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

An Introduction to Coupled Cluster Theory for Computational Chemists

Stark spectroscopy has been applied to a wide range of molecular systems and materials. A generally useful method for obtaining electronic and vibrational Stark spectra that does not require sophisticated equipment is described. By working with frozen glasses it is possible to study nearly any molecular system, including ions and proteins. Quantitative analysis of the spectra provides information on the change in dipole moment and polarizability associated with a transition. The change in dipole moment reflects the degree of charge separation for a transition, a quantity of interest to a variety of fields. The polarizability change describes the sensitivity of a transition to an electrostatic field such as that found in a protein or an ordered synthetic material. Applications to donor-acceptor polyenes, transition metal complexes (metal-to-ligand and metal-to-metal mixed valence transitions), and nonphotosynthetic biological systems are reviewed.

STARK SPECTROSCOPY: Applications in Chemistry, Biology, and Materials Science

The theory for analytic energy derivatives of excited electronic states described by the equation‐of‐motion coupled cluster (EOM‐CC) method has been generalized to treat cases in which reference and final states differ in the number of electrons. While this work specializes to the sector of Fock space that corresponds to ionization of the reference, the approach can be trivially modified for electron attached final states. Unlike traditional coupled cluster methods that are based on single determinant reference functions, several electronic configurations are treated in a balanced way by EOM‐CC. Therefore, this quantum chemical approach is appropriate for problems that involve important nondynamic electron correlation effects. Furthermore, a fully spin adapted treatment of doublet electronic states is guaranteed when a spin restricted closed shell reference state is used—a desirable feature that is not easily achieved in standard coupled cluster approaches. The efficient implementation of analytic gradien...

Analytic energy derivatives for ionized states described by the equation‐of‐motion coupled cluster method

Predicting the electronic structure of extended organic molecules constitutes an important fundamental task of modern chemistry. Studies of electronic excitations, charge-transfer, energy-transfer, and isomerization of conjugated systems form the basis for our understanding of the photophysics and photochemistry of complex molecules1-3 as well as organic nanostructures and supramolecular assemblies.4,5 Photosynthesis and other photochemical biological processes that constitute the basis of life on Earth involve assemblies of conjugated chromophores such as porphyrins, chlorophylls, and carotenoids.6-8 Apart from the fundamental interest, these studies are also closely connected to numerous important technological applications.9 Conjugated polymers are primary candidates for new organic optical materials with large nonlinear polarizabilities.10-19 Potential applications include electroluminescence, light emitting diodes, ultrafast switches, photodetectors, biosensors, and optical limiting materials.20-27 Optical spectroscopy which allows chemists and physicists to probe the dynamics of vibrations and electronic excitations of molecules and solids is a powerful tool for the study of molecular electronic structure. The theoretical techniques used for describing spectra of isolated small molecules are usually quite different from those of molecular crystals, and many intermediate size systems, such as clusters and polymers, are not readily described by the methods developed for either of these limiting cases.28

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Density Matrix Analysis and Simulation of Electronic Excitations in Conjugated and Aggregated Molecules

The crossover from band to correlated states in half-filled quantum cell models is studied in a molecular-exciton framework based on a chain of dimers. Crystal states with one or several excited dimers yield analytical excitation energies to first order in interdimer Coulomb interactions V(p,p') for excitonic chains or interdimer electron transfer ${\mathit{t}}_{\mathrm{\ensuremath{-}}}$=t(1-\ensuremath{\delta}) for Hubbard chains. Molecular-exciton analysis of excitations and transition moments rationalizes exact numerical solutions of oligomers with arbitrary intradimer correlations U, ${\mathit{V}}_{1}$, and electron transfer ${\mathit{t}}_{+}$=t(1+\ensuremath{\delta}), including the number, positions, and transition moments of low-lying excitations. Short correlation lengths of infinite chains with large alternation \ensuremath{\delta}\ensuremath{\ge}0.6 lead to converged crystal states for oligomers containing N=4--7 dimers. The present approach provides a detailed picture of excited-state crossovers with increasing U, ${\mathit{V}}_{1}$, and V(p,p'). Quite generally, the lowest singlet excitation ${\mathit{S}}_{1}$ is one-photon allowed (1B) on the band side of the spin-charge crossover and two-photon allowed (2A) on the correlated side. Intermediate correlations and large \ensuremath{\delta} reveal different crossovers in Hubbard chains, where 1B involves charge transfer between dimers, and excitonic chains, where 1B has an excited dimer.We also obtain two-photon transition moments M and extend vanishing M(2A) in the band limit up to U=2${\mathit{t}}_{+}$, the \ensuremath{\delta}\ensuremath{\sim}1 crossover of Hubbard chains. We find finite M(2A) on the correlated side, however, where 2A contains two triplet dimers in either alternating Hubbard or excitonic chains. Their different spin-charge crossovers appear as an abrupt and continuous increase, respectively, of two-photon intensity on going from the correlated to the band side. The greater delocalization (\ensuremath{\delta}\ensuremath{\sim}0.07--0.33) realized in conjugate polymers is consistent with excitonic chains. The potential V(p,p') in the Pariser-Parr-Pople model for conjugated hydrocarbons distinguishes strongly fluorescent polymers with ${\mathit{S}}_{1}$=1B from others with ${\mathit{S}}_{1}$=2A. We also relate our results at large \ensuremath{\delta} to other approximations for nonlinear optical spectra of conjugated polymers.

Molecular-exciton approach to spin-charge crossovers in dimerized hubbard and excitonic chains

We perform ab initio calculation using quantum chemistry package (MOLPRO) on the excited states of Na3 cluster and present the adiabatic PESs for the electronic states 22E′ and 12A1′, and the non-adiabatic coupling (NAC) terms among those states. Since the ab initio calculated NAC elements for the states 22E′ and 12A1′ demonstrate the numerical validity of so called “Curl Condition,” such states closely form a sub-Hilbert space. For this subspace, we employ the NAC terms to solve the “adiabatic-diabatic transformation (ADT)” equations to obtain the functional form of the transformation angles and pave the way to construct the continuous and single valued diabatic potential energy surface matrix by exploiting the existing first principle based theoretical means on beyond Born-Oppenheimer treatment. Nuclear dynamics has been carried out on those diabatic surfaces to reproduce the experimental spectrum for system B of Na3 cluster and thereby, to explore the numerical validity of the theoretical development o...

Ab initio calculations on the excited states of Na3 cluster to explore beyond Born-Oppenheimer theories: adiabatic to diabatic potential energy surfaces and nuclear dynamics.

Molecular applications of size-extensive quasi-Hilbert- and quasi-Fock-space coupled-cluster formalisms using incomplete model spaces

The tetra-atomic C2H2+ cation is known to form Renner–Teller-type intersections along its collinear axis. Not too long ago, we studied the nonadiabatic coupling terms (NACTs) of this molecule [G. J. Halasz et al., J. Chem. Phys. 126, 154309 (2007)] and revealed two kinds of intersections. (i) By employing one of the hydrogens as a test particle, we revealed the fact that indeed the corresponding (angular) NACTs produce topological (Berry) phases that are equal to 2π, which is a result anticipated in the case of Renner–Teller intersections. (ii) However, to our big surprise, repeating this study when one of the atoms (in this case a hydrogen) is shifted from the collinear arrangement yields for the corresponding topological phase a value that equals π (and not 2π). In other words, shifting (even slightly) one of the atoms from the collinear arrangement causes the intersection to change its character and become a Jahn–Teller intersection. This somewhat unexpected novel result was later further analyzed and ...

Renner-Teller intersections along the collinear axes of polyatomic molecules: H2CN as a case study.

We develop in this paper a consistent superoperator-resolvent-based propagator theory using the extended coupled-cluster (CC) parametrization [Phys. Rev. A 36, 2519 (1987); Ann. Phys. 151, 311 (1983)] of the ground state. The method exploits the underlying non-Hermitian nature of the transformed Hamiltonian appearing in the extended coupled-cluster method. In this method, we obtain finite expressions in powers of cluster coefficients for both the transition amplitudes as the residues and the elements of the effective matrix contributing to the poles of the propagator. There is a natural ``resolution of identity'' involving consistent basis constructed by us, which leads to the biorthogonal sets of ket and bra functions used in the representation of the intermediate states in the inner projection of the propagator. The manifold of operators generating these states satisfies the ``vacuum-annihilation condition'' on the ground state and is thus consistent. There is a natural decoupling of the forward and backward components of the propagator even under the uneven truncation of the CC expansion of the ground state and the operator basis, which should be convenient for practical applications. We have discussed in detail the realization of the consistent representation of the ionized or excited states by taking as illustrative examples the case of one-electron and polarization propagators and have suggested practical truncation schemes for their implementation. An order-by-order perturbative analysis has been made to indicate the relation of our formalism to some of the more recent theories. We have also shown that the now established coupled-cluster-based linear-response theory can be viewed as an approximate version of the consistent propagator theory, which furnishes the same poles as the latter but nonconsistent residues.

Debasis Mukhopadhyay

Papers

Molecular-exciton approach to spin-charge crossovers in dimerized hubbard and excitonic chains

Ab initio calculations on the excited states of Na3 cluster to explore beyond Born-Oppenheimer theories: adiabatic to diabatic potential energy surfaces and nuclear dynamics.

Molecular applications of size-extensive quasi-Hilbert- and quasi-Fock-space coupled-cluster formalisms using incomplete model spaces

Renner-Teller intersections along the collinear axes of polyatomic molecules: H2CN as a case study.

Consistent propagator theory based on the extended coupled-cluster parametrization of the ground state