Excited-state PESs

Figure 14.7 The dependence of solvatochromism on differential solvation of the ground- and excited-state PESs...

Modem quantum mechanics can provide accurate excited-state PESs,14,16,17 but such calculations are demanding and in order to obtain useful answers one must ask the right questions. The chemist s intuition or knowledge from related reactions is instmmental in suggesting conceivable photoproducts of the initial reactant. Qualitative guidelines to... 

Figure 4.1 Important features of ground- and excited-state PESs for ethylene photodynamics and demonstration of the inadequacy of TDDFT and CIS methods for this problem, (a) Sq and PESs for ethylene in the pyramidalization and torsion coordinates (defined in the inset) that dominate the photodynamics. This surface was calculated using multireference perturbation theory — CAS(2/2) PT2. The global minimum on Si occurs at twisted and pyramidalized geometries. (b-d) A quantitative comparison of the Si PES obtained with CAS(2/2) PT2, TDDFT/B3LYP, and CIS, respectively. All calculations use the 6-3IG basis set. The TDDFT and CIS calculations are performed in a spin-unrestricted formalism. Contour values are given in eV, and in all cases the energies are referenced to the Sq equilibrium geometry at the corresponding level of theory. Only the multireference calculation captures the Si minimum correctly.

Recently, we have carried out an ab initio study of the ground- and excited-state PESs of stilbene that showed that pyramidalization is likely to be an important coordinate in stilbene photoisomerization.indeed, the similarities... 

Recent experimental results and new computational methods have provided a new mechanistic picture of photochemical reactions, that can be imderstood in terms of the evolution of an excited-state species toward a conical intersection that acts as a photochemical decay channel. Thus, a theoretical discussion of the mechanism of a photochemical reaction will have to be based on excited-state PESs and on the location of conical intersections. 

As a close related compound to the chemiluminescence systems, the anthracene-9,10-endoperoxide has been used to describe the complex topography which characterises the region of crossing between the ground and excited state PESs in the 0-0 photolysis. Four eleetronic states involving different electron occupations of the aoo> < oo ... 

To date, neural network potentials have been most frequently applied to represent low-dimensional, molecular PESs. Apart from the central role of molecules in chemistry the main reason for this is certainly the comparably simple mapping of the reference points using electronic structure methods. Low-dimensional NN PESs have been constructed for example for the of ground state and excited state PESs and transition dipole moments of the HCl" ion, " for the OH radical in order to calculate the vibrational levels,for Hi " to calculate rovibrational spectra,for the free H2O molecule, for the dissociation of a Si02 molecule, for the HOOH molecule, for the NOCl molecule, for formaldehyde, for the cis-trans isomerization and dissociation dynamics of nitrous add, " for H + HBr, " for the reaction 0H + H2 H20 + H, for the reaction BeH + H2->BeH2 + H, " for small silicon clusters, " for vinyl bromide, to describe the three-body interaction energies in the H2O-... 

In order to adequately describe the coupled motion on two excited-state PESs we have to consider two nuclear wave packets = I prefer the time-dependent... 

The active-space SRCC methods and their EOMCC extensions are very promising and we will continue to develop them. They are relatively easy to use, although, in analogy to multireference approaches, they require choosing active orbitals, which in some cases may be a difficult thing to do. From this point of view, the active-space CC methods are not as easy-to-use as the noniterative perturbative methods, such as CCSD(T) or CCSD(TQf), or their response CC or EOMCC extensions. Undoubtedly, it would be desirable to have an approach that combines the simplicity of the noniterative CC schemes with the effectiveness with which the iterative active-space CC and EOMCC methods, such as CCSDt and EOMCCSDt, describe ground-and excited-state PESs. 

In our view, the MMCC theory represents an interesting development in the area of new CC methods for molecular PESs. The MMCC-bas renormalized CCSD(T), CCSD(TQ), and CCSDT(Q) methods and the noniterative MMCC approaches to excited states provide highly accurate results for ground and excited-state PESs, while preserving the simplicity and the black-box character of the noniterative perturbative CC schemes. In this chapter, we review the MMCC theory and new CC i pnndmations that result firom it and show the examples of the MMCC and renormalized CC calculations for ground and excited state PESs of several benchmark molecules, including HF, F2, N2, and CH" ". The review of the previously published numerical results (7,16-20) is combined with the presentation of new results for the C2, N2, and H2O molecules. 

The CISDt approach, used to generate wave functions x) for the MMCC(2,3) calculations, can be regarded as a Cl analog of the recently developed EOMCCSDt method ( 0, The noniterative character of the MMCC(2,3) method and the fact that the CISDt calculations are less expensive than the EOMCCSDt calculations means that the CISDt-based MMCC(2,3) approximation represents a useful and inexpensive alternative to the already relatively inexpensive EOMCCSDt method. The MMCC(2,3) approach is an alternative to the perturbative triples approaches, such as EOMCCSD(T) (51), EOMCCSD(T) (55), EOMCCSD(r) (55), and CCSDR(3) (55,57), and their iterative EOMCCSDT-n (51,55) and CC3 (34 -37) analogs. The perturbative triples EOMCC or response CC approximations provide erroneous description of excited-state PESs (38) and fail to describe more compUcated excited states, such as the lowest A state of the C2 molecule (57). As demonstrated below, the CISDt-based MMCC(2,3) method has no such problems. 

Representative MMCC Calculations for Ground- and Excited-State PESs... 

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