Excited-state theory, method

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-... 

In this chapter, we have developed the information content of different excited state spectroscopic methods in terms of ligand field theory and the covalency of L—M bonds. Combined with the ground-state methods presented in the following chapters, spectroscopy and magnetism experimentally define the electronic structure of transition metal sites. Calculations supported by these data can provide fundamental insight into the physical properties of inorganic materials and their reactivities in catalysis and electron transfer. The contribution of electronic structure to function has been developed in Ref. 61. 

This chapter, therefore, encompasses two extremes of excited-state theories within the single-reference, linear-response framework One that aims at high and controlled accuracy for relatively small gas-phase molecules such as EOM-CC and the other with low to medium accuracy for large molecules and solids represented by CIS and TDDFT. We aim at clarifying the mutual relationship among these excited-state methods including the two extremes, while delegating a more complete exposition of EOM-CC to the next chapter contributed by Watts. 

Both CIS and TDHF have the correct size dependence and can be applied to large molecules and solids (we will shortly substantiate what is meant by the correct size dependence ) [42-51], It is this property and their relatively low computer cost that render these methods unique significance in the subject area of this book despite their obvious weaknesses as quantitative excited-state theories. They can usually provide an adequate zeroth-order description of excitons in solids [50], Adapting the TDHF or CIS equations (or any methods with correct size dependence, for that matter) to infinitely extended, periodic insulators is rather straightforward. First, we recognize that a canonical HF orbital of a periodic system is characterized by a quantum number k (wave vector), which is proportional to the electron s linear momentum kh. In a one-dimensional extended system, the orbital is... 

CCSD(T) method. The question then naturally arises as to how these methods can be extended to excited states. For the iterative methods, the extension is straightforward by analyzing the correspondence between terms in the CC equations and in H, one can define an H matrix for these methods, even though it is not exactly of the form of a similarity-transformed Hamiltonian. If one follows the linear-response approach, one arrives at the same matrix in the linear response theory, one starts from the CC equations, rather than the CC wave function, and no CC wave function is assumed. This matrix also arises in the equations for derivatives of CC amplitudes. In linear response theory, this matrix is sometimes called the Jacobian [19]. The upshot is that excited states for methods such as CCSDT-1, CCSDT-2, CCSDT-3, and CC3 can be obtained by solving eigenvalue equations in a manner similar to those for methods such as CCSD and CCSDT. 

K. B. Bravaya, D. Zuev, E. Epifanovsky, and A. I. Krylov,/. Chem. Phys., 138,124106 1-15 (2013). Complex-Scaled Equation-of-Motion Coupled-Cluster Method with Single and Double Substitutions for Autoionizing Excited States Theory, Implementation, and Examples. 

To use direct dynamics for the study of non-adiabatic systems it is necessary to be able to efficiently and accurately calculate electronic wave functions for excited states. In recent years, density functional theory (DFT) has been gaining ground over traditional Hartree-Fock based SCF calculations for the treatment of the ground state of large molecules. Recent advances mean that so-called time-dependent DFT methods are now also being applied to excited states. Even so, at present, the best general methods for the treatment of the photochemistry of polyatomic organic molecules are MCSCF methods, of which the CASSCF method is particularly powerful. 

Like Hartree-Fock theory, Cl-Singles is an inexpensive method that can be applied to large systems. When paired with a basis set, it also may be used to define excited state model chemistries whose results may be compared across the full range of practical systems. 

An excited state of a molecule can be regarded as a distinct chemical species, different from the ground state of the same molecule and from other excited states. It is obvious that we need some method of naming excited states. Unfortunately, there are several methods in use, depending on whether one is primarily interested in photochemistry, spectroscopy, or MO theory." One of the most common methods... 

Theory. If two or more fluorophores with different emission lifetimes contribute to the same broad, unresolved emission spectrum, their separate emission spectra often can be resolved by the technique of phase-resolved fluorometry. In this method the excitation light is modulated sinusoidally, usually in the radio-frequency range, and the emission is analyzed with a phase sensitive detector. The emission appears as a sinusoidally modulated signal, shifted in phase from the excitation modulation and partially demodulated by an amount dependent on the lifetime of the fluorophore excited state (5, Chapter 4). The detector phase can be adjusted to be exactly out-of-phase with the emission from any one fluorophore, so that the contribution to the total spectrum from that fluorophore is suppressed. For a sample with two fluorophores, suppressing the emission from one fluorophore leaves a spectrum caused only by the other, which then can be directly recorded. With more than two flurophores the problem is more complicated but a number of techniques for deconvoluting the complex emission curve have been developed making use of several modulation frequencies and measurement phase angles (79). 

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