Efficient generation of Heisenberg Hamiltonian matrices for VB calculations of potential energy surfaces

The spin‐Hamiltonian valence bond theory relies upon covalent configurations formed by singly occupied orbitals differing by their spin counterparts. This theory has been proven to be successful in studying potential energy surfaces of the ground and lowest excited states in organic molecules when used as a part of the hybrid molecular mechanics—valence bond method. The method allows one to consider systems with large active spaces formed by n electrons in n orbitals and relies upon a specially proposed graphical unitary group approach. At the same time, the restriction of the equality of the numbers of electrons and orbitals in the active space is too severe: it excludes from the consideration a lot of interesting applications. We can mention here carbocations and systems with heteroatoms. Moreover, the structure of the method makes it difficult to study charge‐transfer excited states because they are formed by ionic configurations. In the present work we tackle these problems by significant extension of the spin‐Hamiltonian approach. We consider (i) more general active space formed by n ± m electrons in n orbitals and (ii) states with the charge transfer. The main problem addressed is the generation of Hamiltonian matrices for these general cases. We propose a scheme combining operators of electron exchange and hopping, generating all nonzero matrix elements step‐by‐step. This scheme provides a very efficient way to generate the Hamiltonians, thus extending the applicability of spin‐Hamiltonian valence bond theory. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Combined valence bond-molecular mechanics potential-energy surface and direct dynamics study of rate constants and kinetic isotope effects for the H + C2H6 reaction

This article presents a multifaceted study of the reaction H+C(2)H(6)-->H(2)+C(2)H(5) and three of its deuterium-substituted isotopologs. First we present high-level electronic structure calculations by the W1, G3SX, MCG3-MPWB, CBS-APNO, and MC-QCISD/3 methods that lead to a best estimate of the barrier height of 11.8+/-0.5 kcal/mol. Then we obtain a specific reaction parameter for the MPW density functional in order that it reproduces the best estimate of the barrier height; this yields the MPW54 functional. The MPW54 functional, as well as the MPW60 functional that was previously parametrized for the H+CH(4) reaction, is used with canonical variational theory with small-curvature tunneling to calculate the rate constants for all four ethane reactions from 200 to 2000 K. The final MPW54 calculations are based on curvilinear-coordinate generalized-normal-mode analysis along the reaction path, and they include scaled frequencies and an anharmonic C-C bond torsion. They agree with experiment within 31% for 467-826 K except for a 38% deviation at 748 K; the results for the isotopologs are predictions since these rate constants have never been measured. The kinetic isotope effects (KIEs) are analyzed to reveal the contributions from subsets of vibrational partition functions and from tunneling, which conspire to yield a nonmonotonic temperature dependence for one of the KIEs. The stationary points and reaction-path potential of the MPW54 potential-energy surface are then used to parametrize a new kind of analytical potential-energy surface that combines a semiempirical valence bond formalism for the reactive part of the molecule with a standard molecular mechanics force field for the rest; this may be considered to be either an extension of molecular mechanics to treat a reactive potential-energy surface or a new kind of combined quantum-mechanical/molecular mechanical (QM/MM) method in which the QM part is semiempirical valence bond theory; that is, the new potential-energy surface is a combined valence bond molecular mechanics (CVBMM) surface. Rate constants calculated with the CVBMM surface agree with the MPW54 rate constants within 12% for 534-2000 K and within 23% for 200-491 K. The full CVBMM potential-energy surface is now available for use in variety of dynamics calculations, and it provides a prototype for developing CVBMM potential-energy surfaces for other reactions.     

Semiempirical valence-electron calculations of excited state geometries and vibrational frequencies

Summary The use of finite differences and finite second differences in order to approximate gradients and second derivatives of the energy for geometry optimization and determination of normal modes of vibration on the CI level of computation is discussed in connection with the semiempirical MNDOC-CI valence electron method. Results are given for ground and excited states of ethylene, acetylene, formaldehyde, acetaldehyde, acetone, formamide and acetamide and are compared with experimental andab initio data. Mean absolute errors for bond lengths, bond angles, excitation energies and vibrational frequencies indicate that the MNDOC-CI method is well suited to describe ground and excited states of organic molecules on the same level of approximation and with comparable accuracy.     

Determination of the thermodynamic functions of lead carbonate on the basis of the calculation of vibrational states

The force constants of bond angles and bonds and parameters of the interatomic potential for the natural carbonate cerussite were determined from the valence force field calculation of the vibrational states of its crystal structure. The initial force constants were calculated by the semiempirical PM5 method using the MOPAC quantum-chemical program package. As the criterion of adequacy of calculations, the consistency between the simulated IR and Raman spectra and the experimental spectra of the compound was used. The heat capacity of lead carbonate as a function of temperature was calculated based on the theory of crystal lattice dynamics and by quantum-chemical methods. The best fit to the experimental data was provided by the semiempirical PM5 method. From the calculated heat capacities, the entropy values of the compound were found.     

Working tools for theoretical chemistry: Polanyi, eyring, and debates over the "semiempirical method"

Following along with the development of electron theory and quantum mechanics in the 1910s and 1920s, physical chemists began incorporating these new theories and approaches in their studies of activation energies, transition states, and chemical reactions for simple atomic and molecular systems. Among these chemists was Michael Polanyi, one of the founders of modern chemical dynamics, who collaborated with Henry Eyring in the development in the 1930s of a theory of the activated transition state and absolute reaction rates using potential energy surfaces and a semiempirical methodology. This paper examines the circumstances of their collaborative work, its reception, and its implications for further chemical research.     

An examination of a density functional/molecular mechanical coupled potential

In this article we describe the coupling of a density functional (DF) Hamiltonian with the molecular mechanics (MM) potential function AMBER. We examine a series of test cases in which we compare the binding energies and geometries of the complexes predicted by this coupled potential with those predicted by other theoretical methods and experiment to establish the relative accuracy of the DF/MM coupled potential. We find that the DF/MM coupled potential performs well in most cases studied and, in general, outperforms the semiempirical/MM approach. The interaction energies and structures obtained using this method appear to be insensitive to the use of nonlocal (NL) corrections to the DF method. The is fortuitous because the NL treatment is significantly more computationally expensive than the local treatment. However, NL corrections may be required to predict accurately the shape of potential energy surfaces that involve bond breaking and formation. The DF/MM method has also been applied to the determination of the solvation free energy for a series of ions using free-energy perturbation methods. The results obtained are good and can be improved by a simple scaling of the Lennard-Jones parameters for the ion in question. © 1995 by John Wiley & Sons, Inc.     

The electronic structure of tetrahedral III–V compounds: The ground state of boron nitride

The bond-orbital theory of III–V compounds, previously described by Coulson, Redei and Stocker, is used to calculate the effective atomic charges and the binding energy per bond in boron nitride. The theory is reformulated in a manner which is convenient for performing both ab initio and semiempirical calculations. Two different choices for the atomic-orbital exponents are considered and, in both cases, the results obtained from the ab initio method are at variance with the earlier calculations in predicting an electronic charge displacement from nitrogen to boron. The magnitude of the effective charges is found to vary according to the method of partitioning the overlap charge between the nitrogen and boron atoms. The use of orthogonalized Slater 2s functions is also examined. The semiempirical calculations are performed with an explicit inclusion of the Madelung energy from the outset. The ionicity in the bond is shown to be determined by the competition between the difference in orbital electronegativities and the difference in Madelung potential across the ends of the bond. Unfortunately, the semiempirical theory breaks down because the energy per bond passes through a maximum at the optimum value of the polarity parameter. The reasons for this behaviour are examined and discussed.     

Searching for conical intersections of potential energy surfaces with the ONIOM method: application to previtamin D

We demonstrate that the ONIOM method can be used to optimize a conical intersection between the ground and first excited-state potential energy surfaces of previtamin D (precalciferol), with excitation localized in a small part of the molecule: the hexatriene chromophore. These calculations were up to 100 times faster with little loss of accuracy compared to a full non-ONIOM Target calculation. The most accurate ONIOM method combination was CASSCF/4-31G//ROHF/STO-3G(Triplet): in comparison to the Target (CASSCF/4-31G), bond lengths and angles in the hexatriene model region were calculated to within 0.02 A and 0.7 degrees , respectively, and the energy difference between the conical intersection and nearest associated S 1 minimum to within 0.5 kcal x mol (-1). All of the low-level methods selected produced accurate geometries, including the UFF molecular mechanics and AM1 semiempirical methods, suggesting a cheap and efficient way of initially optimizing conical intersections geometries. Furthermore, ONIOM allows for an assessment of the localization of excited states, providing some fundamental insight into the physical processes involved.     

GVB–RP: A reliable MCSCF wave function for large systems

We have developed a version of generalized valence bond (GVB) that overcomes the major weakness of the perfect pairing approximation without requiring a full transformation of the integrals at each step of the self‐consistent orbital optimization. The method, called generalized valence bond–restricted pairing (GVB–RP), describes properly the dissociation of up to triple bonds and provides smooth potential energy surfaces for most chemical reactions. The wave functions obtained are a good starting point for more sophisticated computational techniques. The applicability of the method is illustrated with a few simple examples including multiple‐bond dissociations, transition states for symmetry allowed, symmetry forbidden, and radical reactions, as well as reactions at a transition‐metal center. The cost of the method compares well with other self‐consistent correlated techniques. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 1–22, 1999     

A theoretical study of bond energies in model Si–H–Cl molecules using density functional approaches for representing Si surface chemistry

The reliability of density functional theory (DFT) methods for calculating Si(SINGLE BOND)2H, Si(SINGLE BOND)Cl, and Si(SINGLE BOND)Si bond energies is examined in reactions involving molecules and small clusters representing various surface sites appropriate for Si surface chemistry. Results are presented for systematic studies using a valence double-zeta polarization basis for both all-electron calculations and valence–electron calculations employing effective core potentials (ECPs). All-electron DFT results are comparable to much more demanding MP4, G2, and MC–SCF–CI calculations for computed bond energies. Whereas the use of ECPs introduces systematic energy differences of ca. 3–5 kcal/mol compared to AE results, depending on the type of bond involved, the use of ECPs for carrying out calculations on larger clusters is discussed where AE calculations become more computationally demanding. The convergence of Si bond energies as a function of replacing hydrogens with silyl groups is examined. In constructing models to describe etching processes involving Cl species on Si surfaces, the need for incorporating differences in thermochemistries for one-, two-, and three-coordinate Si surface sites is emphasized. Comparisons of semiempirical approaches for thermochemistries of Si-containing species find these methods somewhat less reliable for obtaining reliable bond energies compared to computationally more demanding DFT and ab initio correlated models. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2075–2085, 1997     

Computational study on hydrolysis of cefotaxime in gas phase and in aqueous solution

We are presenting a theoretical study of the hydrolysis of a β‐lactam antibiotic in gas phase and in aqueous solution by means of hybrid quantum mechanics/molecular mechanics potentials. After exploring the potential energy surfaces at semiempirical and density functional theory (DFT) level, potentials of mean force have been computed for the reaction in solution with hybrid PM3/TIP3P calculations and corrections with the B3LYP and M06‐2X functionals. Inclusion of the full molecule of the antibiotic, Cefotaxime, in the gas phase molecular model has been demonstrated to be crucial since its carboxylate group can activate a nucleophilic water molecule. Moreover, the flexibility of the substrate implies the existence of a huge number of possible conformers, some of them implying formation of intramolecular hydrogen bond interaction that can determine the energetics of the conformers defining the different states along the reaction profile. The results show PM3 provides results that are in qualitative agreement with DFT calculations. The free energy profiles show a step‐wise mechanism that is kinetically determined by the nucleophilic attack of a water molecule activated by the proton transfer to the carboxylate group of the substrate (the first step). However, since the main role of the β‐lactamase would be reducing the free energy barrier of the first step, and keeping in mind the barrier obtained from second intermediate to products, population of this second intermediate could be significant and consequently experimentally detected in β‐lactamases, as shown in the literature. © 2012 Wiley Periodicals, Inc.     

A potential function for computer simulation studies of proton transfer in acetylacetone

A potential energy model is developed to study the intramolecular proton transfer in the enol form of acetylacetone. It makes use of the empirical valence bond approach developed by Warshel to combine standard molecular mechanics potentials for the reactant and product states to reproduce the interconversion between these two states. Most parameters have been fitted to reproduce the key features of an ab initio potential surface obtained from 4-31G^* Hartree-Fock calculations. The partial charges have been fitted to reproduce the electrostatic potential surface of 6-31G^* Hartree-Fock wave functions, subject to total charge and symmetry constraints, using a fitting procedure based on generalized inverses. The resulting potential energy function reproduces the features most important for proton transfer simulations, while being several orders of magnitude faster in evaluation time than ab initio energy calculations. © 1997 by John Wiley & Sons, Inc.     

Properties of ternary insulating systems: the electronic structure of MgSO4.H2O

Structural and electronic properties of (100)-oriented MgSO(4) and MgSO(4).H(2)O surfaces and the adsorption of water on the latter were investigated theoretically with a combination of ab initio and semiempirical methods. Ab initio electronic structure calculations were based on a density functional theory (DFT)-Hartree-Fock (HF) hybrid approach. The semiempirical method MSINDO was used for the determination of the local adsorption geometry of the water molecule. With the hybrid method good agreement was obtained with the experimental band gap of 7.4 eV determined with electron energy loss spectroscopy of polycrystalline MgSO(4).H(2)O samples under ultrahigh vacuum conditions. The valence bands of the (100) surfaces of both MgSO(4) and MgSO(4).H(2)O are formed mainly by the O2p levels, whereas the S2p states contribute to the lower part of the conduction band. The preferred adsorption site of water at MgSO(4).H(2)O (100) is above a surface Mg atom. The water molecule is stabilized by two additional hydrogen bonds with surface atoms. Only small differences between the electronic structure of MgSO(4).H(2)O and MgSO(4) were observed. Also, the molecular adsorption of water on the MgSO(4).H(2)O surface leads to only small shifts of the electronic energy levels.     

Protonated water clusters described by an empirical valence bond potential

The properties of low-lying stationary points on the potential energy surfaces of singly protonated water clusters (H(2)O)(n)H(+), are investigated using an empirical valence bond potential. Candidate global minima are reported for n=2-4, 8, and 20-22. For n=8, the variation in the energies and structures of low-lying minima with the number of valence bond states included in the model is studied. For n=4 and 8, disconnectivity graphs are also reported and are compared to results for the equivalent neutral water clusters as described by the rigid TIP3P potential. For the larger clusters, n=20-22, the structural properties of the low energy minima are compared with recently published spectroscopic data on these systems. The observed differences between the n=20 and n=21 systems are qualitatively reproduced by the model potential, but the similarities between the n=21 and n=22 systems are not.     

Computation of curve-crossing diagrams by approximate valence bond method

Avoided crossing diagram parameters for the radical exchange reaction and the concerted exchange of two and three bonds are computed by using the approximated valence bond method, which is a nonorthogonal configuration interaction (CI) semiempirical method among the valence bond configuration functions. Here, each valence bond configuration function is a spin-adapted combination of Slater determinants constructed from the Heitler-London or Coulson-Fischer hybrid orbitals. Atomic orbitals integrals are evaluated using semiempirical philosophy, and these provide considerable saving of computer time compared with the most standard ab initio multistructure valence bond methods. The results indicate that the approximate valence bond method is capable of yielding reasonable results for the avoided crossing diagram parameters. These results also indicate that the diagram gap (G) is the decisive factor for the stability of symmetric clusters, X_n, although no clear correlation between the gap G and the geometric distortion is found for different values of n. © 1996 John Wiley & Sons, Inc.     

Modeling carbon nanostructures with the self-consistent charge density-functional tight-binding method: vibrational spectra and electronic structure of C(28), C(60), and C(70)

The self-consistent charge density-functional tight-binding (SCC-DFTB) method is employed for studying various molecular properties of small fullerenes: C(28), C(60), and C(70). The computed bond distances, vibrational infrared and Raman spectra, vibrational densities of states, and electronic densities of states are compared with experiment (where available) and density-functional theory (DFT) calculations using various basis sets. The presented DFT benchmark calculations using the correlation-consistent polarized valence triple zeta basis set are at present the most extensive calculations on harmonic frequencies of these species. Possible limitations of the SCC-DFTB method for the prediction of molecular vibrational and optical properties are discussed. The presented results suggest that SCC-DFTB is a computationally feasible and reliable method for predicting vibrational and electronic properties of such carbon nanostructures comparable in accuracy with small to medium size basis set DFT calculations at the computational cost of standard semiempirical methods.