Excitation energy calculations

Hattig C, Weigend F (2000) CC2 excitation energy calculations on large molecules using the resolution of the identity approximation. J Chem Phys 113 5154... 

The electron excitation energy calculated by means of this model causes one to expect, in agreement with experiment, transitions at approximately 25,000 and 31,000 cm, the first one polarized in the direction of the axis of symmetry and the second vertical thereto. The calculated oscillator strengths off = 0-2 and 0-5 satisfactorily agree with the observed values. 

Simonetta and Heilbronner (1964) recently carried out calculations by the valence bond (VB) method for some simple cations, and compared the results obtained by this method, inter alia, with the results of Colpa and collaborators (1963) and of Koutecky and Paldus (1963). In the case of the proton addition complexes of mesitylene and cyclohepta-triene, the electron excitation energies calculated by the VB method agree very well with experiments, and also agree to a good approximation with the results of Cl calculations. The calculations also successfully reproduce the electron density of the cycloheptatriene cation. In this, a perturbation calculation allowed for the AO s adjoining the —CHg—CH2-lihkage. 

Table 5 indicates that HPHF method yields slightly better results than single Cl with same basis functions. The adiabatic excitation energies calculated for the respective states by Mukheijee et al [56] and by Takeshita and Mukheijee [55] are displayed in Table 6. 

Here we will assess the ability of ONIOM to describe the effect of microsolvation on the vertical electronic transition to the tt state in formamide. We can write the excitation energy calculated with ONIOM as the difference of the ONIOM energies of the two states. 

In Figure 4.13 we show the excitation energies calculated with ONIOM. The first observation is that the errors are significantly smaller than those in the stand-alone calculations, up to 0.4 eV (Note the different energy scales between Figures 4.12 and 4.13). The largest errors are found with the small basis set used in CIS and TD-HF. If we exclude the CIS and TD-HF results with the smallest basis set, the errors are all under 0.2 eV. TD-DFT with either the small or medium basis set in the low level gives excellent results, except for the 2W and 3W clusters with the small basis set. This is the... 

As for the PBEO results, the excitation energies calculated for the two lowest excited states of the model complex, cis- [Ru(bpy)2(NCS)2], change very little when the solvent effects are included. The excitation energies computed in vacuo already reproduce the two lowest bands observed in the spectrum of the czs-[Ru(4,4 -COOH-2,2 -bpy)2(NCS)2] complex in water quite well. 

L. Meissner and R. J. Bartlett, J. Chem. Phys., 94, 6670 (1991). Transformation of the Hamiltonian in Excitation Energy Calculations Comparison Between Fock-Space Multireference Coupled-Cluster and Equation-of-Motion Coupled-Cluster Methods. 

Figure 6. Excitation energy calculated in the excitonic approximation against the number of excitons n, for A (left panels), B (middle panels) and C clusters (right panels) with N = 6. v=l, for two different w. The z parameter is fixed to — 1 for the A cluster, to 1 for the B and C clusters. States on the zero energy axis correspond to the gs. Error bars measure the squared transition dipole moment from the gs to the relevant states. Insets show the p(w) mf curve for the relevant parameters, with the dotted vertical line marking the w value for which results are reported in the parent panel...

In the treatment described here, details of molecular connectivity and conformation are not considered, as the mean excitation energy calculated with a Bragg-like rule depends only on the various fragments that make up the molecule and not on their arrangement. Thus, for example, the mean excitation energies of leucine and isoleucine are calculated to be the same, as they differ only in connectivity. 

Excitation energies calculated with the RPA and TDA approaches for N2 with a moderately large basis set are listed in Table 23. Both the RPA and TDA excitation energies are significantly lower than those obtained with the simplest frozen orbital approximation. All these approaches differ only in their treatment of the final state, and the pattern of predicted excitation energies shows this in a rather dramatic way. Both the RPA and TDA allow for a limited amount of relaxation and provide much improved predictions. Inclusion of the... 

In Section III.E, EOM ionization potentials and electron affinities are compared with accurate configuration interaction (Cl) results for a number of atomic and molecular systems. The same one-electron basis sets are utilized in the EOM and Cl calculations, allowing for the separation of basis set errors from errors caused by approximations made in the solution of the EOM equation. EOM results are reported for various approximations including those for the extensive EOM theory developed in Section II. Section III.F presents results of excitation energy calculations for helium and beryllium to address a number of remaining difficult questions concerning the EOM method. 

Let 0> be the exact -electron ground state of the Born-Oppenheimer Hamiltonian H for a given atomic or molecular system. Likewise, let X > be some exact excited state of interest for the same system with the same nuclear geometry. The corresponding state energies are denoted and respectively. For excitation energy calculations X> is an excited N -electron state, whereas in ionization potential or electron affinity cases X > is an - l)-electron state or an (A -l- l)-electron state, respectively. The commutator of H with the operator Oj = X><0 is easily evaluated,... 

For excitation energy calculations, the customary EOM basis set has the form ala ,a] ala a,alala aThe operators, a] a and... 

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