Electron correlation methods excited states

Linear Scaling Techniques Semi-Empirical Methods 3.9.1 Neglect of Diatomic Differential Overlap Approximation (NDDO) 3.9.2 Intermediate Neglect of Differential Overlap Approximation (INDO) 80 81 82 83 4.13 Locahzed Orbital Methods 4.14 Summary of Electron Correlation Methods 4.15 Excited States References 5 Basis Sets 144 144 147 148 150... 

The computationally viable description of electron correlation for stationary state molecular systems has been the subject of considerable research in the past two decades. A recent review1 gives a historical perspective on the developments in the field of quantum chemistry. The predominant methods for the description of electron correlation have been configuration interactions (Cl) and perturbation theory (PT) more recently, the variant of Cl involving reoptimization of the molecular orbitals [i.e., multiconfiguration self-consistent field (MCSCF)] has received much attention.1 As is reasonable to expect, neither Cl nor PT is wholly satisfactory a possible alternative is the use of cluster operators, in the electron excitations, to describe the correlation.2-3... 

States whose zero-order labels are configurations, which are multiply excited (e.g., doubly, triply, or even quadruply excited) with respect to the ground main configuration, for example, see Ref. [10]. They can be created by the absorption of one or more photons. It is important to stress that these states are determined as solutions of their state-specific Schrbdinger equations and do not correspond, except perhaps by occasional accident, to the hierarchy of virtual excitations that appear in the many-electron treatments of electron correlation in ground states by the conventional methods of computational chemistry. 

What about electronic correlation in excited electronic states Not much is known for excited states in general. In our case of Eq. (10.23), the Ritz variational method would give two solutions. One would be of lower energy corresponding to /r < 0 (this solution has been approximated by us using the perturbational approach). The second solution (the excited electronic state) will be of the form xj/exc = in such a simple two-state model, the coefficient k can be found just... 

Two relevant topics have been ignored completely in this short chapter the treatment of electron correlation with more sophisticated methods than DFT (that remains unsatisfactory from many points of view) and the related subject of excited states. Wave function-based methods for the calculation of electron correlation, like the perturbative Moller-Plesset (MP) expansion or the coupled cluster approximation, have registered an impressive advancement in the molecular context. The computational cost increases with the molecular size (as the fifth power in the most favorable cases), especially for molecules with low symmetry. That increase was the main disadvantage of these electron correlation methods, and it limited their application to tiny molecules. This scaling problem has been improved dramatically by modern reformulation of the theory by localized molecular orbitals, and now a much more favorable scaling is possible with the appropriate approximations. Linear scaling with such low prefactors has been achieved with MP schemes that the... 

The PCM model contains the largest variety of extensions for the calculation of the properties for the ground and excites states of molecular systems in solution [44 9] and these extensions have been accomplished at HF level and at various QM electron correlation methods [27, 50-57]. There are also version based on semi-empirical QM methods we quote here only those based on ZINDO [58]. 

Accuracy of Electron Correlation Methods for Actinide Excited States WFT and DFT Methods... 

Each of these tools has advantages and limitations. Ab initio methods involve intensive computation and therefore tend to be limited, for practical reasons of computer time, to smaller atoms, molecules, radicals, and ions. Their CPU time needs usually vary with basis set size (M) as at least M correlated methods require time proportional to at least M because they involve transformation of the atomic-orbital-based two-electron integrals to the molecular orbital basis. As computers continue to advance in power and memory size, and as theoretical methods and algorithms continue to improve, ab initio techniques will be applied to larger and more complex species. When dealing with systems in which qualitatively new electronic environments and/or new bonding types arise, or excited electronic states that are unusual, ab initio methods are essential. Semi-empirical or empirical methods would be of little use on systems whose electronic properties have not been included in the data base used to construct the parameters of such models. 

The parameterization of MNDO/AM1/PM3 is performed by adjusting the constants involved in the different methods so that the results of HF calculations fit experimental data as closely as possible. This is in a sense wrong. We know that the HF method cannot give the correct result, even in the limit of an infinite basis set and without approximations. The HF results lack electron correlation, as will be discussed in Chapter 4, but the experimental data of course include such effects. This may be viewed as an advantage, the electron correlation effects are implicitly taken into account in the parameterization, and we need not perform complicated calculations to improve deficiencies in fhe HF procedure. However, it becomes problematic when the HF wave function cannot describe the system even qualitatively correctly, as for example with biradicals and excited states. Additional flexibility can be introduced in the trial wave function by adding more Slater determinants, for example by means of a Cl procedure (see Chapter 4 for details). But electron cori elation is then taken into account twice, once in the parameterization at the HF level, and once explicitly by the Cl calculation. 

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