Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method

The auxiliary-field quantum Monte Carlo (AFQMC) method provides a computational framework for solving the time-independent Schroedinger equation in atoms, molecules, solids, and a variety of model systems. AFQMC has recently witnessed remarkable growth, especially as a tool for electronic structure computations in real materials. The method has demonstrated excellent accuracy across a variety of correlated electron systems. Taking the form of stochastic evolution in a manifold of non-orthogonal Slater determinants, the method resembles an ensemble of density-functional theory (DFT) calculations in the presence of fluctuating external potentials. Its computational cost scales as a low-power of system size, similar to the corresponding independent-electron calculations. Highly efficient and intrinsically parallel, AFQMC is able to take full advantage of contemporary high-performance computing platforms and numerical libraries. In this review, we provide a self-contained introduction to the exact and constrained variants of AFQMC, with emphasis on its applications to the electronic structure in molecular systems. Representative results are presented, and theoretical foundations and implementation details of the method are discussed.Comment: 22 pages, 11 figure

Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo

We propose an algorithm for accurate, systematic and scalable computation of interatomic forces within the auxiliary-field Quantum Monte Carlo (AFQMC) method. The algorithm relies on the Hellman-Fenyman theorem, and incorporates Pulay corrections in the presence of atomic orbital basis sets. We benchmark the method for small molecules by comparing the computed forces with the derivatives of the AFQMC potential energy surface, and by direct comparison with other quantum chemistry methods. We then perform geometry optimizations using the steepest descent algorithm in larger molecules. With realistic basis sets, we obtain equilibrium geometries in agreement, within statistical error bars, with experimental values. The increase in computational cost for computing forces in this approach is only a small prefactor over that of calculating the total energy. This paves the way for a general and efficient approach for geometry optimization and molecular dynamics within AFQMC.Comment: 5 pages, 4 figure

Hamiltonian symmetries in auxiliary-field quantum Monte Carlo calculations for electronic structure

We describe how to incorporate symmetries of the Hamiltonian into auxiliary-field quantum Monte Carlo calculations (AFQMC). Focusing on the case of Abelian symmetries, we show that the computational cost of most steps of an AFQMC calculation is reduced by $N_k^{-1}$, where $N_k$ is the number of irreducible representations of the symmetry group. We apply the formalism to a molecular system as well as to several crystalline solids. In the latter case, the lattice translational group provides increasing savings as the number of k points is increased, which is important in enabling calculations that approach the thermodynamic limit. The extension to non-Abelian symmetries is briefly discussed.Comment: 13 pages, 7 figure

Efficient ab initio auxiliary-field quantum Monte Carlo calculations in Gaussian bases via low-rank tensor decomposition

We describe an algorithm to reduce the cost of auxiliary-field quantum Monte Carlo (AFQMC) calculations for the electronic structure problem. The technique uses a nested low-rank factorization of the electron repulsion integral (ERI). While the cost of conventional AFQMC calculations in Gaussian bases scales as $\mathcal{O}(N^4)$ where $N$ is the size of the basis, we show that ground-state energies can be computed through tensor decomposition with reduced memory requirements and sub-quartic scaling. The algorithm is applied to hydrogen chains and square grids, water clusters, and hexagonal BN. In all cases we observe significant memory savings and, for larger systems, reduced, sub-quartic simulation time.Comment: 14 pages, 13 figures, expanded dataset and tex

Brane with variable tension as a possible solution to the problem of the late cosmic acceleration

Braneworld models have been proposed as a possible solution to the problem of the accelerated expansion of the Universe. The idea is to dispense the dark energy (DE) and drive the late-time cosmic acceleration with a five-dimensional geometry. Here, we investigate a brane model with variable brane tension as a function of redshift called chrono-brane. We propose the polynomial $\lambda=(1+z)^{n}$ function inspired in tracker-scalar-field potentials. To constrain the $n$ exponent we use the latest observational Hubble data from cosmic chronometers, Type Ia Supernovae from the full JLA sample, baryon acoustic oscillations and the posterior distance from the cosmic microwave background of Planck 2015 measurements. A joint analysis of these data estimates $n\simeq6.19$ which generates a DE-like or cosmological-constant-like term, in the Friedmann equation arising from the extra dimensions. This model is consistent with these data and can drive the Universe to an accelerated phase at late times.Comment: 7 pages, 6 figures, accepted for publication in Phys. Rev. D (Rapid Communication

Adverse health effects of nighttime lighting: comments on american medical association policy statement.

The American Medical Association House of Delegates in June of 2012 adopted a policy statement on nighttime lighting and human health. This major policy statement summarizes the scientific evidence that nighttime electric light can disrupt circadian rhythms in humans and documents the rapidly advancing understanding from basic science of how disruption of circadian rhythmicity affects aspects of physiology with direct links to human health, such as cell cycle regulation, DNA damage response, and metabolism. The human evidence is also accumulating, with the strongest epidemiologic support for a link of circadian disruption from light at night to breast cancer. There are practical implications of the basic and epidemiologic science in the form of advancing lighting technologies that better accommodate human circadian rhythmicity