Automatic derivation and evaluation of vibrational coupled cluster theory equations

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Articles you may be interested inOrbitally invariant internally contracted multireference unitary coupled cluster theory and its perturbative approximation: Theory and test calculations of second order approximation J. Chem. Phys. 137, 014108 (2012); 10.1063/1.4731634 Accurate calculation of vibrational frequencies using explicitly correlated coupled-cluster theory Accurate calculation of anharmonic vibrational frequencies of medium sized molecules using local coupled cluster methods J. Chem. Phys. 126, 134108 (2007); 10.1063/1.2718951 MRCI calculations on the helium dimer employing an interaction optimized basis setThe use of variationally optimized coordinates, which minimize the vibrational self-consistent field (VSCF) ground state energy with respect to orthogonal transformations of the coordinates, has recently been shown to improve the convergence of vibrational configuration interaction (VCI) towards the exact full VCI [K. Yagi, M. Keçeli, and S. Hirata, J. Chem. Phys. 137, 204118 (2012)]. The present paper proposes an incorporation of optimized coordinates into the vibrational coupled cluster (VCC), which has in the past been shown to outperform VCI in approximate calculations where similar restricted state spaces are employed in VCI and VCC. An embarrassingly parallel algorithm for variational optimization of coordinates for VSCF is implemented and the resulting coordinates and potentials are introduced into a VCC program. The performance of VCC in optimized coordinates (denoted oc-VCC) is examined through pilot applications to water, formaldehyde, and a series of water clusters (dimer, trimer, and hexamer) by comparing the calculated vibrational energy levels with those of the conventional VCC in normal coordinates and VCI in optimized coordinates. For water clusters, in particular, oc-VCC is found to gain orders of magnitude improvement in the accuracy, exemplifying that the combination of optimized coordinates localized to each monomer with the size-extensive VCC wave function provides a supreme description of systems consisting of weakly interacting sub-systems.

Section: Introductionmentioning

confidence: 99%

Optimized coordinates in vibrational coupled cluster calculations

Thomsen

Yagi

Christiansen

2014

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“…(13). i m denotes the reference modal of mode m, u m the modal of mode m that is occupied in | µ m ⟩, and v m the modal occupied in |ν m ⟩.…”

Section: B Perturbative Measuresmentioning

confidence: 99%

“…This has been illustrated by automatic derivation and analysis. 13,14 Still, the polynomial scaling quickly leads to costly computations. For VCC, it has been shown that for large model systems that are actually decoupled, the computational cost can be reduced significantly by exploiting this decoupling in the parameterization.…”

Section: Introductionmentioning

confidence: 99%

Automatic determination of important mode–mode correlations in many-mode vibrational wave functions

König

Christiansen

2015

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We introduce new automatic procedures for parameterizing vibrational coupled cluster (VCC) and vibrational configuration interaction wave functions. Importance measures for individual mode combinations in the wave function are derived based on upper bounds to Hamiltonian matrix elements and/or the size of perturbative corrections derived in the framework of VCC. With a threshold, this enables an automatic, system-adapted way of choosing which mode-mode correlations are explicitly parameterized in the many-mode wave function. The effect of different importance measures and thresholds is investigated for zero-point energies and infrared spectra for formaldehyde and furan. Furthermore, the direct link between important mode-mode correlations and coordinates is illustrated employing water clusters as examples: Using optimized coordinates, a larger number of mode combinations can be neglected in the correlated many-mode vibrational wave function than with normal coordinates for the same accuracy. Moreover, the fraction of important mode-mode correlations compared to the total number of correlations decreases with system size. This underlines the potential gain in efficiency when using optimized coordinates in combination with a flexible scheme for choosing the mode-mode correlations included in the parameterization of the correlated many-mode vibrational wave function. All in all, it is found that the introduced schemes for parameterizing correlated many-mode vibrational wave functions lead to at least as systematic and accurate calculations as those using more standard and straightforward excitation level definitions. This new way of defining approximate calculations offers potential for future calculations on larger systems.

“…[18][19][20][21][22][23][24][25][26][27][28][29] The coupled cluster method has been established as one of the most accurate methods for the description of the many body systems. [30][31][32][33][34][35] In this method, the ground state of a many body system is obtained by the action of an exponential wave operator on an optimized a) Electronic mail: s.pal@ncl.res.in.…”

Section: Introductionmentioning

confidence: 99%

Vibrational multi-reference coupled cluster theory in bosonic representation

Banik

Pal

Prasad

2012

The vibrational multi-reference coupled cluster method is developed to calculate the vibrational excitation energies of polyatomic molecules. The method is implemented on ozone and formaldehyde molecules and the results are compared with full vibrational configuration interaction (FVCI) method. A good agreement is found between the vibrational multi-reference coupled cluster method and converged FVCI method for lower lying vibrational states.