Computational Methods for Excited States

The simulation of molecular excited states is, still nowadays, a challenging task in computational chemistry. In fact, an ideal theoretical method, aiming at a broad applicability in the field, should be able to meet a series of requirements  

To be a practical tool in the comparison with experiments, the method of choice should have an absolute accuracy for the excitation energies of less than 0.1-0.2 eV (for all kinds of excitations). It shall also be able to provide a reliable estimation of transition moments, with relative errors smaller than 20%. 

It should provide easy access to all standard one-electron molecular properties and to anal5Aical gradients of the excitation energies. The latter in particular are very important to perform geometry optimizations of excited states, vibrational analyses, and to compute nonadiabatic coupling terms. 

Of course, the ideal theoretical method should possess all those properties that are generally desirable for any computational method, such as a weak basis-set dependence, S5 ematic increasing of accuracy, ease of interpretation (e.g., through a molecular-orbital picture), size consistency, respect of formal known constraints. 

In order to be applicable to medium- and large-size molecules, which are actually the systems of interest for real applications, any method must be extremely efficient. In particular, it must have low CPU and memory requirements (comparable with those of ground-state methods) and a favorable scaling with the S5 em size. 

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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. 

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. 

However, if this is not the case, the perturbations are large and perturbation theory is no longer appropriate. In other words, perturbation methods based on single-determinant wavefunctions cannot be used to recover non-dynamic correlation effects in cases where more than one configuration is needed to obtain a reasonable approximation to the true many-electron wavefunction. This represents a serious impediment to the calculation of well-correlated wavefunctions for excited states which is only possible by means of cumbersome and computationally expensive multi-reference Cl methods. 

The purpose of the present paper is to review the most essential elements of the excited-state MMCC theory and various approximate methods that result from it, including the aforementioned CR-EOMCCSD(T) [49,51,52,59] and externally corrected MMCC ]47-50, 52] approaches. In the discussion of approximate methods, we focus on the MMCC corrections to EOMCCSD energies due to triple excitations, since these corrections lead to the most practical computational schemes. Although some of the excited-state MMCC methods have already been described in our earlier reviews [49, 50, 52], it is important that we update our earlier work by the highly promising new developments that have not been mentioned before. For example, since the last review ]52], we have successfully extended the CR-EOMCCSD(T) methods to excited states of radicals and other open-shell systems ]59]. We have also developed a new type of the externally cor-... 

Quantum Chemical Methods and Software for Excited State Energy and Gradient Computations... 

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