Excited states, ab initio methods for

Merchan M, Serrano-Andres L (2005) Ab Initio Methods for Excited States. In Olivucci M (ed) Computational Photochemistry, Elsevier, Amsterdam. 

M. Merchan and L. Serrano-Andres, Ab initio methods for excited states, in J. Michl, M. Olivucci (Eds.), Computational photochemistry, Elsevier, Amsterdam, 2004. 

Dreuw A, Head-Gordon M (2005) Single-reference ab initio methods for the calculation of excited states of large molecules. Chem Rev 105 4009 1037... 

The simplest ab initio approach which can be used for the characterization of excited states is the configuration interaction with single excitations from the HF reference (CIS) [21]. The CIS method can be considered as the equivalent of the ground-state HF method for excited states. It does not account for so-called nondynamical electron correlation effects associated with the near degeneracy of electronic configurations, nor does it account for so-called dynamical electron correlation effects. The CIS method is computationally cheap and robust and can easily be applied to relatively large systems. 

E. Runge, E.K.U. Gross, Density-Functional Theory for Time-Dependent Systems, Phys. Rev. Lett. 52 (1984) 997 A. Dreuw, M. Head-Gordon, Single-Reference ab Initio Methods for the Galculation of Excited States of Large Molecules, Chem. Rev. 105 (2005) 4009. 

It is hoped that this section provides a useful introduction to ab initio studies of excited states. In this challenging area in quantum chemistry, it is not always straightforward to compare results of such calculations with experimental values because information about molecular excited states (and, in particular, the associated potential energy surfaces) is very scarce. Indeed, while the prediaion of infrared spectra has clearly been the most fruitful area of application for quantum chemical methods in the past decade, it is likely that theoretical studies of electronically excited states will continue to grow in importance. In particular, the availability of accurate (and therefore predictive) methods such as the EOM-CCSD approach in programs such as ACES II will serve to make accurate calculations of these systems accessible to a wide range of users. 

AB INITIO QUANTUM CHEMICAL METHODS FOR EXCITED STATES... 

Although for the [l,7]-sigmatropic shift reaction of CHT the semiempirical calculations yield a reaction mechanism that is in good qualitative agreement with all experimental observations, the quantitative residts, and in particidar the value of 23 kcal moh for the excited-state barrier, require redetermination on the basis of more reliable ab initio methods. For details, see Section 6.6. 

In this paper we will show that quantum chemistry provides suitable approaches to extracting the specific properties of small metallic and mixed nonstochiometric clusters which cannot be obtained by more approximate methods. This accuracy is needed for controlling the properties through size, shape and composition of the cluster. For this purpose the methodological aspects will be briefly sketched in Section 2.2. We will first address the methods used for the determination of cluster structures at zero temperature and outline the ab initio molecular dynamics method which we developed for the determination of temperature-dependent ground-state properties. Then, ab initio methods for calculation of excited states valid at T = 0 will be described. 

Systematically improved approximations for each excited-state ,- are therefore obtained simply by increasing the dimensionality n of that is, expanding the set O, ) toward completeness, with , —> Ejasn —> oo. Theorem (11.7) underlies ab initio methods for computing excited-state properties, limited only by the number and type of excitation functions O, used to constmct in the chosen approximation method. 

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. 

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