2,736 research outputs found
Vibrational Density Matrix Renormalization Group
Variational approaches for the calculation of vibrational wave functions and
energies are a natural route to obtain highly accurate results with
controllable errors. However, the unfavorable scaling and the resulting high
computational cost of standard variational approaches limit their application
to small molecules with only few vibrational modes. Here, we demonstrate how
the density matrix renormalization group (DMRG) can be exploited to optimize
vibrational wave functions (vDMRG) expressed as matrix product states. We study
the convergence of these calculations with respect to the size of the local
basis of each mode, the number of renormalized block states, and the number of
DMRG sweeps required. We demonstrate the high accuracy achieved by vDMRG for
small molecules that were intensively studied in the literature. We then
proceed to show that the complete fingerprint region of the sarcosyn-glycin
dipeptide can be calculated with vDMRG.Comment: 21 pages, 5 figures, 4 table
The density matrix renormalization group for ab initio quantum chemistry
During the past 15 years, the density matrix renormalization group (DMRG) has
become increasingly important for ab initio quantum chemistry. Its underlying
wavefunction ansatz, the matrix product state (MPS), is a low-rank
decomposition of the full configuration interaction tensor. The virtual
dimension of the MPS, the rank of the decomposition, controls the size of the
corner of the many-body Hilbert space that can be reached with the ansatz. This
parameter can be systematically increased until numerical convergence is
reached. The MPS ansatz naturally captures exponentially decaying correlation
functions. Therefore DMRG works extremely well for noncritical one-dimensional
systems. The active orbital spaces in quantum chemistry are however often far
from one-dimensional, and relatively large virtual dimensions are required to
use DMRG for ab initio quantum chemistry (QC-DMRG). The QC-DMRG algorithm, its
computational cost, and its properties are discussed. Two important aspects to
reduce the computational cost are given special attention: the orbital choice
and ordering, and the exploitation of the symmetry group of the Hamiltonian.
With these considerations, the QC-DMRG algorithm allows to find numerically
exact solutions in active spaces of up to 40 electrons in 40 orbitals.Comment: 24 pages; 10 figures; based on arXiv:1405.1225; invited review for
European Physical Journal
Measuring Multi-Configurational Character by Orbital Entanglement
One of the most critical tasks at the very beginning of a quantum chemical
investigation is the choice of either a multi- or single-configurational
method. Naturally, many proposals exist to define a suitable diagnostic of the
multi-configurational character for various types of wave functions in order to
assist this crucial decision. Here, we present a new orbital-entanglement based
multi-configurational diagnostic termed . The correspondence of
orbital entanglement and static (or nondynamic) electron correlation permits
the definition of such a diagnostic. We chose our diagnostic to meet important
requirements such as well-defined limits for pure single-configurational and
multi-configurational wave functions. The diagnostic can be
evaluated from a partially converged, but qualitatively correct, and therefore
inexpensive density matrix renormalization group wave function as in our
recently presented automated active orbital selection protocol. Its robustness
and the fact that it can be evaluated at low cost make this diagnostic a
practical tool for routine applications.Comment: 8 pages, 2 figure, 3 table
Many-Body Expanded Full Configuration Interaction. I. Weakly Correlated Regime
Over the course of the past few decades, the field of computational chemistry
has managed to manifest itself as a key complement to more traditional
lab-oriented chemistry. This is particularly true in the wake of the recent
renaissance of full configuration interaction (FCI)-level methodologies, albeit
only if these can prove themselves sufficiently robust and versatile to be
routinely applied to a variety of chemical problems of interest. In the present
series of works, performance and feature enhancements of one such avenue
towards FCI-level results for medium to large one-electron basis sets, the
recently introduced many-body expanded full configuration interaction (MBE-FCI)
formalism [J. Phys. Chem. Lett., 8, 4633 (2017)], will be presented.
Specifically, in this opening part of the series, the capabilities of the
MBE-FCI method in producing near-exact ground state energies for weakly
correlated molecules of any spin multiplicity will be demonstrated.Comment: 38 pages, 7 tables, 3 figures, 1 SI attached as an ancillary fil
Symmetry adapted ro-vibrational basis functions for variational nuclear motion calculations: TROVE approach
We present a general, numerically motivated approach to the construction of
symmetry adapted basis functions for solving ro-vibrational Schr\"{o}dinger
equations. The approach is based on the property of the Hamiltonian operator to
commute with the complete set of symmetry operators and hence to reflect the
symmetry of the system. The symmetry adapted ro-vibrational basis set is
constructed numerically by solving a set of reduced vibrational eigenvalue
problems. In order to assign the irreducible representations associated with
these eigenfunctions, their symmetry properties are probed on a grid of
molecular geometries with the corresponding symmetry operations. The
transformation matrices are re-constructed by solving over-determined systems
of linear equations related to the transformation properties of the
corresponding wavefunctions on the grid. Our method is implemented in the
variational approach TROVE and has been successfully applied to a number of
problems covering the most important molecular symmetry groups. Several
examples are used to illustrate the procedure, which can be easily applied to
different types of coordinates, basis sets, and molecular systems
ExoMol: molecular line lists for exoplanet and other atmospheres
The discovery of extrasolar planets is one of the major scientific advances
of the last two decades. Hundreds of planets have now been detected and
astronomers are beginning to characterise their composition and physical
characteristics. To do this requires a huge quantity of spectroscopic data most
of which is not available from laboratory studies. The ExoMol project will
offer a comprehensive solution to this problem by providing spectroscopic data
on all the molecular transitions of importance in the atmospheres of
exoplanets. These data will be widely applicable to other problems and will be
used for studies on cool stars, brown dwarfs and circumstellar environments.
This paper lays out the scientific foundations of this project and reviews
previous work in this area.
A mixture of first principles and empirically-tuned quantum mechanical
methods will be used to compute comprehensive and very large rotation-vibration
and rotation-vibration-electronic (rovibronic) line lists. Methodologies will
be developed for treating larger molecules such as methane and nitric acid.
ExoMol will rely on these developments and the use of state-of-the-art
computing.Comment: MNRAS (in press
Genetic Algorithm Optimization of Point Charges in Force Field Development: Challenges and Insights
Evolutionary methods, such as genetic algorithms (GAs), provide powerful tools for optimization of the force field parameters, especially in the case of simultaneous fitting of the force field terms against extensive reference data. However, GA fitting of the nonbonded interaction parameters that includes point charges has not been explored in the literature, likely due to numerous difficulties with even a simpler problem of the least-squares fitting of the atomic point charges against a reference molecular electrostatic potential (MEP), which often demonstrates an unusually high variation of the fitted charges on buried atoms. Here, we examine the performance of the GA approach for the least-squares MEP point charge fitting, and show that the GA optimizations suffer from a magnified version of the classical buried atom effect, producing highly scattered yet correlated solutions. This effect can be understood in terms of the linearly independent, natural coordinates of the MEP fitting problem defined by the eigenvectors of the least-squares sum Hessian matrix, which are also equivalent to the eigenvectors of the covariance matrix evaluated for the scattered GA solutions. GAs quickly converge with respect to the high-curvature coordinates defined by the eigenvectors related to the leading terms of the multipole expansion, but have difficulty converging with respect to the low-curvature coordinates that mostly depend on the buried atom charges. The performance of the evolutionary techniques dramatically improves when the point charge optimization is performed using the Hessian or covariance matrix eigenvectors, an approach with a significant potential for the evolutionary optimization of the fixed-charge biomolecular force fields
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