arXiv subjects

C. J. Umrigar

Publications and source records attributed to C. J. Umrigar.

At least 37 records · Page 2Linked to original sources

arXiv2014

Zigzag Phase Transition in Quantum Wires

We study the quantum phase transition of interacting electrons in quantum wires from a one-dimensional (1D) linear configuration to a quasi-1D zigzag arrangement using quantum Monte Carlo methods. As the density increases from its lowest values, first, the electrons form a linear Wigner crystal; then, the symmetry about the axis of the wire is broken as the electrons order in a quasi-1D zigzag phase; and, finally, the electrons form a disordered liquid-like phase. We show that the linear to zigzag phase transition is not destroyed by the strong quantum fluctuations present in narrow wires; it has characteristics which are qualitatively different from the classical transition.

cond-mat.mes-hall↗

arXiv2014

Energy Density Functionals From the Strong-Coupling Limit Applied to the Anions of the He Isoelectronic Series

Anions and radicals are important for many applications including environmental chemistry, semiconductors, and charge transfer, but are poorly described by the available approximate energy density functionals. Here we test an approximate exchange-correlation functional based on the exact strong-coupling limit of the Hohenberg-Kohn functional on the prototypical case of the He isoelectronic series with varying nuclear charge $Z<2$, which includes weakly bound negative ions and a quantum phase transition at a critical value of $Z$, representing a big challenge for density functional theory. We use accurate wavefunction calculations to validate our results, comparing energies and Kohn-Sham potentials, thus also providing useful reference data close to and at the quantum phase transition. We show that our functional is able to bind H$^-$ and to capture in general the physics of loosely bound anions, with a tendency to strongly overbind that can be proven mathematically. We also include corrections based on the uniform electron gas which improve the results.

physics.chem-ph↗

arXiv2012

Semistochastic Projector Monte Carlo Method

We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix multiplication is partially implemented numerically exactly and partially with respect to expectation values only. Compared to a fully stochastic method, the semistochastic approach significantly reduces the computational time required to obtain the eigenvalue to a specified statistical uncertainty. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem: the fermion Hubbard model and the carbon dimer.

cond-mat.str-el↗

arXiv2012

Approaching Chemical Accuracy with Quantum Monte Carlo

A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete active space Slater-Jastrow trial wavefunction results in near chemical accuracy. In this case, the mean absolute deviation from experimental atomization energies is 1.2 kcal/mol. It is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space.

physics.chem-ph↗

arXiv2011

Optimizing large parameter sets in variational quantum Monte Carlo

We present a technique for optimizing hundreds of thousands of variational parameters in variational quantum Monte Carlo. By introducing iterative Krylov subspace solvers and by multiplying by the Hamiltonian and overlap matrices as they are sampled, we remove the need to construct and store these matrices and thus bypass the most expensive steps of the stochastic reconfiguration and linear method optimization techniques. We demonstrate the effectiveness of this approach by using stochastic reconfiguration to optimize a correlator product state wavefunction with a pfaffian reference for four example systems. In two examples on the two dimensional Hubbard model, we study 16 and 64 site lattices, recovering energies accurate to 1% in the smaller lattice and predicting particle-hole phase separation in the larger. In two examples involving an ab initio Hamiltonian, we investigate the potential energy curve of a symmetrically dissociated 4x4 hydrogen lattice as well as the singlet-triplet gap in free base porphin. In the hydrogen system we recover 98% or more of the correlation energy at all geometries, while for porphin we compute the gap in a 24 orbital active space to within 0.02eV of the exact result. The numbers of variational parameters in these examples range from 4x10^3 to 5x10^5, demonstrating an ability to go far beyond the reach of previous formulations of stochastic reconfiguration.

cond-mat.str-el↗

arXiv2011

Quantum Monte Carlo facing the Hartree-Fock symmetry dilemma: The case of hydrogen rings

When using Hartree-Fock (HF) trial wave functions in quantum Monte Carlo calculations, one faces, in case of HF instabilities, the HF symmetry dilemma in choosing between the symmetry-adapted solution of higher HF energy and symmetry-broken solutions of lower HF energies. In this work, we have examined the HF symmetry dilemma in hydrogen rings which present singlet instabilities for sufficiently large rings. We have found that the symmetry-adapted HF wave function gives a lower energy both in variational Monte Carlo and in fixed-node diffusion Monte Carlo. This indicates that the symmetry-adapted wave function has more accurate nodes than the symmetry-broken wave functions, and thus suggests that spatial symmetry is an important criterion for selecting good trial wave functions.

physics.chem-ph↗

arXiv2011

Quantum Monte Carlo with Jastrow-valence-bond wave functions

We consider the use in quantum Monte Carlo calculations of two types of valence bond wave functions based on strictly localized active orbitals, namely valence bond self-consistent-field (VBSCF) and breathing-orbital valence bond (BOVB) wave functions. Complemented by a Jastrow factor, these Jastrow-Valence-Bond wave functions are tested by computing the equilibrium well depths of the four diatomic molecules C$_2$, N$_2$, O$_2$, and F$_2$ in both variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). We show that it is possible to design compact wave functions based on chemical grounds that are capable of describing both static and dynamic electron correlation. These wave functions can be systematically improved by inclusion of valence bond structures corresponding to additional bonding patterns.

physics.chem-ph↗

arXiv2011

Basis set construction for molecular electronic structure theory: Natural orbital and Gauss-Slater basis for smooth pseudpotentials

A simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multi-configurational self-consistent field calculation supplemented with primitive functions, chosen such that the asymptotics are appropriate for the potential of the system. Primitives are optimized for the homonuclear diatomic molecule to produce a balanced basis set. Two general features that facilitate this basis construction are demonstrated. First, weak coupling exists between the optimal exponents of primitives with different angular momenta. Second, the optimal primitive exponents for a chosen system depend weakly on the particular level of theory employed for optimization. The explicit case considered here is a basis set appropriate for the Burkatzki-Filippi-Dolg pseudopotentials. Since these pseudopotentials are finite at nuclei and have a Coulomb tail, the recently proposed Gauss-Slater functions are the appropriate primitives. Double- and triple-zeta bases are developed for elements hydrogen through argon. These new bases offer significant gains over the corresponding Burkatzki-Filippi-Dolg bases at various levels of theory. Using a Gaussian expansion of the basis functions, these bases can be employed in any electronic structure method. Quantum Monte Carlo provides an added benefit: expansions are unnecessary since the integrals are evaluated numerically.

cond-mat.mtrl-sci↗

arXiv2010

Quantum Monte Carlo calculations of electronic excitation energies: the case of the singlet $n \to π^*$ (CO) transition in acrolein

We report state-of-the-art quantum Monte Carlo calculations of the singlet $n \to π^*$ (CO) vertical excitation energy in the acrolein molecule, extending the recent study of Bouabça {\it et al.} [J. Chem. Phys. {\bf 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.

physics.chem-ph↗

arXiv2010

Phase transformation in Si from semiconducting diamond to metallic beta-Sn phase in QMC and DFT under hydrostatic and anisotropic stress

Silicon undergoes a phase transition from the semiconducting diamond phase to the metallic beta-Sn phase under pressure. We use quantum Monte Carlo calculations to predict the transformation pressure and compare the results to density functional calculations employing the LDA, PBE, PW91, WC, AM05, PBEsol and HSE06 exchange-correlation functionals. Diffusion Monte Carlo predicts a transition pressure of 14.0 +- 1.0 GPa slightly above the experimentally observed transition pressure range of 11.3 to 12.6 GPa. The HSE06 hybrid functional predicts a transition pressure of 12.4 GPa in excellent agreement with experiments. Exchange-correlation functionals using the local-density approximation and generalized-gradient approximations result in transition pressures ranging from 3.5 to 10.0 GPa, well below the experimental values. The transition pressure is sensitive to stress anisotropy. Anisotropy in the stress along any of the cubic axes of the diamond phase of silicon lowers the equilibrium transition pressure and may explain the discrepancy between the various experimental values as well as the small overestimate of the quantum Monte Carlo transition pressure.

cond-mat.mtrl-sci↗

arXiv2010

Compact and Flexible Basis Functions for Quantum Monte Carlo Calculations

Molecular calculations in quantum Monte Carlo frequently employ a mixed basis consisting of contracted and primitive Gaussian functions. While standard basis sets of varying size and accuracy are available in the literature, we demonstrate that reoptimizing the primitive function exponents within quantum Monte Carlo yields more compact basis sets for a given accuracy. Particularly large gains are achieved for highly excited states. For calculations requiring non-diverging pseudopotentials, we introduce Gauss-Slater basis functions that behave as Gaussians at short distances and Slaters at long distances. These basis functions further improve the energy and fluctuations of the local energy for a given basis size. Gains achieved by exponent optimization and Gauss-Slater basis use are exemplified by calculations for the ground state of carbon, the lowest lying excited states of carbon with $^5S^o$, $^3P^o$, $^1D^o$, $^3F^o$ symmetries, carbon dimer, and naphthalene. Basis size reduction enables quantum Monte Carlo treatment of larger molecules at high accuracy.

physics.chem-ph↗

arXiv2009

The energy landscape of silicon systems and its description by force fields, tight binding schemes, density functional methods and Quantum Monte Carlo methods

The accuracy of the energy landscape of silicon systems obtained from various density functional methods, a tight binding scheme and force fields is studied. Quantum Monte Carlo results serve as quasi exact reference values. In addition to the well known accuracy of DFT methods for geometric ground states and metastable configurations we find that DFT methods give a similar accuracy for transition states and thus a good overall description of the energy landscape. On the other hand, force fields give a very poor description of the landscape that are in most cases too rugged and contain many fake local minima and saddle points or ones that have the wrong height.

physics.comp-ph↗

arXiv2009

Interaction-Induced Strong Localization in Quantum Dots

We argue that Coulomb blockade phenomena are a useful probe of the cross-over to strong correlation in quantum dots. Through calculations at low density using variational and diffusion quantum Monte Carlo (up to r_s ~ 55), we find that the addition energy shows a clear progression from features associated with shell structure to those caused by commensurability of a Wigner crystal. This cross-over (which occurs near r_s ~ 20 for spin-polarized electrons) is, then, a signature of interaction-driven localization. As the addition energy is directly measurable in Coulomb blockade conductance experiments, this provides a direct probe of localization in the low density electron gas.

cond-mat.mes-hall↗

arXiv2009

Localization in an Inhomogeneous Quantum Wire

We study interaction-induced localization of electrons in an inhomogeneous quasi-one-dimensional system--a wire with two regions, one at low density and the other high. Quantum Monte Carlo techniques are used to treat the strong Coulomb interactions in the low density region, where localization of electrons occurs. The nature of the transition from high to low density depends on the density gradient--if it is steep, a barrier develops between the two regions, causing Coulomb blockade effects. Ferromagnetic spin polarization does not appear for any parameters studied. The picture emerging here is in good agreement with measurements of tunneling between two wires.

cond-mat.mes-hall↗

arXiv2008

Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules

We pursue the development and application of the recently-introduced linear optimization method for determining the optimal linear and nonlinear parameters of Jastrow-Slater wave functions in a variational Monte Carlo framework. In this approach, the optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. We extend the method to optimize the exponents of the basis functions, simultaneously with all the other parameters, namely the Jastrow, configuration state function and orbital parameters. We show that the linear optimization method can be thought of as a so-called augmented Hessian approach, which helps explain the robustness of the method and permits us to extend it to minimize a linear combination of the energy and the energy variance. We apply the linear optimization method to obtain the complete ground-state potential energy curve of the C_2 molecule up to the dissociation limit, and discuss size consistency and broken spin-symmetry issues in quantum Monte Carlo calculations. We perform calculations of the first-row atoms and homonuclear diatomic molecules with fully optimized Jastrow-Slater wave functions, and we demonstrate that molecular well depths can be obtained with near chemical accuracy quite systematically at the diffusion Monte Carlo level for these systems.

physics.comp-ph↗

arXiv2008

Fixed-node diffusion Monte Carlo study of the structures of m-benzyne

Diffusion Monte Carlo (DMC) calculations are performed on the monocyclic and bicyclic forms of m-benzyne, which are the equilibrium structures at the CCSD(T) and CCSD levels of coupled cluster theory. We employed multi-configuration self-consistent field trial wave functions which are constructed from a carefully selected 8-electrons-in-8-orbitals complete active space [CAS(8,8)], with CSF coefficients that are reoptimized in the presence of a Jastrow factor. The DMC calculations show that the monocyclic structure is lower in energy than the bicyclic structure by 1.9(2) kcal/mole, in excellent agreement with the best coupled cluster results.

physics.chem-ph↗

arXiv2007

Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density

We construct improved quantum Monte Carlo estimators for the spherically- and system-averaged electron pair density (i.e. the probability density of finding two electrons separated by a relative distance u), also known as the spherically-averaged electron position intracule density I(u), using the general zero-variance zero-bias principle for observables, introduced by Assaraf and Caffarel. The calculation of I(u) is made vastly more efficient by replacing the average of the local delta-function operator by the average of a smooth non-local operator that has several orders of magnitude smaller variance. These new estimators also reduce the systematic error (or bias) of the intracule density due to the approximate trial wave function. Used in combination with the optimization of an increasing number of parameters in trial Jastrow-Slater wave functions, they allow one to obtain well converged correlated intracule densities for atoms and molecules. These ideas can be applied to calculating any pair-correlation function in classical or quantum Monte Carlo calculations.

physics.chem-ph↗

arXiv2007

Optimization of quantum Monte Carlo wave functions by energy minimization

We study three wave function optimization methods based on energy minimization in a variational Monte Carlo framework: the Newton, linear and perturbative methods. In the Newton method, the parameter variations are calculated from the energy gradient and Hessian, using a reduced variance statistical estimator for the latter. In the linear method, the parameter variations are found by diagonalizing a non-symmetric estimator of the Hamiltonian matrix in the space spanned by the wave function and its derivatives with respect to the parameters, making use of a strong zero-variance principle. In the less computationally expensive perturbative method, the parameter variations are calculated by approximately solving the generalized eigenvalue equation of the linear method by a nonorthogonal perturbation theory. These general methods are illustrated here by the optimization of wave functions consisting of a Jastrow factor multiplied by an expansion in configuration state functions (CSFs) for the C$_2$ molecule, including both valence and core electrons in the calculation. The Newton and linear methods are very efficient for the optimization of the Jastrow, CSF and orbital parameters. The perturbative method is a good alternative for the optimization of just the CSF and orbital parameters. Although the optimization is performed at the variational Monte Carlo level, we observe for the C$_2$ molecule studied here, and for other systems we have studied, that as more parameters in the trial wave functions are optimized, the diffusion Monte Carlo total energy improves monotonically, implying that the nodal hypersurface also improves monotonically.

physics.chem-ph↗