Today, coupled-cluster theory offers the most accurate results among the practical ab initio electronic-structure theories applicable to moderate-sized molecules. Though it was originally proposed for problems in physics, it has seen its greatest development in chemistry, enabling an extensive range of applications to molecular structure, excited states, properties, and all kinds of spectroscopy. In this review, the essential aspects of the theory are explained and illustrated with informative numerical results.

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Coupled-cluster theory in quantum chemistry

For more than 70 years, researchers in several areas of science have been intrigued by the physical and chemical properties of the lowest excited states of molecular oxygen. With two singlet states lying close above its triplet ground state, the O2 molecule possesses a very unique configuration, which gives rise to a very rich and easily accessible chemistry, and also to a number of important photophysical interactions. In particular, photosensitized reactions of the first excited state, O2(∆g), play a key role in many natural photochemical and photobiological processes, such as photodegradation and aging processes including even photocarcinogenesis. Reactions of O2(∆g) are associated with significant applications in several fields, including organic synthesis, bleaching processes, and, most importantly, the photodynamic therapy of cancer, which has now obtained regulatory approval in most countries for the treatment of several types of tumors. The development of both applications and novel observation techniques has strongly accelerated during the past few years. Significant recent advances include, for example, the development of novel luminescent singlet oxygen probes,1-4 the time-resolved detection of O2(∆g) in a transmission microscope,5 the first time-resolved measurements of singlet oxygen luminescence in vivo,6 and the observation of oxygen quenching of triplet-excited single molecules.7 Experimental and theoretical studies on the mechanisms of photosensitized formation of excited O2 states and of their deactivation have been performed for almost 40 years. While most early liquid-phase studies were exclusively concerned with O2(∆g), recent technological advances also made possible time-resolved investigations of the second excited state, O2(Σg), which can be formed in competition with O2(∆g) in many cases. A significant number of * Corresponding author. Tel.: ++49 69 79829448. Fax: ++49 69 79829445. E-mail: R.Schmidt@chemie.uni-frankfurt.de. 1685 Chem. Rev. 2003, 103, 1685−1757

Physical mechanisms of generation and deactivation of singlet oxygen.

Molcas: a program package for computational chemistry.

Some of the new unique features of the MOLCAS quantum chemistry package version 7 are presented inthis report. In particular, the Cholesky decomposition method applied to some quantum chemical methods is described. This approach is used both in the context of a straight forward approximation of the two-electron integrals and in the generation of so-called auxiliary basis sets. The article describes how the method is implemented for most known wave functions models: self-consistent field, density functional theory, 2nd order perturbation theory, complete-active space self-consistent field multiconfigurational reference 2nd order perturbation theory, and coupled-cluster methods. The report further elaborates on the implementation of a restricted-active space self-consistent field reference function in conjunction with 2nd order perturbation theory. The average atomic natural orbital basis for relativistic calculations, covering the whole periodic table, are described and associated unique properties are demonstrated. Furthermore, the use of the arbitrary order Douglas-Kroll-Hess transformation for one-component relativistic calculations and its implementation are discussed. This section especially focuses on the implementation of the so-called picture-change-free atomic orbital property integrals. Moreover, the ElectroStatic Potential Fitted scheme, a version of a quantum mechanics/molecular mechanics hybrid method implemented in MOLCAS, is described and discussed. Finally, the report discusses the use of the MOLCAS package for advanced studies of photo chemical phenomena and the usefulness of the algorithms for constrained geometry optimization in MOLCAS in association with such studies. (c) 2009 Wiley Periodicals, Inc. J Corn put Chem 31: 224-247, 2010

Software news and update MOLCAS 7 : The Next Generation

Coupled cluster models for electron correlation which include the effects of single, double, and triple excitation operators are analyzed. An alternate version of the approximate CCSDT‐1 method is implemented. In this version, the full CCSDT cluster operator eT1+T2+T3 is preserved in the creation of single and double excitation coefficients, but in calculation of triple excitation coefficients only the T2 operator is used. We also present a theoretical analysis of the simplest improvement for the evaluation of the contribution of triples beyond that obtained with fourth‐order MBPT. In this approximation, an MBPT(4)‐like calculation of the triples energy is evaluated with converged CCSD T2 coefficients. This is found to offer a good approximation to the converged CCSDT‐1 results.

Towards a full CCSDT model for electron correlation

We present a simple a posteriori correction for the state-specific multireference Brillouin–Wigner coupled-cluster (MR BWCCSD) theory, which eliminates its size-extensivity error. In the converged amplitudes we drop terms that were identified to be responsible for the lack of size extensivity. We performed MR BWCCSD calculations with this correction on CH2, SiH2, twisted ethylene, F2, and ozone that are all, from the computational point of view, typical representatives of two-reference problems. Comparison with rigorously size-extensive calculations and experiment shows that the size-extensivity error of the corrected MR BWCCSD is only a few tenths of kcal/mol.

Size-extensivity correction for the state-specific multireference Brillouin–Wigner coupled-cluster theory

Recently developed single-root multireference Brillouin–Wigner coupled-cluster (MR BWCC) theory, which belongs to a broad family of state-selective multireference coupled-cluster methods, has been implemented in the ACES II program package at the CCSD level of approximation. The method represents a new approach to quasidegenerate problems, which is able to continuously switch between the single-reference CC in a nondegenerate situation and the Hilbert-space MRCC in a degenerate case. An assessment of the method has been carried out by means of a comparison with the full configuration interaction (CI) treatments of CH2, SiH2, and twisted ethylene diradicals. The problem of size-extensivity is discussed.

Assessment of the single-root multireference Brillouin–Wigner coupled- cluster method: Test calculations on CH2, SiH2, and twisted ethylene

Recently developed Brillouin-Wigner coupled-cluster theory [I Hubac and P Neogrady, Phys Rev A 50 , 4558 (1994)] is extended to a multireference case using the Hilbert space approach We formulate the so-called single-root (one-state or state-specific) version which deals with one state at a time while employing a multiconfigurational reference wave function Employing the Hilbert space approach to the wave operator, we present an explicit form for cluster amplitudes in a spin-orbital form within the CCSD approximation; ie coupled-cluster method truncated at the single and double excitation level The method is applied to a trapezoidal H4 model system with the use of a two-determinant reference space and the results are compared with the full configuration interaction as well as other correlated multireference techniques The method provides a balanced description of the ground state in both quasidegenerate and nondegenerate regions and deviations from the full configuration interaction energies do not exceed 06 mHartree

Multireference Brillouin-Wigner Coupled-Cluster Theory. Single-root approach.

Recently developed single-root multireference Brillouin-Wigner coupled-cluster (MR BWCC) theory, which deals with one state at a time while employing a multiconfigurational reference wave function, is applied to the ground state of the F2 molecule using a two-determinant reference space at the level of the CCSD approximation. The method represents a brand-new coupled-cluster (CC) approach to quasidegenerate problems which combines merits of two theories: the single-reference CC method in a nondegenerate case and the Hilbert space MR CC method in quasidegenerate case. The method is able to switch itself from a nondegenerate to a fully degenerate case in a continuous manner, providing thus smooth potential energy surfaces. Moreover, in contrast to the Hilbert space MR CC approaches, it does not contain the so-called coupling terms and completely reduces to the standard single-reference CC method in a highly nondegenerate region. Using a [4s,3p,1d] and [4s,3p,2d,1f ] basis sets, the calculated potential ener...

Single-root multireference Brillouin-Wigner coupled-cluster theory: Applicability to the F2 molecule

Hilbert-space state-universal multireference coupled-cluster (MR CC) data on cyclobutadiene [A. Balkova and R. J. Bartlett, J. Chem. Phys. 101, 8972 (1994)] were used as a benchmark for testing our recently developed state-specific (single-root) multireference Brillouin-Wigner coupled-cluster (MR BWCC) theory. For the energy of activation in the automerization of cyclobutadiene (i.e., the energy difference between the square and rectangular structures) at the CCSD/[3s2p1d/2s] level of theory, our MR BWCCSD method gives the value of 6.2 kcal/mol, compared to 6.5 kcal/mol given by MR CCSD. With the cc-pVDZ and cc-pVTZ/cc-pVDZ basis sets, the MR BWCCSD activation barrier is 6.4 and 7.0 kcal/mol, respectively. The effect of the triple excitations [in MR CCSD(T)] and of the frozen core approximation were estimated previously to be below 0.1 kcal/mol and in the opposite direction. This shows the way of how to arrive at a more accurate automerization barrier in future calculations: extension of the basis set see...

Multireference coupled-cluster calculations on the energy of activation in the automerization of cyclobutadiene: Assessment of the state-specific multireference Brillouin–Wigner theory

Ivan Hubač

Papers

Size-extensivity correction for the state-specific multireference Brillouin–Wigner coupled-cluster theory

Assessment of the single-root multireference Brillouin–Wigner coupled- cluster method: Test calculations on CH2, SiH2, and twisted ethylene

Multireference Brillouin-Wigner Coupled-Cluster Theory. Single-root approach.

Single-root multireference Brillouin-Wigner coupled-cluster theory: Applicability to the F2 molecule

Multireference coupled-cluster calculations on the energy of activation in the automerization of cyclobutadiene: Assessment of the state-specific multireference Brillouin–Wigner theory