Session W37: Theoretical Methods and Algorithms

X-ray absorption spectra of ice and water: a first principles study with the GW method

We calculated the X-ray absorption spectra of ice and liquid water by adopting an approach based on the GW method to describe the excited electron in presence of a frozen core hole. We used the static Coulomb-hole and screened exchange approximation for the self-energy and used Maximally Localized Wannier functions to make GW calculations feasible in the large supercell needed to model a disordered system like water. The calculated spectra considerably improve the agreement with experiment, compared with previous DFT calculations. In particular, the three main features observed in experiments are well reproduced in terms of position and intensity for both ice and water. We also find that the difference between the ice and water spectra can be understood in terms of the electronic structures of these systems, manifested by a distorted, tetrahedral hydrogen bond network in the liquid.   

Iterative Monte Carlo for Quantum Dynamics

We present a fully quantum mechanical methodology for calculating complex-time correlation functions by evaluating the discretized path integral expression iteratively on a grid selected by a Monte Carlo procedure [1]. Both the grid points and the summations performed in each iteration utilize importance sampling, leading to favorable scaling with the number of particles, while the stepwise evaluation of the integrals circumvents the exponential growth of statistical error with time.\newline [1] V. Jadhao and N. Makri J.Chem.Phys. 129, 161102 (2008)   

Resonating Valence Bond wave function with molecular orbitals: first application to dimers

We introduce a method for accurate quantum chemical calculations based on a single determinant wave function, the Antisymmetrized Geminal Power (AGP), and a real space correlation factor (the so called Jastrow factor), that can be efficiently sampled by means of standard quantum Monte Carlo techniques. This allows to obtain a very accurate description of the chemical bond even in extremely difficult cases (such as $Be_2$, $N_2$ and $C_2$) where strong dynamical correlations and/or weak vdW interactions are present. The method is based on a constrained variational optimization, obtained with an appropriate number $n$ of molecular orbitals in the AGP wavefunction. It is shown that the most relevant dynamical correlations are correctly reproduced, once $n$ is univocally determined by the requirement to have size consistent results upon atomization to correlated Hartree-Fock Slater determinants in presence of the Jastrow factor. We apply this method to the Iron dimer molecule and obtain an accurate description of the ground state energy and excitations of this molecule, which is compatible with the experimental findings.   

Representing quantum environments

Understanding dissipative and decohering processes is fundamental to the study of non-equilibrium systems and quantum computing, and such processes can even induce quantum phase transitions. A typical construction is to have a system connected to a continuum environment, which acts as the source of dissipation or decoherence, or as a reservoir of particles. If the connection is strong or the environment has long- range correlations in time, the system dynamics are not easily separated from the dynamics of the environment. To study this situation numerically, one option is to simulate both the system and environment. This is a viable option so long as an efficient finite representation of the environment can be constructed. We will discuss recent results on constructing finite representations of environments for use in computational simulations.   

Application of the Finite-Element Space-Time Algorithm to Bound States

The implementation of the Dirac representation is facilitated by the finite element space-time algorithm.[1] Multicenter integral computations are also facilitated by this same algorithm. The present work is the first application of this original algorithm to the computation of bound states of atoms and molecules. The Dirac representation is employed such that H$_0$ is the sum of the one-electron operators while the residual H$_1$ is the sum of the two-electron operators. Soft-Coulomb geminals are then used as the basis for the time-dependent calculation of a superposition of the bound-states. The eigenstates and eigenvalues are then extracted by filter-diagonalization. An addition theorem is given for the soft-coulomb geminals and the geminals are translated again using the space-time algorithm, so that multicenter integrals may be computed. Several small atoms and molecules are considered as an illustration of the method. [1]D.H. Gebremedhin, C.A. Weatherford, X. Zhang, A. Wynn III, and G. Tanaka, ``Evaluation of the matrix exponential function using finite elements in time,'' arXiv:0811.2612v1 [math-ph] 17 Nov 2008.   

Test of Current Variational Procedures for Electronic Structures and Properties of Molecular and Solid State Systems by application to Atomic Systems-H$^{- }$Ion

Electronic properties of atomic systems are obtainable using Linked Cluster Many-Body Perturbation Theory(LCMBPT) with high accuracy and excellent agreement with experiment, using complete sets of states obtained by differential equation procedures [1,2]. Unfortunately such procedures are not practicable for multi-center molecular and solid state problems and variational procedures have to be used for obtaining the occupied and excited one electron states to work on electronic properties of the latter systems. With the aim to assess the accuracies of the latter procedures with Gaussian basis states, like the first principles Hartree-Fock procedure together with many body perturbation theory, and density functional based procedures, we are testing them for both energy and wave function dependent properties of atoms. Results will be presented for H$^{-}$ ion, where Hartree-Fock theory predicts instability with respect to auto ionization to H atom and electron correlation effects obtained by the LCMBPT procedure [3] restore stability, providing nearly exact experimental affinity for H$^{-}$.[1] Alfred Owusu et al., Phys. Rev. A\underline {56}, 305(1997) [2] T.Lee et al., Phys. Rev. A4 1410(1971) [3]C.M. Dutta et al., Phys. Rev. A2, 2289(1970)   

Computation of Nonlinear Impedance Spectra in Samaria Doped Ceria

Samarium Doped Ceria (SDC) electrodes are currently of great interest for solid oxide fuel cells (SOFC) applications. For example, ceria-containing anodes can be operated directly on hydrocarbons without coking, and in addition can be used at lower temperatures than Ni/YSZ. In order to design, optimize, and characterize electrodes, it is very useful to have models to aid in interpreting experimental results. In this work, we present a non-linear, time-dependent model for the study of SDC. This model allows us to compute species concentrations, electric potential and currents under medium bias conditions. A regular perturbation of the drift diffusion equations and Poisson's equation is used to derive the model for the behavior of bulk of the material. We also include the kinetics of reactions occurring at the SDC-gas surface where the SDC is exposed to a spatially uniform hydrogen-water-argon mixture at fixed total pressure. The numerical procedure allows for fast computations and for the direct determination of fast and rate limiting steps. Impedance spectra are computed in the 2D case and a quantitative comparison between experimental (symmetric cell) and numerical results is presented. Our model can be naturally extended to the non-symmetric case, i.e. the case under which the two sides of the SDC assembly are exposed to different atmospheres.   

An Analytical Approach to Computing Biomolecular Electrostatic Potential

Analytical approximations to fundamental equations of continuum electrostatics on simple shapes can lead to computationally inexpensive prescriptions for calculating electrostatic properties of realistic molecules. Here, we derive a closed form, analytical approximation to the Poisson equation for an arbitrary distribution of point charges and a spherical dielectric boundary. The simple, parameter-free formula defines continuous electrostatic potential everywhere in space and is obtained from the exact infinite series (Kirkwood) solution by an approximate summation method that avoids truncating the infinite series. We show that keeping all the terms proves critical for the accuracy of this approximation, which is fully controllable for the sphere. We apply the approximation to 580 biomolecules under realistic solvation conditions, where the effects of mobile ions are included at the Debye-H\"{u}ckel level. The accuracy of the approximation as applied to the biomolecules is assessed through comparisons with numerical Poisson-Boltzmann (NPB) reference solutions. For each structure, the deviation from the reference is computed for a large number of test points placed near the dielectric boundary (molecular surface). The accuracy of the approximation is within 1 $kT$ per unit charge for 91.5\% of the individual test points.   

{\em Ab Initio} Study of Atomic and Molecular Polarizabi-lities

We calculate the static electric dipole polarizabilities for a variety of atoms and molecules using a finite field method implemented in the framework of an {\it ab initio} density functional formalism. Our calculations employ several different representations of the exchange-correlation potential, including the local density approximation, generalized gradient approximation, and asymptotically correct functionals introduced by Leeuwen-Baerends [1] and Casida-Salahub [2]. We observe that the computed values of polarizabilities are strongly influenced by the asymptotic behavior of the density functional exchange-correlation potential. The accuracy of theoretical atomic and molecular polarizabilities is substantially improved by the use of asymptotically correct exchange-correlation functionals. This result can be explained in terms of electronic excitation energies and the polarizability sum rule.\\[0pt] [1] R. van Leeuwen and E. J. Baerends, Phys. Rev. A 49, 2421 (1994).\\[0pt] [2] M. E. Casida and D. R. Salahub, J. Chem. Phys. 113, 8918 (2000).   

Theoretical predictions of the impact of nuclear dynamics and environment on core-level spectra of organic molecules

Core-level spectroscopy provides an element-specific probe of local electronic structure and bonding, but linking details of atomic structure to measured spectra relies heavily on accurate theoretical interpretation. We present first principles simulations of the x-ray absorption of a range of organic molecules both in isolation and aqueous solvation, highlighting the spectral impact of internal nuclear motion as well as solvent interactions. Our approach uses density functional theory with explicit inclusion of the core-level excited state within a plane-wave supercell framework. Nuclear degrees of freedom are sampled using various molecular dynamics techniques. We indicate specific cases for molecules in their vibrational ground state at experimental conditions, where nuclear quantum effects must be included. Prepared by LBNL under Contract DE-AC02-05CH11231.   

Efficient free energy calculations of quantum systems through computer simulations

In general, the classical limit is assumed in computer simulation calculations of free energy. This approximation, however, is not justifiable for a class of systems in which quantum contributions for the free energy cannot be neglected. The inclusion of quantum effects is important for the determination of reliable phase diagrams of these systems. In this work, we present a new methodology to compute the free energy of many-body quantum systems [1]. This methodology results from the combination of the path integral formulation of statistical mechanics and efficient non-equilibrium methods to estimate free energy, namely, the adiabatic switching and reversible scaling methods. A quantum Einstein crystal is used as a model to show the accuracy and reliability the methodology. This new method is applied to the calculation of solid-liquid coexistence properties of neon. Our findings indicate that quantum contributions to properties such as, melting point, latent heat of fusion, entropy of fusion, and slope of melting line can be up to 10\% of the calculated values using the classical approximation. \noindent [1] R. M. Ramirez, C. P. Herrero, A. Antonelli, and E. R. Hern$\rm \acute{a}$ndez, Journal of Chemical Physics \textbf{129}, 064110 (2008)   

Applications of a novel QM/MM method incorporating a polarizable force field.

In conventional QM/MM methods the MM region is modeled by a force field that uses a set of point charges to represent the electrostatics. However, recently developed force fields use multipole expansions combined with polarizable sites to to represent electrostatic interactions. A novel algorithm is presented to interface this class of force fields with a QM region by allowing the QM region and the MM region to polarize each other self-consistently. It is implemented using the QChem electronic structure code and the AMOEBA force field as implemented in the software package TINKER. The algorithm is general and can be used with a variety of QM methods including MP2 and DFT. Examples of both ground state and excited state calculations are presented, including the investigation of the effectiveness of many-body expansions in modeling the solvation of charged species and the effect of charged environments on biomolecules.