Expressions for static and dynamic properties in coupled-cluster (CC) theory are derived. In the static case, using diagrammatic techniques, it is shown how consideration of orbital relaxation effects in the theory introduces higher-order correlation effects. For the dynamic case, excitation energy expressions are obtained without consideration of orbital relaxation effects and shown to be equivalent to an equation of motion (EOM) approach subject to a coupled-cluster ground-state wave function and an excitation operator consisting of single and double excitations. Illustrative applications for excited states of ethylene are reported.

The long-range correction (LC) scheme for the exchange functional of density-functional theory (DFT) was combined with the coupled-perturbed Kohn-Sham (CPKS) method to calculate nonlinear optical response properties. By using this LC-CPKS method, we calculated the hyperpolarizabilities of typical molecules and the dipole moments, polarizabilities, and hyperpolarizabilities of push-pull pi-conjugated systems: p-nitroaniline, 4-amino-4'-nitrostilbene, and alpha,omega-nitroaminopolyenes. It was found that the LC scheme clearly improved the calculation of these optical properties for all of these systems, which have been significantly overestimated by conventional DFTs. We therefore concluded that the long-range exchange interaction played an important role in calculating the optical properties using the DFT formalism.

Electron correlation effects to the four coupling mechanisms which contribute to the isotropic nuclear spin–spin coupling constant, the Fermi contact (FC), paramagnetic spin–orbit (PSO), spin-dipole (SD), and diamagnetic spin–orbit (DSO) are studied using the equation of motion coupled-cluster (EOM-CC) method. The second-order properties are expressed as a sum-over state (SOS) using EOM-CC intermediate state wave functions. This formulation is simple, accurate, computationally convenient, and involves no truncation. Several molecules, HF, CO, N2, H2O, NH3, and HCl which have been previously shown to have large noncontact contributions are investigated using the EOM-CC method and the results are compared with experiment and other theoretical methods, including polarization propagator and finite-field MBPT(2) methods. Using fairly large basis sets, the EOM-CCSD provides results which agree with experimental indirect nuclear spin–spin coupling constants to within an average error of 13%.

;i -" "070 4-01881 I Publfic rfoort"'n burd•n for this cOI|eCtIOfl Of Infoer iio'm u *s C•(slt. ld to / i I 1 I I i .$, Hevcrth*q 4 d7t. to gathering and mninfi-ning thdatanmedl, and complqeting a•dre,, ife nq % 1 lfptfl of on, other ifbi:tl of this CoII on of tInorImation, ntcluding suggitions lor re duclt tt'i Ourdemn tI( &tion and R.9o41l., •2tIS )2*ItfW OClv igh''way. Sut|W 1204, Arlirnqton. VA 2220J-43021. and to the IffIt@ of F IthIng1fOn. OC 1OS03 basis; 6230 for a 6-3 1 G + diffuse (sp) basis, and 6440 w ith and Yi'kl being the components of the first and second hya (5s3p2d/3s2pld) basis. Of course, the SCF result reflects perpolarizability tensor. In addition to potential applicajust a part of a basis set's effect, as the introduction of tions to optical material design, which requires a knowlelectron correlation requires a much larger and more flexedge of the ( and y tensors, there are also a number of ible Hilbert space. other unsolved questions. Some of these concern inconsisAfter basis sets, the accurate inclusion of electron cortencies in the experimental values which cannot be exrelation is the next most important factor in attaining replained by the different dispersion effects encountered in liable values.-1 9 The initial studies of correlated molecular the various experimental procedures. However, there are hyperpolarizabilities 6 ' 7 already demonstrated that for the also significant inconsistencies between theory and experismall, polar molecules FH and H 2 0, correlation could ment, and between theory and theory. An understanding of change the predicted P3 static hyperpolarizabilities by as molecular nonlinear optical behavior requires resolving much as a factor of 2 and have a large effect on y. This fact these existing differences. The objective of this paper is to has now been supported by several other correlated studpresent a systematic study of theoretical calculations for iesi-I and also applies to recent results for larger moleseveral small molecules whose gas phase experimental valcules like para-nitroaniline. ' For nonpolar molecules like ues are well known. 4 , 5 This, combined with comparisons N2,10.16 trans-butadiene,1 6 ,1 7 benzene,1 2 and the nearly nonwith other calculations, provides some calibration of the polar CO,1 7 there are similarly significant (40%-60%) inaccuracy of high-level quantum chemical methods. creases in yll due to effects of electron correlation. PowerThe reliable ab initio prediction of molecular hyperpoful, coupled-cluster (CC)() 1 and many-body perturbation larizabilities requires several elements: basis sets, electron theory (MBPT) 2 1 methods are used here for the treatment correlation, frequency dependent (dispersion) effects, and of electron correlation for static hyperpolarizabilities. vibrational corrections. First, basis sets have to be adeSince hyperpolarizabilities require third and fourth dequate. The prediction of hyperpolarizabilities depends rivatives of the energy with respect to a field, a purely upon products of matrix elements of the ...