http://www.mdpi.com/journal/ijms/special_issues/recent-advances-in-coupled-cluster-theory/ http://www.mdpi.com/1422-0067/3/5/570/ In a previous paper, we have avoided an infinite order perturbation expansion and obtained a closed expression which consists of the second-order Møller-Plesset energy component together with a remainder term. The applicabilty of second-order many-body perturbation theory with a Møller-Plesset reference hamiltonian then rests upon the magnitude of this remainder term rather than the behaviour of the higher order terms on the perturbation series. In the present work, we show how this remainder term can be estimated by limited configuration interaction. http://www.mdpi.com/1422-0067/3/5/570/ Fri, 31 May 2002 00:00:00 CEST International Journal of Molecular Sciences 2002-05-31 3 5 Article 570 578 1422-0067 On the Estimation of the Remainder Term in Møller-Plesset MP2 Theory from Limited Configuration Interaction 2002-05-31 doi: 10.3390/i3050570 I. Hubac S. Wilson http://www.mdpi.com/1422-0067/3/5/550/ We have presented in this paper a new cluster Ansatz for the wave operator for open-shell and/or quasidegenerate states, which takes care of strong relaxation and correlation effects in a compact and efficient manner. This Ansatz allows contraction among the various cluster operators via spectator orbitals, accompanied by suitable combinatorial factors. Since both the orbital and the correlation relaxations are treated on the same footing, it allows us to develop a very useful direct method for energy differences for open shell states relative to a closed-shell ground state, where the total charge for the two states may differ. We have discussed a new spin-free coupled cluster (CC) based direct method and illustrated its performance by evaluating electron affinity of a neutral doublet radical. We have also indicated how the scope of the theory can be extended to compute the state energies of simple open shell configurations as well. In that case, the CC equations terminate after the quartic power of cluster operators – exactly as in the closed-shell situation, which is not the case for the current methods. http://www.mdpi.com/1422-0067/3/5/550/ Fri, 31 May 2002 00:00:00 CEST International Journal of Molecular Sciences 2002-05-31 3 5 Article 550 569 1422-0067 Use of a New Cluster Ansatz to Treat Strong Relaxation and Correlation Effects: A Direct Method for Energy Differences 2002-05-31 doi: 10.3390/i3050550 Debasis Jana Uttam Sinha Mahapatra Debashis Mukherjee http://www.mdpi.com/1422-0067/3/5/522/ An analysis of alternative expressions of the state–specific (SS) multi–reference (MR) coupled cluster (CC) wave functions is presented. The approach utilizes the CASSCF (complete active space self consistent field) wave function as the reference. It is designed specifically for calculating excited electronic states. The cluster structure of the CC wave operator and the origin(s) for the cluster expansion(s) are the key features of the development. Test calculations reveal some interesting features of the SMRCC approaches. http://www.mdpi.com/1422-0067/3/5/522/ Fri, 31 May 2002 00:00:00 CEST International Journal of Molecular Sciences 2002-05-31 3 5 Article 522 549 1422-0067 Alternative Multi–reference State–specific Coupled Cluster Wave Functions 2002-05-31 doi: 10.3390/i3050522 Ludwik Adamowicz Jean–Paul Malrieu Vladimir V. Ivanov http://www.mdpi.com/1422-0067/3/5/508/ We examine the possibility of introducing a new class of so called noniterative corrections to coupled cluster energies, based on the connected moments expansion (CMX). Approximate Coupled Cluster (CC) wave functions are used as reference states and then the “improved energies” can be formally obtained either by CMX in terms of the moments of CC similarity transformed Hamiltonian, or in CMX of the usual Hamiltonian. Numerical results are given for some model systems that show the superiority of the latter approach. http://www.mdpi.com/1422-0067/3/5/508/ Fri, 31 May 2002 00:00:00 CEST International Journal of Molecular Sciences 2002-05-31 3 5 Article 508 521 1422-0067 On the Use of Connected Moments Expansion with Coupled Cluster Reference 2002-05-31 doi: 10.3390/i3050508 Jozef Noga Agnes Szabados Péter R. Surján http://www.mdpi.com/1422-0067/3/5/498/ Potential functions of the ground and low excited states of Al2 are calculated by the relativistic Fock-space coupled cluster method in the framework of the projected Dirac-Coulomb Hamiltonian. A moderate-size basis [16s11p3d3f/6s6p3d2f] is used. 3Πu is confirmed as the ground state of the system. Its spin orbit splittings are reproduced well, with the Λ = 1, 2 states lying 32.5 and 66.1 cm−1, respectively, above the Λ = 0 minimum (experimental values are 30.4 and 63.4 cm−1). The bond is somewhat too weak, with De 0.14 eV below experiment, Re too high by 0.08 ˚A, and ωe 21 cm−1 too low. It is speculated that the better agreement obtained in earlier calculations may be due to neglect of basis set superposition errors. The description of bonding in the molecule may be improved by the use of a better basis and the inclusion of more correlation by the intermediate Hamiltonian coupled cluster method, which makes it possible to handle larger P spaces and extend the potential functions to the whole range of internuclear separations. http://www.mdpi.com/1422-0067/3/5/498/ Fri, 31 May 2002 00:00:00 CEST International Journal of Molecular Sciences 2002-05-31 3 5 Article 498 507 1422-0067 Potential Functions of Al2 by the Relativistic Fock-Space Coupled Cluster Method 2002-05-31 doi: 10.3390/i3050498 Arie Landau Ephraim Eliav Lucas Visscher Uzi Kaldor http://www.mdpi.com/1422-0067/3/5/475/ A new approach to the many-electron correlation problem, termed the method of moments of coupled-cluster equations (MMCC), is further developed and tested. The main idea of the MMCC theory is that of the noniterative energy corrections which, when added to the energies obtained in the standard coupled-cluster calculations, recover the exact (full configuration interaction) energy. The MMCC approximations require that a guess is provided for the electronic wave function of interest. The idea of using simple estimates of the wave function, provided by the inexpensive configuration interaction (CI) methods employing small sets of active orbitals to define higher–than–double excitations, is tested in this work. The CI-corrected MMCC methods are used to study the single bond breaking in HF and the simultaneous breaking of both O–H bonds in H2O. http://www.mdpi.com/1422-0067/3/5/475/ Fri, 31 May 2002 00:00:00 CEST International Journal of Molecular Sciences 2002-05-31 3 5 Article 475 497 1422-0067 Method of Moments of Coupled-Cluster Equations: Externally Corrected Approaches Employing Configuration Interaction Wave Functions 2002-05-31 doi: 10.3390/i3050475 Piotr Piecuch Karol Kowalski Ian S.O. Pimienta http://www.mdpi.com/1422-0067/3/5/459/ We recently developed an explicitly correlated method using the transcorrelated Hamiltonian, which is preliminarily parameterized in such a way that the Coulomb repulsion is compensated at short inter-electronic distances. The extra part of the effective Hamiltonian features short-ranged, size-consistent, and state-universal. The localized and frozen nature of the correlation factor makes the enormous three-body interaction less important and enables us to bypass the complex nonlinear optimization. We review the basic strategy of the method mainly focusing on the applications to single-reference many electron theories using modified Møller-Plesset partitioning and biorthogonal orbitals. Benchmark calculations are performed for 10-electron systems with a series of basis sets. http://www.mdpi.com/1422-0067/3/5/459/ Fri, 31 May 2002 00:00:00 CEST International Journal of Molecular Sciences 2002-05-31 3 5 Article 459 474 1422-0067 New Transcorrelated Method Improving the Feasibility of Explicitly Correlated Calculations 2002-05-31 doi: 10.3390/i3050459 Seiichiro Ten-no Osamu Hino http://www.mdpi.com/1422-0067/3/5/447/ A time dependent coupled cluster approach to the calculation of Resonance Raman excitation profiles on general anharmonic surfaces is presented. The vibrational wave functions on the ground electronic surface are obtained by the coupled cluster method (CCM). It is shown that the propagation of the vibrational ground state on the upper surface is equivalent to propagation of the vacuum state by an effective hamiltonian generated by the similarity transformation of the vibrational hamiltonian of that surface by the CCM wave operator of the lower surface up to a normalization constant. This time propagation is carried out by the time-dependent coupled cluster method in a time dependent frame. Numerical studies are presented to asses the validity of the approach. http://www.mdpi.com/1422-0067/3/5/447/ Fri, 31 May 2002 00:00:00 CEST International Journal of Molecular Sciences 2002-05-31 3 5 Article 447 458 1422-0067 Time Dependent Coupled Cluster Approach to Resonance Raman Excitation Profiles from General Anharmonic Surfaces 2002-05-31 doi: 10.3390/i3050447 M. Durga Prasad http://www.mdpi.com/1422-0067/3/5/445/ n/a http://www.mdpi.com/1422-0067/3/5/445/ Fri, 31 May 2002 00:00:00 CEST International Journal of Molecular Sciences 2002-05-31 3 5 Editorial 445 446 1422-0067 Special Issue on Recent Advances in Coupled Cluster Theory 2002-05-31 doi: 10.3390/i3050445 Sourav Pal