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

Central retinal vein occlusion associated with high blood levels of lipoprotein (a). Is lipoprotein (a) a reliable marker for identification of predisposed individuals?

AbstractTo report a case of central retinal vein occlusion (CRVO) associated with abnormal elevation of Lipoprotein (a) [Lp(a)] plasma levels, without local or systemic risk factors.A 74-year-old man was referred to our department for cataract surgery in his left eye, and his anamnesis was negative for systemic diseases. Two months later, the patient presented with sudden visual loss in his operated eye, and comprehensive ophthalmic examination was performed, including Fluorescein Angiography (FA) and Optical Coherent Tomography (OCT). Serum concentrations of anticardiolipin and antiphospholipids antibodies, homocysteine and Lp(a) were measured.Ophthalmoscopy showed the classic features of acute CRVO, FA and OCT confirmed the initial diagnosis. Blood tests were negative for hyperhomocysteinemia, anticardiolipin and antiphospholipids antibodies, and an abnormal Lp(a) plasma concentration of 1.7g/L was found. The patient was sent to the internist for further investigation and treatment.Lp(a) can be an useful marker for early identification of predisposed individuals to CRVO and may be involved in its pathogenesis, presumably through its pro-atherogenic and antifibrinolytic action

Solar cooling systems utilizing concentrating solar collectors - An overview

Abstract The objective of this review article is to draw a picture about a promising solar cooling concept, based on the use of concentrating solar collectors, and to define the aspects that need to be considered in future developments. The following topics are covered: an overview of solar cooling systems utilizing concentrating solar collectors worldwide; the reasons behind the selection of these solar collection technologies for solar cooling applications; a quick assessment of the main performance figures for the different solar cooling schemes based on Monte Carlo simulations; the technical requirements of the technologies for future developments. Air-conditioning and refrigeration facilities driven by concentrating solar collectors are still infrequent and the outcomes of this review clearly present the small but steadily growing market of solar cooling systems coupled with concentrating solar collection technologies