Equation Of Motion Coupled Cluster Method Research Articles

Effects of Donor/Acceptor Strengths on the Multiphoton Absorption: An EOM-CCSD Correction Vector Study

We have developed a correction method (CV) to calculate the single- and multiphoton absorption (MPA) spectra of organic pi-conjugated systems within the equation of motion coupled-cluster method with single and double excitations (EOM-CCSD). The effects of donor/acceptor strengths on the multiphoton absorption in a series of symmetrically substituted stilbene derivatives have been reinvestigated at both the ab initio and the semiempirical intermediate neglect of differential overlap (INDO) Hamiltonian levels. Both ab initio and INDO calculations show that the electron-donating or electron-withdrawing substituents lead to enhancements of two- and three-photon absorption cross sections, more pronounced for two-photon absorption than for three-photon absorption. The ab initio calculations usually produce larger excitation energies than the semiempirical, which lead to lower MPA cross sections.

Active-space symmetry-adapted-cluster configuration-interaction and equation-of-motion coupled-cluster methods for high accuracy calculations of potential energy surfaces of radicals

The electron-attached (EA) and ionized (IP) symmetry-adapted-cluster configuration-interaction (SAC-CI) methods and their equation-of-motion coupled-cluster (EOMCC) analogs provide an elegant framework for studying open-shell systems. As shown in this study, these schemes require the presence of higher-order excitations, such as the four-particle-three-hole (4p-3h) or four-hole-three-particle (4h-3p) terms, in the electron attaching or ionizing operator R in order to produce accurate ground- and excited-state potential energy surfaces of radicals along bond breaking coordinates. The full inclusion of the 4p-3h/4h-3p excitations in the EA/IP SAC-CI and EOMCC methods leads to schemes which are far too expensive for calculations involving larger radicals and realistic basis sets. In order to reduce the large costs of such schemes without sacrificing accuracy, the active-space EA/IP EOMCC methodology [J. R. Gour et al., J. Chem. Phys. 123, 134113 (2005)] is extended to the EA/IP SAC-CI approaches with 4p-3h/4h-3p excitations. The resulting methods, which use a physically motivated set of active orbitals to pick out the most important 3p-2h/3h-2p and 4p-3h/4h-3p excitations, represent practical computational approaches for high-accuracy calculations of potential energy surfaces of radicals. To illustrate the potential offered by the active-space EA/IP SAC-CI approaches with up to 4p-3h/4h-3p excitations, the results of benchmark calculations for the potential energy surfaces of the low-lying doublet states of CH and OH are presented and compared with other SAC-CI and EOMCC methods, and full CI results.

First principles simulation of the UV absorption spectrum of ethylene using the vertical Franck-Condon approach.

A new method which we refer to as vertical Franck-Condon is proposed to calculate electronic absorption spectra of polyatomic molecules. In accord with the short-time picture of spectroscopy, the excited-state potential energy surface is expanded at the ground-state equilibrium geometry and the focus of the approach is more on the overall shape of the spectrum and the positions of the band maxima, rather than the precise position of the 0-0 lines. The Born-Oppenheimer approximation and the separability of the excited-state potential energy surface along the excited-state normal mode coordinates are assumed. However, the potential surface is not necessarily approximated as harmonic oscillator potentials along the individual normal modes. Instead, depending upon the nature of the potential surface along a particular normal mode, it is treated either in the harmonic approximation or the full one-dimensional potential is considered along this mode. The vertical Franck-Condon approach is applicable therefore even in cases where the excited state potential energy surface is highly anharmonic and the conventional harmonic Franck-Condon approach is inadequate. As an application of the method, the ultraviolet spectrum of ethylene between 6.2 eV (50,000 cm(-1)) and 8.7 eV (70,000 cm(-1)) is simulated, using the Similarity Transformed Equation of Motion Coupled-Cluster method to describe the required features of the potential energy surfaces. The spectrum is shown to be a result of sharp doublet structures stemming from the pi --> 3s (Rydberg) state superimposed on top of a broad band resulting from the pi --> pi* (valence) state. For the Rydberg state, the symmetric C=C stretch and the torsion mode contribute to the spectrum, while the broad valence band results from excitation into the C=C stretch, CH2 scissors, and the torsion mode. For both states, the potential along the torsion mode is highly anharmonic and the full treatment of the potential along this mode in the vertical Franck-Condon method is required.

Simplified methods for equation-of-motion coupled-cluster excited state calculations

Simplified equation-of-motion coupled-cluster (EOM-CC) methods derived from matrix partitioning and perturbation approximations are presented and applied to a variety of molecules. By combining a partitioned EOM-CC method with an MBPT(2) treatment of the ground state, we obtain an iterative n 5 method which gives excitation energies that normally fall within 0.2 eV of the full EOM-CCSD excitation energy. Results are shown to be superior to other simplified approaches that have been proposed.

The equation of motion coupled-cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties

A comprehensive overview of the equation of motion coupled-cluster (EOM-CC) method and its application to molecular systems is presented. By exploiting the biorthogonal nature of the theory, it is shown that excited state properties and transition strengths can be evaluated via a generalized expectation value approach that incorporates both the bra and ket state wave functions. Reduced density matrices defined by this procedure are given by closed form expressions. For the root of the EOM-CC effective Hamiltonian that corresponds to the ground state, the resulting equations are equivalent to the usual expressions for normal single-reference CC density matrices. Thus, the method described in this paper provides a universal definition of coupled-cluster density matrices, providing a link between EOM-CC and traditional ground state CC theory. Excitation energy, oscillator strength, and property calculations are illustrated by means of several numerical examples, including comparisons with full configuration interaction calculations and a detailed study of the ten lowest electronically excited states of the cyclic isomer of C4.