Search results for "basis"
showing 10 items of 760 documents
Explicitly correlated connected triple excitations in coupled-cluster theory.
2009
A way to incorporate explicit electron correlation into connected triple excitations in coupled-cluster theory is proposed. The new ansatz is applied to the coupled-cluster singles and doubles model with noniterative triple excitations [CCSD(T)] and does not introduce any further sets of equations to be solved. A first implementation using automated generation and string-based evaluation of the explicit expressions is reported. The results demonstrate that the ansatz significantly enhances the basis set convergence of the noniterative triple excitation correction and thus improves upon previous approaches to explicitly correlated CCSD(T).
Towards the Hartree-Fock and coupled-cluster singles and doubles basis set limit: A study of various models that employ single excitations into a com…
2010
In explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] calculations, the basis set incompleteness error in the double excitations is reduced to such an extent that the error in the Hartree–Fock energy and the error in the single excitations become important. Using arguments from perturbation theory to systematically truncate the coupled-cluster singles and CCSD(F12) Lagrangians, a series of coupled-cluster models are proposed and studied that reduce these basis set incompleteness errors through additional single excitations into a complementary auxiliary basis. Convergence with model and size of complementary basis is rapid and there appears to be no need to go beyond seco…
From correlation-consistent to polarization-consistent basis sets estimation of NMR spin–spin coupling constant in the B3LYP Kohn–Sham basis set limit
2008
Abstract Based on B3LYP spin–spin coupling constants (SSCC) of several molecules calculated with cc-pV x Z, cc-pCV x Z, cc-pCV x Z-sd and cc-pCV x Z-sd+ t basis sets, a reasonably fit, using the two-parameter formula, to the Kohn–Sham complete basis set limit (CBS) is shown. Improvement in the CBS values going from cc-pV x Z to the most elaborated cc-pCV x Z-sd+ t basis set family is observed: standard deviation for all data drops from 33.7 to 23.1, and from 6.0 to 4.8 Hz after excluding problematic 1 J (F,H) and 1 J (F,C). Calculation of water’s 1 J (OH) using B3LYP/cc-pCV x Z and B3LYP/pcJ- n significantly improved the FC term convergence.
Improved Algorithms for the Modeling of Vibrational Polyads of Polyatomic Molecules: Application toT,O, andC3Molecules
1997
Abstract Improved algorithms for the construction of rovibrational operators of polyatomic molecules are presented. Vibrationally diagonal and off-diagonal terms are obtained by a specific coupling scheme of creation and annihilation elementary operators. Recursive procedures are used to generate all possible terms and associated basis functions as well as to calculate matrix elements and commutators. Explicit formulations are given forTd,Oh, andC3vmolecules.
Explicitly correlated coupled-cluster theory using cusp conditions. I. Perturbation analysis of coupled-cluster singles and doubles (CCSD-F12)
2010
Geminal functions based on Slater-type correlation factors and fixed expansion coefficients, determined by cusp conditions, have in recent years been forwarded as an efficient and numerically stable method for introducing explicit electron correlation into coupled-cluster theory. In this work, we analyze the equations of explicitly correlated coupled-cluster singles and doubles (CCSD-F12) theory and introduce an ordering scheme based on perturbation theory which can be used to characterize and understand the various approximations found in the literature. Numerical results for a test set of 29 molecules support our analysis and give additional insight. In particular, our results help ration…
Explicitly correlated coupled-cluster theory using cusp conditions. II. Treatment of connected triple excitations.
2010
The coupled-cluster singles and doubles method augmented with single Slater-type correlation factors (CCSD-F12) determined by the cusp conditions (also denoted as SP ansatz) yields results close to the basis set limit with only small overhead compared to conventional CCSD. Quantitative calculations on many-electron systems, however, require to include the effect of connected triple excitations at least. In this contribution, the recently proposed [A. Köhn, J. Chem. Phys. 130, 131101 (2009)] extended SP ansatz and its application to the noniterative triples correction CCSD(T) is reviewed. The approach allows to include explicit correlation into connected triple excitations without introducin…
Natural occupation numbers: When do they vanish?
2013
The non-vanishing of the natural orbital occupation numbers of the one-particle density matrix of many-body systems has important consequences for the existence of a density matrix-potential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the extended Koopmans' Theorem. On the basis of Weyl's theorem we give a connection between the differentiability properties of the ground state wave function and the rate at which the natural occupations approach zero when ordered as a descending series. We show, in particular, that the presence of a Coulomb cusp in the wave function leads, in general, to a power law decay of the natural occupations, whe…
Origin invariant calculation of optical rotation without recourse to London orbitals
2004
We propose an inherently origin invariant formulation of specific optical rotation obtained from the conventional velocity gauge expression by subtracting the static limit from the electric dipole-magnetic dipole polarizability: ããpâ,LâããÏâããpâ,LâããÏ-ããpâ,Lâãã0. London (gauge including) atomic orbitals are therefore not needed to ensure origin invariance and, consequently, this modified velocity gauge formulation may be employed in conjunction with variational and non-variational quantum chemical methods alike. Sample calculations on S-propylene oxide and 3,4- methylenedioxymethamphetamine using self-consistent field and coupled cluster wave functions…
Revised values for the nuclear quadrupole moments ofS33andS35
2014
High-level quantum-chemical calculations are reported for the sulfur electric-field gradients of the CS and SiS molecules. Highly accurate values are obtained in these calculations by using coupled-cluster methods for the treatment of electron correlation together with large atomic-orbital basis sets and by taking into account relativistic effects. The computational results for the sulfur electric-field gradient are used to determine revised values for the $^{33}\mathrm{S}$ and $^{35}\mathrm{S}$ quadrupole moments, thereby taking advantage of available accurate values for the sulfur quadrupole couplings of CS and SiS from the analysis of rotational spectra. The derived values of $\ensuremat…
Modeling vibrating panels excited by a non-homogeneous turbulent boundary layer
2021
Abstract Predicting the vibration response of an elastic structure excited by a turbulent flow is of interest for the civil and military transportation sector. The models proposed in the literature are generally based on the assumption that the turbulent boundary layer (noted TBL in the following) exciting the structure is spatially homogeneous. However, this assumption is not always fulfilled in practice, in particular when the excited area is close to the starting point of the TBL or with curved structures. To overcome this issue, this work proposes to extend two approaches generally used for dealing with homogeneous TBL, namely the spatial and the wavenumber approaches. The extension of …