79 research outputs found
Symplectic integration and physical interpretation of time-dependent coupled-cluster theory
The formulation of the time-dependent Schrodinger equation in terms of
coupled-cluster theory is outlined, with emphasis on the bivariational
framework and its classical Hamiltonian structure. An indefinite inner product
is introduced, inducing physical interpretation of coupled-cluster states in
the form of transition probabilities, autocorrelation functions, and explicitly
real values for observables, solving interpretation issues which are present in
time-dependent coupled-cluster theory and in ground-state calculations of
molecular systems under influence of external magnetic fields. The problem of
the numerical integration of the equations of motion is considered, and a
critial evaluation of the standard fourth-order Runge--Kutta scheme and the
symplectic Gauss integrator of variable order is given, including several
illustrative numerical experiments. While the Gauss integrator is stable even
for laser pulses well above the perturbation limit, our experiments indicate
that a system-dependent upper limit exists for the external field strengths.
Above this limit, time-dependent coupled-cluster calculations become very
challenging numerically, even in the full configuration interaction limit. The
source of these numerical instabilities is shown to be rapid increases of the
amplitudes as ultrashort high-intensity laser pulses pump the system out of the
ground state into states that are virtually orthogonal to the static
Hartree-Fock reference determinant.Comment: 14 pages, 13 figure
Reduced scaling in electronic structure calculations using Cholesky decompositions
We demonstrate that substantial computational savings are attainable in electronic structure calculations using a Cholesky decomposition of the two-electron integral matrix. In most cases, the computational effort involved calculating the Cholesky decomposition is less than the construction of one Fock matrix using a direct O(N2) [email protected]
Polarizability and optical rotation calculated from the approximate coupled cluster singles and doubles CC2 linear response theory using Cholesky decompositions
A new implementation of the approximate coupled cluster singles and doubles CC2 linear response model using Cholesky decomposition of the two-electron integrals is presented. Significantly reducing storage demands and computational effort without sacrificing accuracy compared to the conventional model, the algorithm is well suited for large-scale applications. Extensive basis set convergence studies are presented for the static and frequency-dependent electric dipole polarizability of benzene and C60, and for the optical rotation of CNOFH2 and (−)-trans-cyclooctene (TCO). The origin-dependence of the optical rotation is calculated and shown to persist for CC2 even at basis set [email protected]
Theoretical absorption spectrum of the Ar–CO van der Waals complex
The three-dimensional intermolecular electric dipole moment surface of Ar–CO is calculated at the coupled cluster singles and doubles level of theory with the aug-cc-pVTZ basis set extended with a 3s3p2d1f1g set of midbond functions. Using the rovibrational energies and wave functions of our recent study [J. Chem. Phys. 117, 6562 (2002)], temperature-dependent spectral intensities are evaluated and compared to available experimental data. Based on the theoretical spectrum, alternative assignments of the experimentally observed lines in the fundamental band of CO around 2160 and 2166 cm−1 are [email protected]
Rovibrational structure of the Ar–CO complex based on a novel three-dimensional ab initio potential
The first three-dimensional ab initio intermolecular potential energy surface of the Ar–CO van der Waals complex is calculated using the coupled cluster singles and doubles including connected triples model and the augmented correlation-consistent polarized valence quadruple zeta (aug-cc-pVQZ) basis set extended with a (3s3p2d1f1g) set of midbond functions. The three-dimensional surface is averaged over the three lowest vibrational states of CO. Rovibrational energies are calculated up to 50 cm−1 above the ground state, thus enabling comprehensive comparison between theory and available experimental data as well as providing detailed guidance for future spectroscopic investigations of higher-lying states. The experimental transitions are reproduced with a root-mean-square error of 0.13 cm−1, excluding states observed around 25 cm−1 above the ground state. The latter states are at variance with the experimentally deduced ordering
Numerical stability of time-dependent coupled-cluster methods for many-electron dynamics in intense laser pulses
We investigate the numerical stability of time-dependent coupled-cluster
theory for many-electron dynamics in intense laser pulses, comparing two
coupled-cluster formulations with full configuration interaction theory. Our
numerical experiments show that orbital-adaptive time-dependent coupled-cluster
doubles (OATDCCD) theory offers significantly improved stability compared with
the conventional Hartree-Fock-based time-dependent coupled-cluster
singles-and-doubles (TDCCSD) formulation. The improved stability stems from
greatly reduced oscillations in the doubles amplitudes, which, in turn, can be
traced to the dynamic biorthonormal reference determinants of OATDCCD theory.
As long as these are good approximations to the Brueckner determinant, OATDCCD
theory is numerically stable. We propose the reference weight as a diagnostic
quantity to identify situations where the TDCCSD and OATDCCD theories become
unstable.Comment: 5 pages, 6 figures (supplemental material, 7 pages, 11 figures
Interpretation of Coupled-Cluster Many-Electron Dynamics in Terms of Stationary States
We demonstrate theoretically and numerically that laser-driven many-electron
dynamics, as described by bivariational time-dependent coupled-cluster theory,
may be analyzed in terms of stationary-state populations. Projectors
heuristically defined from linear response theory and equation-of-motion
coupled-cluster theory are proposed for the calculation of stationary-state
populations during interaction with laser pulses or other external forces, and
conservation laws of the populations are discussed. Numerical tests of the
proposed projectors, involving both linear and nonlinear optical processes for
the He and Be atoms, and for the LiH, CH, and LiF molecules, show that the
laser-driven evolution of the stationary-state populations at the
coupled-cluster singles-and-doubles (CCSD) level is very close to that obtained
by full configuration-interaction theory provided all stationary states
actively participating in the dynamics are sufficiently well approximated. When
double-excited states are important for the dynamics, the quality of the CCSD
results deteriorate. Observing that populations computed from the
linear-response projector may show spurious small-amplitude, high-frequency
oscillations, the equation-of-motion projector emerges as the most promising
approach to stationary-state populations.Comment: 58 pages, 14 figure
Cost-Efficient High-Resolution Linear Absorption Spectra Through Extrapolating the Dipole Moment from Real-Time Time-Dependent Electronic-Structure Theory
Accepted manuscript, submitted to Journal of Chemical Theory and Computation: https://pubs.acs.org/action/doSearch?AllField=Journal+of+Chemical+Theory+and+Computation.We present a novel function fitting method for approximating the propagation of the time-dependent electric dipole moment from real-time electronic structure calculations. Real-time calculations of the electronic absorption spectrum require discrete Fourier transforms of the electric dipole moment. The spectral resolution is determined by the total propagation time, i.e. the trajectory length of the dipole moment, causing a high computational cost. Our developed method uses function fitting on shorter trajectories of the dipole moment, achieving arbitrary spectral resolution through extrapolation. Numerical testing shows that the fitting method can reproduce high-resolution spectra using short dipole trajectories. The method converges with as little as 100 a.u. dipole trajectories for some systems, though the difficulty converging increases with the spectral density. We also introduce an error estimate of the fit, reliably assessing its convergence and hence the quality of the approximated spectrum
Fast noniterative orbital localization for large molecules
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 implementation scales cubically, the algorithm is significantly faster than any of the conventional localization schemes. In addition, since this approach does not require starting orbitals, it will be useful in local correlation treatments on top of diagonalization-free Hartree-Fock optimization [email protected]
The -diagnostic -- an a posteriori error assessment for single-reference coupled-cluster methods
We propose a novel a posteriori error assessment for the single-reference
coupled-cluster (SRCC) method called the -diagnostic. We provide a
derivation of the -diagnostic that is rooted in the mathematical analysis of
different SRCC variants. We numerically scrutinized the -diagnostic, testing
its performance for (1) geometry optimizations, (2) electronic correlation
simulations of systems with varying numerical difficulty, and (3) the
square-planar copper complexes [CuCl], [Cu(NH)], and
[Cu(HO)]. Throughout the numerical investigations, the
-diagnostic is compared to other SRCC diagnostic procedures, that is, the
, , and diagnostics as well as different indices of
multi-determinantal and multi-reference character in coupled-cluster theory.
Our numerical investigations show that the -diagnostic outperforms the
, , and diagnostics and is comparable to the indices of
multi-determinantal and multi-reference character in coupled-cluster theory in
their individual fields of applicability. The experiments investigating the
performance of the -diagnostic for geometry optimizations using SRCC reveal
that the -diagnostic correlates well with different error measures at a high
level of statistical relevance. The experiments investigating the performance
of the -diagnostic for electronic correlation simulations show that the
-diagnostic correctly predicts strong multi-reference regimes. The
-diagnostic moreover correctly detects the successful SRCC computations for
[CuCl], [Cu(NH)], and [Cu(HO)], which
have been known to be misdiagnosed by and diagnostics in the past.
This shows that the -diagnostic is a promising candidate for an a posteriori
diagnostic for SRCC calculations
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