Integral-direct coupled cluster calculations of frequency-dependent polarizabilities, transition probabilities and excited-state properties (original) (raw)
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The Journal of chemical …, 1996
Algorithms for calculating singlet excitation energies in the coupled cluster singles and doubles ͑CCSD͒ model are discussed and an implementation of an atomic-integral direct algorithm is presented. Each excitation energy is calculated at a cost comparable to that of the CCSD ground-state energy. Singlet excitation energies are calculated for benzene using up to 432 basis functions. Basis-set effects of the order of 0.2 eV are observed when the basis is increased from augmented polarized valence double-zeta ͑aug-cc-pVDZ͒ to augmented polarized valence triple-zeta ͑aug-cc-pVTZ͒ quality. The correlation problem is examined by performing calculations in the hierarchy of coupled cluster models CCS, CC2, CCSD, and CC3, as well as by using the CCSDR͑3͒ perturbative triples corrections. The effect of triple excitations are less than 0.2 eV for all excitations except for the 2 1 E 2g state. The calculated excitation energies are compared with experiment and other theoretical results.
WIREs Computational Molecular Science, 2019
While methodological developments in the last decade made it possible to compute coupled cluster (CC) energies including excitations up to a perturbative triples correction for molecules containing several hundred atoms, a similar breakthrough has not yet been reported for excited state computations. Accurate CC methods for excited states are still expensive, although some promising candidates for an efficient and accurate excited state CC method have emerged recently. This review examines the various approximation schemes with particular emphasis on their performance for excitation energies and summarizes the best state-of-the-art results which may pave the way for a robust excited state method applicable to molecules of hundreds of atoms. Among these, special attention will be given to exploiting the techniques of similarity transformation, perturbative approximations as well as integral decomposition, local and embedding techniques within the equation of motion CC framework.
Chemical Physics Letters, 2000
General-order equation-of-motion coupled-cluster methods for ionization potentials and electron anities (IP-EOM-CC and EA-EOM-CC) are developed by employing a determinantal algorithm. With these, principal ionization potentials or electron anities of diatomic molecules and the excitation energies of their ionized or electron-attached counterparts are computed across dierent approximations of the cluster operator and the ionization (electron-attachment) operator. IP-EOM-CC(2,2h-1p) IP-EOM-CCSD and EA-EOM-CC(2,1h-2p) EA-EOM-CCSD or EA-EOM-CC(2,2h-3p) prove to be well-balanced models for principal ionization potentials and electron anities, whereas for the quantitative descriptions of non-Koopmans ionization or electron-attachment processes IP-EOM-CC(3, 3h-2p) IP-EOM-CCSDT and EA-EOM-CC(2,2h-3p) appear to be the minimal levels. Ó 2000 Elsevier Science (R.J. Bartlett). 0009-2614/00/$ -see front matter Ó 2000 Elsevier Science B.V. PII: S 0 0 0 9 -2 6 1 4 ( 0 0 ) 0 0 9 6 5 -9
Direct evaluation of one-electron properties in coupled cluster methods
Theoretica Chimica Acta, 1990
An analysis of a method for approximate calculations of expectation values for one-electron operators from available coupled cluster amplitudes is presented and illustrated numerically for the polarizability of the Be atom. The one-particle density matrix resulting from the present approach is accurate through the fourth order in the electron correlation perturbation. It has been found that, in order to obtain quantitative agreement between the energy derivative results and the approximate expectation value formalism, the third order TIT21,(°)> wave function term must be included into the calculation of the one-particle density matrix. The present method is also considered as a promising tool for calculations of higher-order atomic and molecular properties from high level correlated wave functions.
The Journal of Chemical Physics, 2003
The calculation of frequency-dependent polarizabilities is discussed for the iterative approximate coupled-cluster singles, doubles and triples model CC3. A new implementation of the linear response functions is reported, which has the same computational O(N 7 ) scaling as CC3 ground state calculations and uses an explicitly spin-coupled excitation space. Sample calculations are presented for the static and frequency-dependent polarizabilities of Ne and ethylene, as well as for the static polarizabilities of HF. The largest calculation employs the t-aug-cc-pVTZ basis set for ethylene giving a total of 328 basis functions. The results obtained agree well with the experimental data.
Coupled cluster methods including triple excitations for excited states of radicals
The Journal of Chemical Physics, 2005
We report an extension of the coupled cluster iterative-triples model, CC3, to excited states of open-shell molecules, including radicals. We define the method for both spin-unrestricted Hartree-Fock ͑UHF͒ and spin-restricted open-shell Hartree-Fock ͑ROHF͒ reference determinants and discuss its efficient implementation in the PSI3 program package. The program is streamlined to use at most O(N 7) computational steps and avoids storage of the triple-excitation amplitudes for both the ground-and excited-state calculations. The excitation-energy program makes use of a Löwdin projection formalism ͑comparable to that of earlier implementations͒ that allows computational reduction of the Davidson algorithm to only the single-and double-excitation space, but limits the calculation to only one excited state at a time. However, a root-following algorithm may be used to compute energies for multiple states of the same symmetry. Benchmark applications of the new methods to the lowest valence 2 B 1 state of the allyl radical, low-lying states of the CH and CO ϩ diatomics, and the nitromethyl radical show substantial improvement over ROHF-and UHF-based CCSD excitation energies for states with strong double-excitation character or cases suffering from significant spin contamination. For the allyl radical, CC3 adiabatic excitation energies differ from experiment by less than 0.02 eV, while for the 2 ⌺ ϩ state of CH, significant errors of more than 0.4 eV remain.
Simplified methods for equation-of-motion coupled-cluster excited state calculations
Chemical Physics Letters, 1996
Simplified equation-of-motion coupled-cluster (EOM-CC) methods derived from matrix partitioning and perturbation approximations are presented and applied to a variety of molecules. By combining a partitioned EOM-CC method with an MBPT(2) treatment of the ground state, we obtain an iterative n s method which gives excitation energies that normally fall within 0.2 eV of the full EOM-CCSD excitation energy. Results are shown to be superior to other simplified approaches that have been proposed.
Molecular Physics, 2005
The frequency-dependent polarizabilities and hyperpolarizabilities of HF, CO, H 2 O and para-nitroaniline calculated by density-functional theory are compared with accurate coupledcluster results. Whereas the local-density approximation and the generalized gradient approximation (BLYP) perform very similarly and overestimate polarizabilities and, in particular, the hyperpolarizabilities, hybrid density-functional theory (B3LYP) performs better and produces results similar to those obtained by coupled-cluster singles-and-doubles theory. Comparisons are also made for singlet excitation energies, calculated using linear response theory.
Local correlation in coupled cluster calculations of molecular response properties
Chemical Physics Letters, 2004
We have extended the local coupled cluster approach of Pulay and Saebø, which has seen great success in the computation of ground-state energies, to molecular response properties such as dipole polarizabilities. This scheme uses an atom-based coupledperturbed Hartree-Fock breakdown of the desired property to expand the usual ground-state orbital domains. Benchmark tests of the static polarizabilities of helium chains, linear alkanes, and non-saturated systems up to N-acetylglycine indicate that the method can reproduce untruncated coupled cluster properties to within 1% given appropriately chosen cutoffs, even without including orbital relaxation in the method. The method requires increased computational demands, but crossover points between non-local and local approaches are still well within reach of production-level implementations.
The Journal of Chemical Physics, 1998
We have calculated the static and frequency-dependent polarizability tensors of a series of (5,5)-and (9,0)carbon nanotubes. The calculations have been performed by a dipole-dipole interaction model based on classical electrostatics and an Unsöld dispersion formula. The model has previously been shown to predict successfully the frequency-dependent polarizability tensors of both aliphatic and aromatic molecules. In comparison we have carried out ab initio calculations at the Hartree-Fock level of the static polarizability of C 60 , C 70, and the smaller carbon nanotubes using the STO-3G basis set. We find that the interaction model is in good agreement with the self-consistent field calculations and can be used to predict the polarizability tensors of carbon nanotubes. In addition, we find that the symmetry and intramolecular geometry of the tube have great influence on the polarizability.