CASSCF method

Techniques have been developed within the CASSCF method to characterize the critical points on the excited-state PES. Analytic first and second derivatives mean that minima and saddle points can be located using traditional energy optimization procedures. More importantly, intersections can also be located using constrained minimization [42,43]. Of particular interest for the mechanism of a reaction is the minimum energy path (MEP), defined as the line followed by a classical particle with zero kinetic energy [44-46]. Such paths can be calculated using intrinsic reaction coordinate (IRC) techniques... 

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. 

In this exercise, we will introduce the Complete Active Space Multiconfiguration SCF (CASSCF) method, using it to compute the excitation energy for the first excited state of acrolein (a singlet). The CIS job we ran in Exercise 9.3 predicted an excitation energy of 4.437 eV, which is rather for from the experimental value of 3.72 eV. We ll try to improve this prediction here. 

A CASSCF calculation is a combination of an SCF computation with a full Configuration Interaction calculation involving a subset of the orbitals. The orbitals involved in the Cl are known as the active space. In this way, the CASSCF method optimizes the orbitals appropriately for the excited state. In contrast, the Cl-Singles method uses SCF orbitals for the excited state. Since Hartree-Fock orbitals are biased toward the ground state, a CASSCF description of the excited state electronic configuration is often an improvement. 

C=C stretch 80 C-13 chemical shifts 22, 53 C60 31,32 C60O isomers 54 carbon dioxide 120, 182 carbon monoxide 175,191 carbonyl series 84 carbonyl stretch 84, 220 in solution 244 Carmichael 136 Carpenter 152, 196 Cartesian coordinates 52, 286, 287 CASSCF keyword 228 CASSCF method 228,229,230,231, 232,233, 234,235 state-averaged 233... 

Chapter 9, Modeling Excited States, discusses predicting the properties of excited states of molecules, including structures and vibrational frequencies. An exercise in the advanced track considers CASSCF methods. 

The full Cl expansion within the active space severely restricts the number of orbitals and electrons that can be treated by CASSCF methods. Table 4.3 shows how many singlet CSFs are generated for an [n, n]-CASSCF wave function (eq. (4.13)), without any reductions arising from symmetry. 

It should be noted that CASSCF methods inherently tend to give an unbalanced description, since all the electron correlation recovered is in die active space, but none in the inactive space, or between the active and inactive electrons. This is not a problem if all the valence electrons are included in the active space, but this is only possible for small systems. If only part of die valence electrons are included in the active space, the CASSCF methods tend to overestimate the importance of biradical structures. Consider for example acetylene where the hydrogens have been bent 60° away from hnearity (this may be considered a model for ort/zo-benzyne). The in-plane jt-orbital now acquires significant biradical character. The true structure may be described as a hnear combination of the three configurations shown in Figure 4.11. 

In a combined experimental/computational study, the vibrational spectra of the N9H and N7H tautomers of the parent purine have been investigated [99SA(A) 2329]. Solvent effects were estimated by SCRF calculations. Vertical transitions, transition dipole moments, and permanent dipole moments of several low-lying valence states of 2-aminopurine 146 were computed using the CIS and CASSCF methods [98JPC(A)526, 00JPC(A)1930]. While the first excited state of adenine is characterized by an n n transition, it is the transition for 146. The... 

In terms of quantum chemistry, one needs to employ a method that can properly represent the 15 magnetic sublevels of the T2 manifold. This is, unfortunately, not the case for DFT since it is restricted to nondegenerate mono-determinantal states. Thus, the simplest method which does justice to the actual physics is the CASSCF method. 

The first study, by Ismail et al. [153], used the CASSCF method with a 6-31G basis set and an active space of 14 electrons in 10 orbitals to locate conical intersections and pathways connecting them to the Franck Condon region. Two such conical intersections were identified in that work, the ci2 and ci3, as defined above. In that work the barrier leading to ci2 was calculated to be 10 kcal/mol, too high to make this conical intersection relevant. But the barrier leading to ci3 was found to be much smaller, 3.6 kcal/mol, and it was concluded that ci3 is involved in the dominant decay path. Reaching this intersection requires first a conical intersection between the nn state, which is vertically the Si state, and the non state, which is vertically the S2 state. Merchan and Serrano-Andres followed up this study [140] using a method... 

Table 6.1 Energies of the low-lying J-multiplets predicted within the CASSCF/RASSI approach for the free Ln3+ ions. ANO-RCC of single-zeta quality were employed. The active space of the CASSCF method included only n electrons spanning the 4f shell. 

The treatment of systems where non-dynamic correlation is critical is quite more complicated from a methodological point of view. As mentioned above, non-dynamic correlation is associated to the presence of neardegeneracies in the electronic ground state of the system, which means that there are Slater determinants with a weight similar to that of the HF solution in equation 4. The problem of non-dynamic correlation is usually treated successfully by the CASSCF method [43] for organic systems. This method introduces with high accuracy the correlation in the orbitals involved in the near degeneracy, which constitute the so called active space. The problem in... 

With regard to the former, one would like to include as many important configurations as possible. Unfortunately, the definition of an important configuration is often debatable. One popular remedy is the full-valence complete active space SCF (CASSCF) approach in which configurations arising from all excitations from valence-occupied to valence-virtual orbitals are chosen. [29] Since this is equivalent to performing a full Cl within the valence space, the full-valence CASSCF method is limited to small systems. Nevertheless, the CASSCF approach using a well-chosen (often chemically motivated) subspace of the valence orbitals has been shown to yield a much improved depiction of the wave function at all points on a potential surface. Furthermore, the choice of an active space can be adjusted to describe excited state wave functions. 

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