Search results for "Statistical physics"
showing 10 items of 1402 documents
Tripotential data processing for HES interpretation
1994
In this paper some methods are proposed and compared to correct the experimental measurements for preliminary processing of tripotential data which are acquired for HES prospecting. However, the use of those methods should be based upon an accurate analysis of all experimental data. Such an analysis ought to involve: 1) an estimate of the averaged measurement errors with their variance and distribution in both the space and the three apparent-resistivities domains; 2) the choice of a resistivity model capable of describing the actual volume under study. The differences among the three values of apparent resistivity measured on a point are generally influenced both by the resistivity distrib…
On new efficient algorithms for PIMC and PIMD
2002
Abstract The properties of various algorithms, estimators, and high-temperature density matrix (HTDM) decompositions relevant for path integral simulations are discussed. It is shown that Fourier accelerated path integral molecular dynamics (PIMD) completely eliminates slowing down with increasing Trotter number P . A new primitive estimator of the kinetic energy for use in PIMD simulations is found to behave less pathologically than the original virial estimator. In particular, its variance does not increase significantly with P . Two non-primitive HTDM decompositions are compared as well: one decomposition used in the Takahashi Imada algorithm and another one based on an effective propaga…
Multi-level coupled cluster theory
2014
We present a general formalism where different levels of coupled cluster theory can be applied to different parts of the molecular system. The system is partitioned into subsystems by Cholesky decomposition of the one-electron Hartree-Fock density matrix. In this way the system can be divided across chemical bonds without discontinuities arising. The coupled cluster wave function is defined in terms of cluster operators for each part and these are determined from a set of coupled equations. The total wave function fulfills the Pauli-principle across all borders and levels of electron correlation. We develop the associated response theory for this multi-level coupled cluster theory and prese…
Fast noniterative orbital localization for large molecules
2006
We use Cholesky decomposition of the density matrix in atomic orbital basis to define a new set of occupied molecular orbital coefficients. Analysis of the resulting orbitals ("Cholesky molecular orbitals") demonstrates their localized character inherited from the sparsity of the density matrix. Comparison with the results of traditional iterative localization schemes shows minor differences with respect to a number of suitable measures of locality, particularly the scaling with system size of orbital pair domains used in local correlation methods. The Cholesky procedure for generating orthonormal localized orbitals is noniterative and may be made linear scaling. Although our present implem…
Convergence of density-matrix expansions for nuclear interactions
2010
We extend density-matrix expansions in nuclei to higher orders in derivatives of densities and test their convergence properties. The expansions allow for converting the interaction energies characteristic to finite- and short-range nuclear effective forces into quasi-local density functionals. We also propose a new type of expansion that has excellent convergence properties when benchmarked against the binding energies obtained for the Gogny interaction.
Fast evaluation of a linear number of local exchange matrices
2002
A fast method is described for evaluating multiple exchange matrices in a Gaussian atomic orbital basis. For insulators, it is asymptotically linear scaling, and is a generalization of the linear scaling exchange (LinK) method, which was formulated for a single exchange matrix [J. Chem. Phys. 109 (1998) 1663]. It is employed to evaluate exchange-type contractions of all derivative density matrices with two-electron integrals for a series of linear alkanes, linear polyacenes, and water clusters using STO-3G, 3-21G, and 6-31G* basis sets. Significant computational savings are obtained for molecules with as few as 10 non-hydrogen atoms.
Adiabatic Elimination and Sub-space Evolution of Open Quantum Systems
2020
Efficient descriptions of open quantum systems can be obtained by performing an adiabatic elimination of the fast degrees of freedom and formulating effective operators for the slow degrees of freedom in reduced dimensions. Here, we perform the construction of effective operators in frequency space, and using the final value theorem or alternatively the Keldysh theorem, we provide a correction for the trace of the density matrix which takes into account the non trace-preserving character of the evolution. We illustrate our results with two different systems, ones where the eliminated fast subspace is constituted by a continuous set of states and ones with discrete states. Furthermore, we sh…
Fluids of hard ellipsoids: Phase diagram including a nematic instability from Percus-Yevick theory
1999
An important aspect of molecular fluids is the relation between orientation and translation parts of the two-particle correlations. Especially the detailed knowledge of the influence of orientation correlations is needed to explain and calculate in detail the occurrence of a nematic phase. The simplest model system which shows both orientation and translation correlations is a system of hard ellipsoids. We investigate an isotropic fluid formed of hard ellipsoids with Percus-Yevick theory. Solving the Percus-Yevick equations self-consistently in the high density regime gives a clear criterion for a nematic instability. We calculate in detail the equilibrium phase diagram for a fluid of hard …
Analytic gradients for the coupled-cluster singles, doubles, and triples (CCSDT) model
2002
The first implementation of analytic gradients for the coupled-cluster singles, doubles, triples (CCSDT) model is described. The relevant theoretical expressions are given in a diagrammatic form together with the corresponding algebraic formulas. The computational requirements of CCSDT gradient calculations are discussed and their applicability demonstrated by performing benchmark calculations for molecular geometries with large correlation-consistent basis sets. A statistical analysis of the data reveals that CCSDT and CCSD(T) in most cases perform equally well. The CCSDT calculations thus provide further evidence for the high accuracy of the CCSD(T) approach.
Selected dissociation‐ and correlation‐consistent configuration interaction by a perturbative criterion
1990
We propose a perturbative criterion to select the most important dissociation‐ or correlation‐consistent type of contributions to perform generalized valence bond‐configuration interaction (GVB‐CI) calculations, dissociation‐consistent configuration interaction (DCCI) or correlation‐consistent configuration interaction (CCCI) approach, respectively. The procedure presented is computationally less demanding than the CCCI proposed by Goddard and co‐workers. To ensure the distance consistency of the MOs used, the nonvalence virtual orbitals are obtained by a projection technique. The results obtained for a few test calculations show the ability of the suggested approach to get close results to…