Abstract:Some recent advances in the area of multi-reference coupled-cluster theory of the state-universal type are overviewed. An emphasis is placed on the following new developments: (i) the idea of combining the state-universal multi-reference coupled-cluster singles and doubles method (SUMRCCSD) with the multi-reference many-body perturbation theory (MRMBPT), in which cluster amplitudes of the SUM-RCCSD formalism that carry only core and virtual orbital indices are replaced by their first-order MRMBPT estimates; an… Show more
“…The MRexpT method of Hanrath [112,[139][140][141][142] and the C-conditions method of Li and Paldus [92][93][94][95][96][97] seem to offer a promising solution of the first problem. On should also point out that the incomplete model spaces and the C-conditions can also be used in the state-selective framework -in the BW-CC [119] and [60,151], who approximated the core-virtual bi-excited amplitudes by perturbation theory and obtained very good results with a greatly reduced number of variables in the nonlinear CC equations. In fact, this core-virtual bi-excited amplitudes are, through the first order of perturbation theory, independent of µ and one may contemplate to determine them nonperturbatively from MRCC equation assuming that they are the same for all µ's through all orders [152].…”
Section: Discussionmentioning
confidence: 99%
“…The difficulties to converge the solutions of MRCC equations may be overcome by using better convergence acceleration or equation regularization techniques [134], or by including higher excitations in T µ , which should reduce the number of unphysical solutions [60,86] hampering convergence to the physical ones. A promising way of solving these convergence difficulty, successfully applied in the context of the Fock space CC theory [42], is to use the intermediate-Hamiltonian approach to reformulate the SU-CC equations [153].…”
Section: Discussionmentioning
confidence: 99%
“…This is certainly not a situation conducive to black-box type applications of the SU-CC theory. There is some hope, however, that the inclusion of higher than doubly-excited clusters will help to reduce the number of multiple solutions [60,87,88] and will alleviate problems with converging the SU-CC equations in physically relevant applications.…”
“…The MRexpT method of Hanrath [112,[139][140][141][142] and the C-conditions method of Li and Paldus [92][93][94][95][96][97] seem to offer a promising solution of the first problem. On should also point out that the incomplete model spaces and the C-conditions can also be used in the state-selective framework -in the BW-CC [119] and [60,151], who approximated the core-virtual bi-excited amplitudes by perturbation theory and obtained very good results with a greatly reduced number of variables in the nonlinear CC equations. In fact, this core-virtual bi-excited amplitudes are, through the first order of perturbation theory, independent of µ and one may contemplate to determine them nonperturbatively from MRCC equation assuming that they are the same for all µ's through all orders [152].…”
Section: Discussionmentioning
confidence: 99%
“…The difficulties to converge the solutions of MRCC equations may be overcome by using better convergence acceleration or equation regularization techniques [134], or by including higher excitations in T µ , which should reduce the number of unphysical solutions [60,86] hampering convergence to the physical ones. A promising way of solving these convergence difficulty, successfully applied in the context of the Fock space CC theory [42], is to use the intermediate-Hamiltonian approach to reformulate the SU-CC equations [153].…”
Section: Discussionmentioning
confidence: 99%
“…This is certainly not a situation conducive to black-box type applications of the SU-CC theory. There is some hope, however, that the inclusion of higher than doubly-excited clusters will help to reduce the number of multiple solutions [60,87,88] and will alleviate problems with converging the SU-CC equations in physically relevant applications.…”
“…, M). Aside from various mathematical difficulties that this assumption creates, the requirement of having a separate cluster operator T ð pÞ for each reference configuration jÈ p i leads to an excessively large number of cluster amplitudes when the dimension of the model space (M) is large, particularly when we are only interested in a few lowlying states whose number is much less than M. We have recently addressed an issue of an excessively large number of cluster amplitudes in the SUMRCCSD theory by proposing the SUMRCCSD(1) approach, which is based on the idea of combining the SUMRCCSD method with the MRMBPT approach [133,134]. In the SUMRCCSD(1) method, the most numerous doubly excited cluster amplitudes, which carry only core and virtual orbital indices, are approximated by their firstorder MRMBPT estimates.…”
Section: Introductionmentioning
confidence: 99%
“…The SUMRCC methods are also capable of providing the spectroscopically accurate description of electronic energy separations in small molecular systems, as has been illustrated by the calculations of the singlettriplet (A 1 A 1 À X 3 B 1 ) [125,126] and singlet-singlet (2 1 A 1 À 1 1 A 1 ; 1 1 A 1 A 1 A 1 ) [124,132] energy gaps in methylene. Unfortunately, apart from the earlier advances in formulating, implementing, and testing the spin-adapted and spin-orbital SUMRCCSD methods [6,8,[111][112][113][114][115][116][117][118][119][120][121][122][123][124][125][126][127][128][129][130] and apart from the limited recent activities in our group (see, e.g., [131][132][133][134]), the group of Pal [135], who formulated the response SUMRCC theory, and the Paldus Waterloo group [136][137][138][139], who introduced the generalized version of the SUMRCC method enabling the systematic use of incomplete model spaces in SUMRCC calculations, the development of the genuine SUMRCC method has practically stopped. We believe that this situation should change, since the SUMRCC theory has the potential of offering an elegant and, at the same time, well balanced description of many classes of ground and excited electronic states, particularly when the quasi-degeneracies and the degree of non-dynamic correlation are too severe to be handled by other CC methods.…”
Two new classes of non-iterative corrections to the ground-and excited-state energies obtained in the state-universal multi-reference coupled-cluster (SUMRCC) calculations have been developed using the multi-reference extension of the method of moments of coupledcluster equations (MMCC) [KOWALSKI, K., and PIECUCH, P., 2001, J. molec. Struct. (THEOCHEM), 547, 191]. In the first class of the configuration interaction (CI) corrected multi-reference MMCC (MRMMCC) approximations, the non-iterative corrections due to triply or triply and quadruply excited clusters are constructed with the help of multi-reference CI (MRCI) calculations employing the same active space as used in the SUMRCC calculations. In the second class of the completely renormalized (CR) SUMRCC methods, which can be viewed as the multi-reference extensions of the single-reference CR-CCSD(T) theory [KOWALSKI, K., and PIECUCH, P., 2000, J. chem. Phys., 113, 18], the non-iterative corrections due to triply excited clusters are constructed with the help of the multi-reference many-body perturbation theory. In both cases, the non-iterative corrections due to higherorder clusters are added to the energies obtained with the SUMRCC method with singles and doubles. It is demonstrated that the newly developed corrections, including the CR-SUMRCC methods, offer considerable improvements in the SUMRCCSD results, reducing, in particular, the large errors in the SUMRCCSD results due to intruders.
We have tested the linked version of a iterative (partial) triples correction for the Jeziorski-Monkhorst ansatz based state-specific multireference coupled cluster (SS-MRCC) approach with singles and doubles (SD) excitations [abbreviated as SS-MRCCSDT-1a and SS-MRCCSDT-1a+d]. The assessments of SS-MRCCSDT-1a and SS-MRCCSDT-1a+d schemes have been performed on the ground potential energy surface (PES) of P4, Li(2),Be(2) systems which demand the MR description, and on study of the excitation energy between the ground and first excited state for P4 system. Illustrations in the isomerization of cyclobutadiene also show the power of the schemes. One of the designed features of the SS-MRCCSDT-n methods introduced here is that they do not require storage of the triples amplitudes. In the entire range of geometries, we found a definite improvement provided by SS-MRCC with SDT-1a and SDT-1a+d schemes over the standard SD one. In the nondegenerate regions of PES, the closeness of the performance of the single-reference CC to the SS-MRCC methods increases after inclusion of even partial triple excitations. Generally, the performance of the SS-MRCCSDT-1a+d approach is closer to the corresponding full configuration interaction (FCI) one than to the SS-MRCCSDT-1a specially in the degenerate geometries (as is evident from nonparallelism error). The deviation from FCI for the first excited state of the P4 model using various SS-MRCC theories with different truncation schemes obtained by converging on the second root of the effective Hamiltonian has also been reported. We also compare our results with the current generation state-of-the-art single and multireference CC calculations to envisage the usefulness of the present approach. Initial implementation indicates that the SS-MRCCSDT-n formalism can provide not only reliable excitation energies and barrier height even when used in a relatively small model space, but also offers a considerable promise in generating the entire energy surface with low nonparallelity error.
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