set superposition error. However, we find that the fully valence split #8 set, (8433111/84111/711111), yields essentially the same results as a large GTF set, (22s15p12d), with a general contraction, when p-, d-, and f-type polarization functions are augmented. The present #7 and #8 CGTF sets are recommended for ab initio molecular calculations including fourth-row atoms. Received: 15 January 2002 / Accepted: 16 April 2002 / Published online: 24 June 2002     

Comments on relativistic basis sets

 Adding the tight and diffuse Gaussian-type functions (GTFs), Faegri's variationally determined double-zeta-quality basis sets for molecular relativistic calculations are examined. An example atom is Cm. When the tight s-type GTF is added the total energy increases, whereas when diffuse GTFs are added the total energy decreases. The reasons for these findings are clarified. It is also pointed out that not only the Faegri's sets but also other variationally determined basis sets would show similar behavior so far as the expansion terms are not sufficient. Received: 22 July 2002 / Accepted: 21 October 2002 / Published online: 31 January 2003 Correspondence to: H. Tatewaki e-mail: htatewaki@nsc.nagoya.cu.ac.jp     

Two-electron distribution functions and intracules

 Two-electron distribution functions and intracules are functions of electronic coordinates and occupy an important, and frequently overlooked, middle ground between the beguiling simplicity of electron densities and the bewildering complexity of wavefunctions. We survey the functions that have been considered by earlier workers and introduce two new ones, the Wigner intracule and the action intracule, that have not previously been discussed. To illustrate their usefulness, we consider the intracules of jellium, a few small atoms and the dissociating hydrogen molecule. Received: 26 July 2002 / Accepted: 20 October 2002 / Published online: 30 January 2003 Correspondence to: P.M.W. Gill e-mail: peter.gill@nott.ac.uk     

Valence 4p functions for the first-row transition metal atoms

For the valence 4p orbitals of the first-row transition metal atoms Sc through Zn, Gaussian-type basis functions are developed referring to excited 3d ^m 4s ¹4p ¹ electronic configurations. Molecular tests of the present work 4p sets are performed for the Cu atom, the diatomic Cu₂ molecule, and Cu₉ and Cu₁₃ clusters, and the results are compared with those from two literature sets. Received: 17 January 2000 / Accepted: 30 May 2000 / Published Online: 11 September 2000     

Rydberg character of the higher excited states of free-base porphin

 The Rydberg character of the excited states of free-base porphin (FBP) has been investigated by the ab initio configuration interaction singles (CIS) method and the state-averaged complete-active-space self-consistent-field method. Double-zeta basis sets augmented with s, p, and d Rydberg functions and d polarization functions have been employed. Two types of molecular orbitals sets, the restricted Hartree–Fock molecular orbitals obtained for the ground state (¹A _g ) and for the cation state (²A _u ), have been used in the CIS calculations. All the calculations show that Rydberg-type excitations play important roles especially in the N bands. In this article we propose applying the model of a perturbed Rydberg series to interpret the excited states of FBP. By using this model, we have succeeded in analyzing the characteristics of the excited states as well as the experimental oscillator strengths, which have considerable magnitude even in the higher excited states. Received: 27 November 2000 / Accepted: 11 April 2001 / Published online: 27 June 2001     

Contracted polarization functions for the atoms Ca, Ga–Kr, Sr, and In–Xe

 Contracted Gaussian-type function sets are proposed for polarization functions of the atoms Ga–Kr and In–Xe. We also report polarization functions for Ca and Sr. A segmented contraction scheme is used for its compactness and computational efficiency. The contraction coefficients and orbital exponents are fully optimized to minimize the deviation from accurate atomic natural orbitals. The present polarization functions yield more than 99% of atomic correlation energies predicted by accurate natural orbitals of the same size. Received: 23 February 2001 / Accepted: 19 April 2001 / Published online: 13 June 2001     

Molecular dynamics study of the tautomeric equilibrium in the 4-nitro- and 2,4,6-trichloro derivatives of 2-(N,N-dialkyloaminomethyl)phenol

 Molecular dynamics thermodynamic integration (MDTI) method and quantum chemical calculations at the density functional theory B3LYP 6-31+(d,p) level, which included the Tomasi model of the solvent reaction field, were applied to study the tautomeric equilibrium of Mannich base in methanol solution. The values obtained for the free-energy difference are in good agreement with experimental data. However, the results from quantum mechanical calculations were not as good as the results of MDTI simulations owing to inappropriate treatment of intermolecular hydrogen bonds between the solute molecule and the first shell of solvent molecules in the Tomasi model of the solvent reaction field. The radial distribution functions between solute atoms and solvent atoms confirmed the formation of hydrogen bonds between the solute molecule and surrounding methanol molecules and indicated that the zwitterionic form is associated more with an organized solvent structure at the level of the first solvation shell than is the molecular form. Received: 26 April 2002 / Accepted: 9 September 2002 / Published online: 31 March 2003     

Relativistic and nonrelativistic finite nucleus optimized double zeta basis sets for the 4p, 5p and 6p elements (Theor Chem Acc (1998) 99:366-371): addendum

 The coefficients of the atomic Foldy-Wout-huysen transformed large component, which can be used in scalar relativistic calculations, are provided in an internet archive for the relativistic double zeta basis sets for the 4p, 5p and 6p elements previously published by the author. Published online: 14 November 2002 Correspondence to: K.G. Dyall e-mail: dyall@schrodinger.com     

Physical analysis of the diatomic “chemical” energy components

 The recent “chemical energy component analysis” permits the total energy of a molecule to be presented approximately but to good accuracy as a sum of atomic and diatomic energy contributions. Here the diatomic energy components are further decomposed into terms of different physical origin: electrostatics (in point-charge approximation and the distributed charge corrections), exchange effects, diatomic overlap and atomic basis extension terms. This analysis may provide us with a deeper insight into the factors influencing both the chemical bonds and the nonbonded interatomic interactions. Received: 6 May 2002 / Accepted: 13 November 2002 / Published online: 19 March 2003 Acknowledgements. The authors are indebted to the Hungarian Scientific Research Fund for partial financial support (grant no. OTKA T29716). Correspondence to: I. Mayer e-mail: mayer@chemres.hu     

Variational calculations for helium-like ions using generalized Kinoshita-type expansions

 Variational calculations are reported for the ground states of the helium atom and its isoelectronic ions H⁻, Li⁺, …, Ne⁸⁺. The calculations use generalized Kinoshita expansions with freely optimized, noninteger powers of the Hylleraas coordinates s and u. One hundred-term expansions of this type lead to better energies than any other expansions in the literature with comparable numbers of terms. Received: 4 September 2002 / Accepted: 14 October 2002 / Published online: 21 January 2003 Correspondence to: T. Koga e-mail: koga@mmm.muroran−it.ac.jp Acknowledgements. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada, and in part by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan. The final 100-term computations with real powers were performed at the Advanced Computational Research Laboratory of the University of New Brunswick.     

The electron affinities of transition metal atoms at the CCSD(T) and density functional levels of theory

 The electron affinities of Ti, V, Cr, Fe, Co, Ni, and Cu are computed using the density function theory and CCSD(T) approaches. Overall the CCSD(T) approach yields the best results. For this property, the B3LYP, BLYP, and BP86 functionals perform better than the BPW91, PBEPBE, and PBE1PBE ones. The accuracy of all the methods is higher if the number of 3delectrons is the same in the neutral atom and the anion. This is especially true for the density functional theory methods. Received: 23 January 2002 / Accepted: 1 April 2002 / Published online: 24 June 2002     

Ab initio and density functional theory studies on the mechanism of nucleophilic vinylic substitution of 4<Emphasis Type="Italic">H</Emphasis>-pyran-4-one and 2-methyl-4<Emphasis Type="Italic">H</Emphasis>-pyran-4-one with ammonia

 Nucleophilic vinylic substitutions of 4H-pyran-4-one and 2-methyl-4H-pyran-4-one with ammonia were calculated by the B3LYP method using the 6-31G(d,p) basis set. Bulk solvent effects of aqueous solution were estimated by the polarized continuum and Poisson–Boltzmann self-consistent reaction field models using the 6-311+G(d,p) basis set. In the gas phase different mechanisms were found for the two reaction systems calculated. The reaction of 4H-pyran-4-one proceeds through enol, whereas a feasible path for the less reactive 2-methyl-4H-pyran-4-one is the mechanism through a keto intermediate. Addition of ammonia in concert with proton transfer is the rate-determining step ofthe reaction. The mechanism proceeding either by a bimolecular nucleophilic substitution (S_N2) or by one involving a tetrahedral zwitterionic intermediate is shown to be unlikely in the gas phase or nonpolar solution. The effects of bulk solvent not only consist in a reduction of the various activation barriers by about 25–40 kJ mol⁻¹ but also in a change in the reaction mechanism. Received 26 May 2002 / Accepted 26 July 2002 / Published online: 14 February 2003     

Evaluation of the Coulomb energy in relativistic self-consistent-field theory

 Computational schemes are presented with which to evaluate the electrostatic Coulomb energy in relativistic molecular electronic structure calculations using a basis of four-component Dirac spinor amplitudes. We demonstrate that algorithms may be constructed and implemented which differ only in minor details from those in common use in nonrelativistic quantum chemistry, and that the four-component formalism is neither as complicated nor as expensive as has been suggested recently in the literature. Spherically symmetrical atomic basis sets are presented which indicate that accurate representations of the Coulomb energy may be obtained using modest expansions of the electronic density in a scalar auxiliary basis set of spherical harmonic Gaussian-type functions. Received: 15 April 2002 / Accepted: 15 May 2002 / Published online: 29 July 2002     

Second-order Møller–Plesset perturbation theory with terms linear in the interelectronic coordinates and exact evaluation of three-electron integrals

 The second-order correlation energy of M?ller–Plesset perturbation theory is computed for the neon atom using a wave function that depends explicitly on the interelectronic coordinates (MP2-R12). The resolution-of-identity (RI) approximation, which is invoked in the standard formulation of MP2-R12 theory, is largely avoided by rigorously computing the necessary three-electron integrals. The basis-set limit for the second-order correlation energy is reached to within 0.1 mE _h. A comparison with the conventional RI-based MP2-R12 method shows that only three-electron integrals over s and p orbitals need to be computed exactly, indicating that the RI approximation can be safely used for integrals involving orbitals of higher angular momentum. Received: 9 May 2001 / Accepted: 31 October 2001 / Published online: 9 January 2002     

Dual-level direct dynamics calculations of deuterium kinetic isotope effects for the Cl(2P)+C2H6 abstraction reaction

 Kinetic isotope effects, KIEs, for hydrogen abstraction from C₂H₆ and C₂D₆ by chlorine atom have been studied by the dual-level direct dynamics approach. A low-level potential energy surface is obtained with the MNDO-SRP method. High-level structural properties of the reactants, transition state, and products were obtained at the MP2 level with the cc-pVDZ, aug-cc-pVDZ, and the cc-pVTZ basis sets. Using the variational transition state theory with microcanonical optimized multidimensional tunneling, the values of deuterium KIE, at 300 K, range from 2.28 to 3.27, in good agreement with the experimental values (2.69–5.88). Received: 6 June 2001 / Accepted: 12 July 2001 / Published online: 19 November 2001