Search results for "Matrix"
showing 10 items of 3205 documents
General restrictions for the relaxation constants of the polarization moments of the density matrix
1992
General inequalities for the relaxation constants of polarization moments are examined. Concrete numerical limitations for the values of these constants are obtained. In recent years it has been generally accepted to characterize the distribution of the angular momentum j of atomic as well as molecular states in the framework of the irreducible tensorial operators PG. The state is described by means of polarization moments p& which are the expansion coefficients of the angular momentum density matrix pm,,,, on the tensorial operators pz:
NMR chemical shift calculations within local correlation methods: the GIAO-LMP2 approach
2000
A scheme for the calculation of NMR chemical shifts using local second-order Moller–Plesset (LMP2) perturbation theory together with gauge-including atomic orbitals (GIAOs) is presented. Test calculations on the basis of a preliminary implementation within a conventional GIAO-MP2 code show that the deviations between GIAO-LMP2 and GIAO-MP2 are small, e.g., for 13C typically less than 1 ppm, and that the GIAO-LMP2 approach holds great promise for application to larger molecules.
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…
Cholesky decomposition-based definition of atomic subsystems in electronic structure calculations
2010
Decomposing the Hartree-Fock one-electron density matrix and a virtual pseudodensity matrix, we obtain an orthogonal set of normalized molecular orbitals with local character to be used in post-Hartree-Fock calculations. The applicability of the procedure is illustrated by calculating CCSD(T) energies and CCSD molecular properties in reduced active spaces. © 2010 American Institute of Physics.
Dissipation of vibronic energy in a dimer
1992
Abstract The density matrix theory is used for the study of the dissipative quantum dynamics of electron transfer in a dimer. The vibrational modes of the dimer are divided into a single interaction coordinate coupling to the transfered electron and the remaining modes which form a dissipative environment. To correlate the dissipative dynamics with the exact eigenlevels computed for the model system without dissipative environment we analyse the time dependence of the expectation value of the number of vibrational quanta. We analyse the renormalisation of the eigenvalues due to the damping and the relaxation of an excitation into these states.
Integral-geometrical consideration of density matrices
1995
The ensemble N-representability problem for the k-th order reduced density matrix (k-RDM) as well as the problem of reconstruction of the N-particle system density matrices (N-DM) from a given k-RDM are studied. The spatial parts of the k-RDM expansion in terms of spin tensorial operators {Theta}{sub {lambda}} are represented using particular values (at specially chosen {Xi} = {Xi}{sub o}) of the Radon transform D{sub N{lambda}} D{sub N{lambda}}({Xi}) of the N-DM spatial parts (or their sums) D{sub N{lambda}}({chi}{prime}{vert_bar}{chi}{double_prime}) (here, {Xi} is a d-plane in the n-space {Re}{double_prime} of {chi} = ({chi}{prime}, {chi}{double_prime}), with n = 6N, d = 3(N - k), {chi}{p…
Perturbative treatment of triple excitations in coupled‐cluster calculations of nuclear magnetic shielding constants
1996
A theory for the calculation of nuclear magnetic shielding constants at the coupled‐cluster singles and doubles level augmented by a perturbative correction for connected triple excitations (CCSD(T)) has been developed and implemented. The approach, which is based on the gauge‐including atomic orbital (GIAO) ansatz, is illustrated by several numerical examples. These include a comparison of CCSD(T) and other highly correlated methods with full configuration interaction for the BH molecule, and a systematic comparison with experiment for HF, H2O,NH3, CH4, N2, CO, HCN, and F2. The results demonstrate the importance of triple excitations in establishing quantitative accuracy. Finally, the abil…
Effective pseudopotential for energy density functionals with higher-order derivatives
2011
We derive a zero-range pseudopotential that includes all possible terms up to sixth order in derivatives. Within the Hartree-Fock approximation, it gives the average energy that corresponds to a quasi-local nuclear Energy Density Functional (EDF) built of derivatives of the one-body density matrix up to sixth order. The direct reference of the EDF to the pseudopotential acts as a constraint that divides the number of independent coupling constants of the EDF by two. This allows, e.g., for expressing the isovector part of the functional in terms of the isoscalar part, or vice versa. We also derive the analogous set of constraints for the coupling constants of the EDF that is restricted by sp…
Electron-transfer dynamics in a donor—acceptor complex
1991
Abstract Density matrix theory is used for the study of the dissipative quantum dynamics of electron transfer in a donor—acceptor complex. The vibrational modes of the complex are divided into a single interaction coordinate coupling to the transferred electron and the remaining modes which form a dissipative environment. With increase of the coupling of the interaction coordinate to the environment and, thus, of the corresponding damping rate of the vibrational quanta, the results of the numerical calculations display a change from the coherent to the incoherent transfer regime. In contrast to the case of small values of the damping, the transfer dynamics become independent of the number o…
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…