Showing papers in "Theoretical Chemistry Accounts in 2000"

Perspective on “Electrostatic interactions of a solute with a continuum. A direct utilization of ab initio molecular potentials for the prevision of solvent effects”

Abstract: This paper provides an overview of the title paper by Miertus, Scrocco and Tomasi, including the impact that it has had on the theoretical description of solvation by means of continuum models.

Perspective on “Density functional approach to the frontier-electron theory of chemical reactivity”

Abstract: The Fukui function, f(→), was proposed as a tool for deducing the relative reactivity of different positions in a molecule by Parr and Yang in 1984. Herein we sketch the theory of the Fukui function, with special emphasis on its logical motivation, interpretation, qualitative characteristics, and practical computation. We conclude with some words about the Fukui function's extensions, limitations, and importance.

Orthogonalization corrections for semiempirical methods

Abstract: Based on a general discussion of orthogonalization effects, two new one-electron orthogonalization corrections are derived to improve existing semiempirical models at the neglect of diatomic differential overlap level. The first one accounts for valence-shell orthogonalization effects on the resonance integrals, while the second one includes the dominant repulsive core–valence interactions through an effective core potential. The corrections for the resonance integrals consist of three-center terms which incorporate stereodiscriminating properties into the two-center matrix elements of the core Hamiltonian. They provide a better description of conformational properties, which is rationalized qualitatively and demonstrated through numerical calculations on small model systems. The proposed corrections are part of a new general-purpose semiempirical method which will be described elsewhere.

Magnetic coupling in biradicals, binuclear complexes and wide-gap insulators: a survey of ab initio wave function and density functional theory approaches

Abstract: State-of-the-art computational approaches to magnetic coupling in biradicals, dinuclear complexes and wide-gap insulators are reviewed with the aim to provide a unified point of view. The most rigorous wave-function-based methods provide an accurate description of magnetic coupling in all these systems, whereas density-functional-based methods within the broken symmetry approach provide an alternative, yet efficient, computational tool. The use of mapping procedures permits the broken symmetry solution to be related to the appropriate spin state. Different arguments are given to show that the neglect of this procedure may lead to values in agreement with experiment, but at the cost of serious contradictions.

Perspective on “Density functional thermochemistry. III. The role of exact exchange”

Abstract: Recent developments in density functional theory have transformed the entire field of quantum chemistry. This paper provides a perspective on Becke’s landmark papers in 1992 and 1993 that led to the popular density functionals such as B3LYP.

Does the topological approach characterize the hydrogen bond

Abstract: The topological analysis of the electron localization function has been applied to complexes representative of the weak, medium and strong hydrogen bond For both the weak and the medium hydrogen bonds, the number of basins in the complexes is the sum of those of the moieties In this case, the formation of a weak or a medium hydrogen-bonded complex does not involve a chemical reaction In the weak hydrogen bond case, the reduction of the localization domain yields two domains in the first step, which can be partitioned afterwards into valence and core domains In contrast, for medium complexes the core–valence separation is the first event which occurs during the reduction process and therefore the complex should be considered as a single molecular species Moreover, the analysis of the basin population variance indicates in this case a noticeable delocalization between the V(A, H) and V(B) basins Finally, the symmetrical strong hydrogen bond has a protonated basin V(H) at the bond midpoint Such a topology corresponds to an incomplete proton transfer and to a rather covalent bond

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

Abstract: 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.

A small-core multiconfiguration Dirac–Hartree–Fock-adjusted pseudopotential for Tl – application to TlX (X = F, Cl, Br, I)

Abstract: A relativistic pseudopotential of the energy-consistent variety simulating the Tl21+ (1s– 4f) core has been generated by adjustment to multiconfiguration Dirac–Hartree–Fock data based on the Dirac–Coulomb–Breit Hamiltonian. Valence ab initio calculations using this pseudopotential have been performed for atomic excitation energies and for spectroscopic constants of the X0+ and A0+ states of TlX (X = F, Cl, Br, I). Comparison is made to experiment and to four-component density functional results.

A genetic algorithm for the structural optimization of Morse clusters

Abstract: This article describes the application of a genetic algorithm for the structural optimization of 19–50-atom clusters bound by medium-range and short-range Morse pair potentials. The GA is found to be efficient and reliable for finding the geometries corresponding to the previously published global minima [Doye JPK, Wales DJ (1997) J Chem Soc Faraday Trans 93: 4233]. Using the genetic algorithm, only a relatively small number of energy evaluations and minimizations are required to find the global minima. By contrast, a simple random search algorithm often cannot find the global minima of the larger clusters, even after many thousands of searches.

The generalized hybrid orbital method for combined quantum mechanical/molecular mechanical calculations: formulation and tests of the analytical derivatives

Abstract: Hybrid quantum mechanical (QM) and molecular mechanical (MM) potentials are becoming increasingly important for studying condensed-phase systems but one of the outstanding problems in the field has been how to treat covalent bonds between atoms of the QM and MM regions. Recently, we presented a generalized hybrid orbital (GHO) method that was designed to tackle this problem for hybrid potentials using semiempirical QM methods [Gao et al. (1998) J Phys Chem A 102: 4714–4721]. We tested the method on some small molecules and showed that it performed well when compared to the purely QM or MM potentials. In this article, we describe the formalism for the determination of the GHO energy derivatives and then present the results of more tests aimed at validating the model. These tests, involving the calculation of the proton affinities of some model compounds and a molecular dynamics simulation of a protein, indicate that the GHO method will prove useful for the application of hybrid potentials to solution-phase macromolecular systems.

Performance of recently developed kinetic energy density functionals for the calculation of hydrogen binding strengths and hydrogen-bonded structures

Abstract: The accuracy of predicted hydrogen binding energies and equilibrium structures for a benchmark set of molecules is compared for some recently developed density functionals, Becke's three parameter hybrid method with the Lee, Yang, and Parr (LYP) correlation functional (B3LYP), Becke's half and half functional combined with the LYP correlation functional (BHLYP), Perdew, Burke and Ernzerhof functional (PBE), Van Voorhis, Scuseria exchange correlation functional (VSXC), the hybrid Perdew, Burke and Ernzerhof functional (PBE1PBE), and meta-generalized gradient approximation (meta-GGA). Overall, the hybrid functionals which contain a portion of Hartree–Fock exchange (B3LYP, BHLYP, and PBE1PBE) yield the most accurate results. The kinetic-energy-density-dependent functionals, VSXC and meta-GGA, are significantly less accurate.

Analytical Hartree–Fock wave functions for the atoms Cs to Lr

Abstract: Analytical approximations to Hartree–Fock wave functions are constructed using Slater-type functions for the ground states of all 49 neutral atoms from Cs (Z=55) to Lr (Z=103). The current compilation is more extensive and more accurate than previous ones. The wave functions are available upon request from the authors or from the Web page http://www.unb.ca/chem/ajit/download.htm on the Internet.

Perspective on “Density-functional theory for fractional particle number: derivative discontinuities of the energy”

Abstract: This paper provides an overview of the title paper by Perdew, Parr, Levy and Balduz [Phys Rev Lett 49:1691 (1982)]. The title paper extended density functional theory to fractional electron number by an ensemble approach and proved that the energy is a series of straight lines interpolating its values at integer numbers of electrons. It also established that the highest-occupied exact Kohn—Sham orbital energy is the negative of the ionization energy, and showed that the exchange-correlation potential jumps by a constant as the number of electrons increases by an integer. These results are fundamental and continue to inspire developments in density functional theory.

Perspective on "Self-Consistent Equations Including Exchange and Correlation Effects" by W. Kohn and L.J. Sham (Physical Review A 140, 1133-1138)

Abstract: Abstract. The paper by Kohn and Sham (KS) is important for at least two reasons. First, it is the basis for practical methods for density functional calculations. Second, it has endowed chemistry and physics with an independent particle model with very appealing features. As expressed in the title of the KS paper, correlation effects are included at the level of one-electron equations, the practical advantages of which have often been stressed. An implication that has been less widely recognized is that the KS molecular orbital model is physically well-founded and has certain advantages over the Hartree–Fock model. It provides an excellent basis for molecular orbital theoretical interpretation and prediction in chemistry.

Perspective on “Self-consistent equations including exchange and correlation effects”

Abstract: The paper by Kohn and Sham (KS) is important for at least two reasons. First, it is the basis for practical methods for density functional calculations. Second, it has endowed chemistry and physics with an independent particle model with very appealing features. As expressed in the title of the KS paper, correlation effects are included at the level of one-electron equations, the practical advantages of which have often been stressed. An implication that has been less widely recognized is that the KS molecular orbital model is physically well-founded and has certain advantages over the Hartree—Fock model. It provides an excellent basis for molecular orbital theoretical interpretation and prediction in chemistry.

Valence and correlated basis sets for the first-row transition atoms from Sc to Zn

Abstract: Contracted Gaussian-type function sets are developed for the valence 4s and 3d orbitals and for correlated functions of the first-row transition atoms from Sc to Zn. A segmented contraction scheme is used for its compactness and computational efficiency. The contraction coefficients and exponents of the valence and correlated sets are determined by minimizing the differences from weighted averages of accurate atomic natural orbitals for the 4s23dn−2 and 4s13dn−1 atomic states. The new basis sets give a well-balanced description for these configurations at the Hartree–Fock level and yield more than 97% of the atomic correlation energies predicted by accurate natural orbitals of the same size. Molecular tests of the present basis functions are performed for the FeCO molecule at complete-active-space self-consistent-field and at single and double excitation configuration interaction levels. The present sets show an accuracy similar to that of the averaged atomic natural orbital sets in spite of 3–5 times shorter computation time in the generation of two-electron integrals.

Unified analytical treatment of one-electron two-center integrals with noninteger n Slater-type orbitals

Abstract: A unified treatment of one-electron two-center integrals over noninteger n Slater-type orbitals is described. Using an appropriate prolate spheroidal coordinate system with the two atomic centers as foci, all the molecular integrals are expressed by a single analytical formula which can be readily and compactly programmed. The analysis of the numerical performance of the computational algorithm is also presented.

Ab initio study of tautomerism and hydrogen bonding of β-carbonylamine in the gas phase and in water solution

Abstract: All the possible conformations of the three tautomeric isomers of simple β-carbonylamine were fully optimized at ab initio MP2/6-31G** and B3LYP/6-31G** levels in order to determine the conformational equilibrium and the energies of the O—H···N and O···H—N hydrogen bridges. For the most interesting conformations, further calculations in water solution were also carried out. It was found that carbonylamine is the most stable tautomer, followed by enolimine and carbonylimine. This order of stability does not change in solution. O—H···N is the strongest hydrogen bridge, but in solution its energy as well as that of the O···H—N one are dramatically lowered. The deprotonation energy was also calculated and discussed.

Computation of the influence of chemical substitution on the p K a of pyridine using semiempirical and ab initio methods

Abstract: The physical properties of chemicals are strongly influenced by their protonation state, affecting, for example, solubility or hydrogen-bonding characteristics. The ability to accurately calculate protonation states in the form of pK as is, therefore, desirable. Calculations of pK a changes in a series of substituted pyridines are presented. Computations were performed using both ab initio and semiempirical approaches, including free energies of solvation via reaction-field models. The selected methods are readily accessible with respect to both software and computational feasibility. Comparison of calculated and experimental pK as shows the experimental trends to be reasonably reproduced by the computations with root-mean-square differences ranging from 1.22 to 4.14 pK a units. Of the theoretical methods applied the best agreement occurred using the second-order Moller–Plesset/6-31G(d)/isodensity surface polarized continuum solvation model, while the more computationally accessible Austin model 1/Solvent model 2 (SM2) approach yielded results similar to the ab initio methods. Analysis of component contributions to the calculated pK as indicates the largest source of error to be associated with the free energies of solvation of the protonated species followed by the gas-phase protonation energies; while the latter may be improved via the use of higher levels of theory, enhancements in the former require improvements in the solvation models. The inclusion of alternate minimum in the computation of pK as is also indicated to contribute to differences between experimental and calculated pK a values.

The basis set convergence of the Hartree–Fock energy for H3+, Li2 and N2

Abstract: By using completely optimized basis functions it is shown that the convergence of the Hartree–Fock energy for the H3+, Li2 and N2 molecules is significantly better described by exponential behavior than by inverse power dependence. This is the case both with respect to the number of basis functions of a given type and with respect to the highest angular momentum function included. The Hartree–Fock limit for H3+ is estimated to be −1.300372125 hartree.

Perspective on Norman Ramsey’s theories of NMR chemical shifts and nuclear spin—spin coupling

Abstract: The theories connecting the observed NMR chemical shifts and nuclear spin–spin coupling constants to electronic wave functions were published by Norman Ramsey in eight connected Physical Review papers from 1950 to 1953. At the nonrelativistic limit these expressions still stand as the final answer.

Perspective on “Zur Quantentheorie der Molekeln”

Abstract: The Born—Oppenheimer approximation, introduced in the 1927 paper “On the quantum theory of molecules”, provides the foundation for virtually all subsequent theoretical and computational studies of chemical binding and reactivity, as well as the justification for the universal “ball and stick” picture of molecules as atomic centers attached at fixed distances by electronic glue.

Perspective on “The activated complex in chemical reactions”

Abstract: A general theory of the absolute rates of chemical reactions proved to be an elusive goal for nineteenth century chemists. This goal would only be achieved through a combination of statistical mechanics with the new quantum mechanics of the early twentieth century, when the insights of Henry Eyring and his contemporaries lead to the absolute rate equation that we are only now beginning to rigorously evaluate. The conceptual focus of absolute rate theory is the transition state (or activated complex), the window through which the future plunges into the past, and this is still the foundation of our understanding of chemical reaction rates as we enter the new millennium.

Isotope effect of hydrogen and lithium hydride molecules. Application of the dynamic extended molecular orbital method and energy component analysis

Abstract: In order to explore the isotope effect including the nuclear–electronic coupling and nuclear quantum effects under the one-particle approximation, we apply the dynamic extended molecular orbital (DEMO) method and energy component analysis to the hydrogen and lithium hydride isotope molecules. Since the DEMO method determines both electronic and nuclear wave functions simultaneously by variationally optimizing all parameters embedded in the basis sets, the virial theorem is completely satisfied and guarantees the relation of the kinetic and potential energies. We confirm the isotope effect on internuclear distances, nuclear and electronic wave functions, dipole moment, the polarizability, and each energy component. In the case of isotopic species of the hydrogen molecule, the total energy decreases from the H2 to the T2 molecule due to the stabilization of the nuclear–electronic potential component, as well as the nuclear kinetic one. In the case of the lithium hydride molecule, the energy lowering by replacing 6Li with 7Li is calculated to be greater than that by replacing H with D. This is mainly caused by the small destabilization of electron–electron and nuclear–nuclear repulsion in 7LiH compared to 6LiH, while the change in the repulsive components from 6LiH to 6LiD increases.

Harmonic analysis and discrete polynomials. From semiclassical angular momentum theory to the hyperquantization algorithm

Abstract: Orthogonal polynomials of a discrete variable have been widely investigated as fundamental tools of numerical analysis. This work aims to propose the extension of their use to quantum mechanical problems. By exploiting both their connection with coupling and recoupling coefficients of angular momentum theory and their asymptotic relationships (semiclassical limit) with spherical and hyperspherical harmonics, a discretization procedure, the hyperquantization algorithm, has been developed and applied to the study of anisotropic interactions and of reactive scattering. One of the most appealing features of this method turns out to be a drastic reduction of memory requirements and computing time for extensive dynamical calculations. Examples of the application of this technique to stereodirected dynamics via an exact representation for the S matrix as well as to the characterization of molecular beam polarization are also illustrated.

A modified variation–perturbation approach to zero-point vibrational motion

Abstract: We present a detailed investigation of the perturbation approach for calculating zero-point vibrational contributions to molecular properties. It is demonstrated that if the sum of the potential energy and the zero-point vibrational energy is regarded as an effective potential energy, the leading contribution to the first-order wave function vanishes in the perturbation approach. Two different perturbation approaches have been investigated numerically by calculations of some magnetic properties for a few diatomic molecules and the results obtained have been compared to the exact numerical results. It is shown that only a few terms need to be included in a perturbation expansion to obtain an accuracy in the calculated rovibrational contribution better than the quality normally obtained for the potential and property surfaces in electronic structure calculations.

Intramolecular proton transfer of serine in aqueous solution. Mechanism and energetics

Abstract: Serine amino acid in aqueous solution is theoretically studied at the B3PW91/6-31+G** level using a dielectric continuum solvent model. Neutral and zwitterionic structures in the gas phase and in solution are described and the proton-transfer mechanism is discussed. A neutral conformation in which the carboxyl hydrogen atom is already oriented toward the amino group seems to be the absolute energy minimum in the gas phase and the most stable neutral form in solution. The absolute energy minimum in solution is a zwitterionic form. The energy barrier for proton transfer is predicted to be very small, in particular when zero-point-energy contributions are added. Our calculations allow the dynamic aspects of the ionization mechanism to be discussed by incorporating nonequilibrium effects.

Hydrogenation of acetylene–ethylene mixtures on Pd catalysts: study of the surface mechanism by computational approaches. Metal dispersion and catalytic activity

Abstract: The hydrogenation mechanism of acetylene–ethylene mixtures on Pd catalysts under different experimental conditions was studied by employing a time-dependent Monte Carlo approach set to use a fixed series of event probabilities. The dependence of the catalyst activity and selectivity on the sizes of the metal particles was simulated at microscopic level and the results, also refined by fitting procedures, suggested proper explanations for the apparent nonuniformity of the related experimental findings. The use of the steric hindrance parameter of the surface species and the available surface energy on the metallic catalyst sites was decisive for reproducing the experimental results.

Following the streambed reaction on potential-energy surfaces: a new robust method

Abstract: A simple procedure with low computational efforts is proposed to follow the reaction path of the potential-energy hypersurface (PES) starting from minima or saddle points. The method uses a modification of the so-called “following the reduced gradient” [Quapp W, Hirsch M, Imig O, Heidrich D (1998) J Comput Chem 19:1087]. The original method connects points where the gradient has a constant direction. In the present article the procedure is replaced by taking iterative varying directions of the gradient controlled by the last tangent of the searched curve. The resulting minimum energy path is that valley floor gradient extremal (GE) which belongs to the smallest (absolute) eigenvalue of the Hessian and, hence, that GE which usually leads along the streambed of a chemical reaction. The new method avoids third derivatives of the PES and obtains the GE of least ascent by second-order calculations only. Nevertheless, we are able to follow the streambed GE uphill or downhill. We can connect a minimum with its saddles if the streambed leads up to a saddle, or we find a turning point or a bifurcation point. The effectiveness and the characteristic properties of the new algorithm are demonstrated by using polynomial test surfaces, an ab initio PES of H2O, and the analytic potentials of Lennard-Jones (LJ) clusters. By tracing the streambeds we located previously identified saddle points for LJN with N=3, 7, 8, and 55. Saddles for LJN with N=15, 20, and 30 as presented here are new results.

Azido-, hydroxo-, and oxo-bridged copper(II) dimers: spin population analysis within broken-symmetry, density functional methods

Abstract: Within the general context of homometallic spin-coupled Cu(II) dimers, we propose to relate the antiferromagnetic part of the exchange coupling constant, JAF, to the quantity ΔP2(Cu), the difference of copper squared spin populations as calculated for the high-spin (i.e. triplet) and broken-symmetry spin states, through JAF≈−UΔP2(Cu), where U is interpreted as the covalent–ionic term. This proportionality is illustrated for three “bare” Cu(II) dimers (i.e. without peripheral ligation, so as to enhance the antiferromagnetic contribution) bridged by azido, hydroxo, or oxo groups. This provides an alternative quantifier of the exchange phenomenon to that usually used, i.e. Δ2, the square of the singly occupied molecular orbital splitting in the triplet state. Moreover, and quite interestingly, the quantity ΔP2(Cu) can become negative (i.e. induce ferromagnetism) without apparently affecting the proportionality relation.