Excited electronic states coupled-cluster

NONITERATIVE COUPLED-CLUSTER METHODS FOR EXCITED ELECTRONIC STATES... 

Generalization of the method of moments of coupled-cluster equations to excited electronic states Exact formalism... 

M. Wloch, J.R. Gour, K. Kowalski, P. Piecuch, Extension of renormalized coupled-cluster methods including triple excitations to excited electronic states of open-shell molecules, J. Chem. Phys. 122 (2005) 214107. 

A superior method for the calculation of excited-state PE surfaces is CC2, which is a simplified and computationally efficient variant of coupled-cluster theory with single and double excitations [22], CC2 can be considered as the equivalent of MP2 for excited electronic states. Efficient implementations of CC2 with density fitting [23] and analytic gradients [24] allow reaction path calculations for rather large systems. Being a singlereference method, CC2 fails in the vicinity of conical intersections of excited states with the electronic ground state. 

Watts JD, Bartlett RJ (1996) Iterative and non-iterative triple excitation corrections in coupled-cluster methods for excited electronic states The EOM-CCSDT-3 and EOM-CCSD(r) methods. Chem Phys Lett 258 581-588. 

Kucharski SA, Wloch M, Musial M, Bartlett RJ (2001) Coupled-cluster theory for excited electronic states The full equation-of-motion coupled-cluster single, double, and triple excitation method. J Chem Phys 115 8263-8266. 

Kowalksi K, Piecuch P (2004) New coupled-cluster methods with singles, doubles, and noniterative triples for high accuracy calculations of excited electronic states. J Chem Phys 120 1715-1738. 

Till recently, computations of vibronic spectra have been limited to small systems or approximated approaches, mainly as a consequence of the difficulties to obtain accurate descriptions of excited electronic states of polyatomic molecules and to computational cost of full dimensional vibronic treatment. Recent developments in electronic structure theory for excited states within the time-dependent density functional theory (TD-DFT) and resolution-of-the-identity approximation of coupled cluster theory (R1-CC2) and in effective approaches to simulate electronic spectra have paved the route toward the simulation of spectra for significantly larger systems. 

A. Baikova and R. J. Bartlett,/. Chem. Phys., 99, 7907 (1993). The 2-Determinant Coupled-Cluster Method for Electric Properties of Excited Electronic States The Lowest and States of the Water Molecule. 

J. D. Watts and R. J. Bartlett, Chem. Phys. Lett., 258, 581 (1996). Iterative and Noniterative Triple Excitation Corrections in Coupled-Cluster Methods for Excited Electronic States— The EOM-CCSDT-3 and EOM-CCSD(T) Methods. 

As discussed in section 2.4, several new developments are in progress in order to make the EFP-QM interface fully viable. In addition, EFP interfaces are being built with methods that can treat excited electronic states. In addition to the existing MCSCF interface, these include Cl singles and time-dependent density functional theory in the short term and more sophisticated Cl and coupled cluster methods in the longer term. 

Quadratic response theory in combination with self-consistent field (SCF), MCSCF, and coupled-cluster electronic structure methods have been used for calculation of excitation energies and transition dipole moments between excited electronic states <2000PCP5357>. The excited state polarizabilities for r-tetrazine are given by the double residues of the cubic response functions <1997CPFl(224)201>. 

Fig. 11. The Mott non-metal to metal transition as a function of the average sei>aration between the atoms of a cluster of 91 atoms. Shown are the computed energies in units of t (logarithmic scale) of the excited electronic states relative to the ground state. Metallic behavior requires that there is a quasi-continuum of states. In the lowest approximation, shown as dashed lines, states where an electron has moved have excess energies of U above the covalent states, t measures the strength of the exchange coupling between adjacent atoms and hence decreases exponentially with the spacing between atoms. When tsiU, the exchange coupling can overcome the Coulomb repulsion. See Refs. 229 and 334 for details of the computational method.

Ah initio quantum chemical calculations are primarily used to describe the electronic character of individual molecules in the gas phase. Quantum chemical methods can vary widely in their accuracy, depending on the specific approximations taken. Those most applicable to the study of ionic liquids are medium level methods such as DFT and MP2 [20]. Hartree-Fock(HF) level calculations may be carried out as a starting point or to obtain geometries but should be followed by calculations that include some level of electronic correlation. Higher level methods such as Coupled Cluster methods (ie CCSD(T)) are only just accessible, and will not be routine. They do however allow for an estimation of effects hard to recover with the lower level DFT and MP2 methods, such as dispersion, more dynamic correlation, and an estimation of other neglected effects (such as the stabilization afforded by mixing in excited electronic states). The method employed (HF< DFT < MP2 < CCSD(T)) and sophistication of the basis set used are typically used to indicate the quality of an ab initio quantum chemical calculation. 

In the PCM-EOM-CC/SACCI approximation the excited electronic states are represented by a linear (Cl-like) expansion build-up on the coupled-cluster wavefunction for the ground state [6-8]. We use the PTE couple-cluster wavefunction, computed in the presence of the frozen Hartree-Fock reaction field, as it leads to a more simpler and physically transparent PCM-EOM theory. The EOM-CC theory leads to a non-Hermitian eigenvalue problem with right and left eigenvalues. 

Of the 33 invited speakers and the seven who contributed talks, 17 accepted our invitation to contribute a chapter to this book. These chapters are complemented by three additional chapters from individuals to help develop a more cohesive book as well as an overview chapter. Approximately half of the chapters are focused on the development of ab initio electronic structure methods and consideration of specific challenging molecular systems using electronic structure theory. Some of these chapters document the dramatic developments in the range of applicability of the coupled-cluster method, including enhancements to coupled-cluster wavefunctions based on additional small multireference configuration interaction (MR-CISD) calculations, the method of moments, the similarity transformed equation of motion (STEOM) method, a state-specific multireference coupled-cluster method, and a computationally efficient approximation to variational coupled-cluster theory. The concentration on the coupled-cluster approach is balanced by an approximately equal number of chapters discussing other aspects of modem electronic stracture theory. In particular, other methods appropriate for the description of excited electronic states, such as multireference... 

There is a variation on the coupled cluster method known as the symmetry adapted cluster (SAC) method. This is also a size consistent method. For excited states, a Cl out of this space, called a SAC-CI, is done. This improves the accuracy of electronic excited-state energies. 

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