Philip E. Hoggan

Rotation matrices for real spherical harmonics: general rotations of atomic orbitals in space-fixed axes

The angular factors of atomic orbitals are real spherical harmonics. This is independent of the choice of basis function. In the course of molecular electronic structure calculations, numerous rotations of real spherical harmonics are required in a suitably defined space-fixed coordinate system. The origin and axes are space-fixed and rotation matrices defined on the basis of spherical harmonics. Typically, rotations are used to align the local axes for atoms with a unique interatomic direction in a fixed frame for integral evaluations. In this work, a highly compact expression and efficient evaluation of the rotation matrices are given for a real spherical harmonic basis. Relations to Gaunt coefficients are shown explicitly as are recurrence formulae for rotation matrices. This leads to extremely rapid and precise rotation algorithms. The Wigner rotation matrices which are still often used in orbital rotations are shown to be completely surpassed by this approach. The present work is related to a method described by Kautz in the field of image processing but significant improvements have been made, especially in the study of structure and storage of the rotation matrices. After complete testing using computer algebra, a numerical program was written in C. Numerical tests are cited in the closing sections of this work.

New methods for accelerating the convergence of molecular electronic integrals over exponential type orbitals

This review on molecular integrals for large electronic systems (MILES) places the problem of analytical integration over exponential-type orbitals (ETOs) in a historical context. After reference to the pioneering work, particularly by Barnett, Shavitt and Yoshimine, it focuses on recent progress towards rapid and accurate analytic solutions of MILES over ETOs. Software such as the hydrogenlike wavefunction package Alchemy by Yoshimine and collaborators is described. The review focuses on convergence acceleration of these highly oscillatory integrals and in particular it highlights suitable nonlinear transformations. Work by Levin and Sidi is described and applied to MILES. A step by step description of progress in the use of nonlinear transformation methods to obtain efficient codes is provided. The recent approach SĐ developed by Safouhi is also presented. The current state of the art in this field is summarized to show that ab initio analytical work over ETOs is now a viable option.

Diffusion Monte Carlo for Accurate Dissociation Energies of 3d Transition Metal Containing Molecules

Transition metals and transition metal compounds are important to catalysis, photochemistry, and many superconducting systems. We study the performance of diffusion Monte Carlo (DMC) applied to transition metal containing dimers (TMCDs) using single-determinant Slater-Jastrow trial wavefunctions and investigate the possible influence of the locality and pseudopotential errors. We find that the locality approximation can introduce nonsystematic errors of up to several tens of kilocalories per mole in the absolute energy of Cu and CuH if Ar or Mg core pseudopotentials (PPs) are used for the 3d transition metal atoms. Even for energy differences such as binding energies, errors due to the locality approximation can be problematic if chemical accuracy is sought. The use of the Ne core PPs developed by Burkatzki et al. (J. Chem. Phys. 2008, 129, 164115), the use of linear energy minimization rather than unreweighted variance minimization for the optimization of the Jastrow function, and the use of large Jastrow parametrizations reduce the locality errors. In the second section of this article, we study the general performance of DMC for 3d TMCDs using a database of binding energies of 20 TMCDs, for which comparatively accurate experimental data is available. Comparing our DMC results to these data for our results that compare best with experiment, we find a mean unsigned error (MUE) of 4.5 kcal/mol. This compares well with the achievable accuracy in CCSDT(2)Q (MUE = 4.6 kcal/mol) and the best all-electron DFT results (MUE = 4.5 kcal/mol) for the same set of systems (Truhlar et al. J. Chem. Theory Comput. 2015, 11, 2036-2052). The mean errors in DMC depend less on the exchange-correlation functionals used to generate the trial wavefunction than the corresponding mean errors in the underlying DFT calculations. Furthermore, the QMC results obtained for each molecule individually vary less with the functionals used. These observations are relevant for systems such as molecules interacting with transition metal surfaces where the DFT functionals performing best for molecules (hybrids) do not yield improvements in DFT. Overall, the results presented in this article yield important guidelines for both the assessment of the achievable accuracy with DMC and the design of DMC calculations for systems including transition metal atoms.

USEFUL INTEGRALS FOR AB-INITIO MOLECULAR QUANTUM SIMILARITY MEASUREMENTS USING SLATER TYPE ATOMIC ORBITALS

Molecular quantum similarity measurements are based on a quantitative comparison of the one-electron densities of two molecules superposed and aligned to optimize a well-defined similarity function. In most previous work the densities have been related using a Dirac delta leading to the overlap-like quantum similarity function. The densities for the two molecules compared have generally been approximated often with a simple LCAO of s-gaussian functions. In this work, we present a one center two range expansion method for the evaluation of the overlap integrals involved in the overlap-like quantum similarity function over Slater type orbitals (STO). The single center and three types of two-center overlap integrals (involving four atomic orbitals; two in each molecule) have led to finite sums using a single center approach combined with selection rules obtained by analysis of orbital angular momentum (conservation). The three- and four-center integrals are also obtained analytically but involve infinite sums which require further study before leading to a complete set of integral codes for ab-initio quantum similarity.

Solution of Poisson's equation using spectral forms

A new technique is presented for the solution of Poissons equation in spherical coordinates. The method employs an expansion of the solution in a new set of functions defined herein for the first time, called ‘spectral forms’. The spectral forms have spherical harmonics as their angular part, but use a new set of radial functions that automatically statisfy the boundary conditions, up to a multiplicative constant, on the Poisson solution. The resultant problem reduces to a set of simultaneous equations for the expansion coefficients . The matrix A is block diagonal in the spherical harmonic indices l,m and is independent of any parameters. The simultaneous equations may be solved by LU decomposition. The LU decomposition only needs to be done once and multiple right hand sides (B-vectors) can be treated by a matrix-vector multiply. For a parallel computing platform, each such B-vector may be dealt with on a separate processor. Thus the algorithm is highly parallel. This technique may be used to calculate Coulomb energy integrals efficiently on a parallel computer.

A QUANTUM CHEMISTRY GIAO MOLECULAR SITE APPROACH OF NMR CHEMICAL SHIFTS GENERALIZED TO THE WHOLE PERIODIC TABLE

An accurate and rapid quantum chemistry approach to predicting chemical shifts is applied to 15N natural abundance NMR spectra of benzothiazoles. This method is of interest in the study of toxic contaminants of biological media. A GIAO approach is used to calculate the nuclear shielding tensor in a perturbational scheme. Similar methods had previously been used for both ab initio and semi-empirical calculations programmed in Gaussian and MOPAC respectively but atomic orbitals specific to molecular sites are shown to improve accuracy in the present work. Some molecular sites are defined in order to polarize the molecular orbitals in the presence of the solvent interactions. For convenience, the extensions are carried out in an independent NMR module designed to work with the MOPAC package and the present application is generalized to the third row elements for the first time. This new theoretical work is described. The application to 15N chemical shifts for benzothiazoles led to results within 0.5 ppm of values measured in this work. Structural investigations were carried out using the Gaussian98 suite of programs at the DFT B3LYP level of calculation over an extended basis set. These studies show the single chemical shift for benzothiazoles could be the result of rapid tautomeric equilibria. Further investigations show that solvent interactions involving hydrogen bonds should also be taken into account.

Quantum Monte Carlo Calculations on a Benchmark Molecule - Metal Surface Reaction : H2 + Cu(111)

Accurate modeling of heterogeneous catalysis requires the availability of highly accurate potential energy surfaces. Within density functional theory, these can—unfortunately—depend heavily on the exchange-correlation functional. High-level ab initio calculations, on the other hand, are challenging due to the system size and the metallic character of the metal slab. Here, we present a quantum Monte Carlo (QMC) study for the benchmark system H2 + Cu(111), focusing on the dissociative chemisorption barrier height. These computationally extremely challenging ab initio calculations agree to within 1.6 ± 1.0 kcal/mol with a chemically accurate semiempirical value. Remaining errors, such as time-step errors and locality errors, are analyzed in detail in order to assess the reliability of the results. The benchmark studies presented here are at the cutting edge of what is computationally feasible at the present time. Illustrating not only the achievable accuracy but also the challenges arising within QMC in such a calculation, our study presents a clear picture of where we stand at the moment and which approaches might allow for even more accurate results in the future.

Vapor liquid solid-hydride vapor phase epitaxy (VLS-HVPE) growth of ultra-long defect-free GaAs nanowires: Ab initio simulations supporting center nucleation

High aspect ratio, rod-like and single crystal phase GaAs nanowires (NWs) were grown by gold catalyst-assisted hydride vapor phase epitaxy (HVPE). High resolution transmission electron microscopy and micro-Raman spectroscopy revealed polytypism-free zinc blende (ZB) NWs over lengths of several tens of micrometers for a mean diameter of 50 nm. Micro-photoluminescence studies of individual NWs showed linewidths smaller than those reported elsewhere which is consistent with the crystalline quality of the NWs. HVPE makes use of chloride growth precursors GaCl of which high decomposition frequency after adsorption onto the liquid droplet catalysts, favors a direct and rapid introduction of the Ga atoms from the vapor phase into the droplets. High influxes of Ga and As species then yield high axial growth rate of more than 100 μm/h. The diffusion of the Ga atoms in the liquid droplet towards the interface between the liquid and the solid nanowire was investigated by using density functional theory calculations. The diffusion coefficient of Ga atoms was estimated to be 3 × 10(-9) m(2)/s. The fast diffusion of Ga in the droplet favors nucleation at the liquid-solid line interface at the center of the NW. This is further evidence, provided by an alternative epitaxial method with respect to metal-organic vapor phase epitaxy and molecular beam epitaxy, of the current assumption which states that this type of nucleation should always lead to the formation of the ZB cubic phase.

Quantum Monte Carlo Calculations of Electronic Excitation Energies: The Case of the Singlet n→π∗ (CO) Transition in Acrolein

We report state-of-the-art quantum Monte Carlo calculations of the singlet n→π∗ (CO) vertical excitation energy in the acrolein molecule, extending the recent study of Bouabca et al. (J Chem Phys 130:114107, 2009). We investigate the effect of using a Slater basis set instead of a Gaussian basis set, and of using state-average versus state-specific complete-active-space (CAS) wave functions, with or without reoptimization of the coefficients of the configuration state functions (CSFs) and of the orbitals in variational Monte Carlo (VMC). It is found that, with the Slater basis set used here, both state-average and state-specific CAS(6,5) wave functions give an accurate excitation energy in diffusion Monte Carlo (DMC), with or without reoptimization of the CSF and orbital coefficients in the presence of the Jastrow factor. In contrast, the CAS(2,2) wave functions require reoptimization of the CSF and orbital coefficients to give a good DMC excitation energy. Our best estimates of the vertical excitation energy are between 3.86 and 3.89 eV.

Why Specific ETOs are Advantageous for NMR and Molecular Interactions

This paper advocates use of the atomic orbitals which have direct physical interpretation, i.e., Coulomb Sturmians and hydrogen-like orbitals. They are exponential type orbitals (ETOs). Their radial nodes are shown to be essential in obtaining accurate local energy for Quantum Monte Carlo, molecular interactions a nuclear and shielding tensors for NMR work. The NMR work builds on a 2003 French PhD and many numerical results were published by 2007. The improvements in this paper are noteworthy, the key being the actual basis function choice. Until 2008, their products on different atoms were difficult to manipulate for the evaluation of two-electron integrals. Coulomb resolutions provide an excellent approximation that reduces these integrals to a sum of one-electron overlap-like integral products that each involve orbitals on at most two centers. Such two-center integrals are separable in prolate spheroidal co-ordinates. They are thus readily evaluated. Only these integrals need to be re-evaluated to change basis functions. In this paper, a review of the translation procedures for Slater type orbitals (STO) and for Coulomb Sturmians follows that of the more recent application to ETOs of a particularly convenient Coulomb resolution.