CASSCF 372 Subject

Gas-Phase Spectroscopy. The 336-nm absorption band of triplet imidogen was first observed by Eder in 1892 and has been the subject of numerous subsequent studies. The singlet state of NH absorbs at 324 nm. The CASSCF (6,5)/ CASPT2 level of theory predicts transitions at 323 and 293 nm for singlet and triplet imidogen, respectively. In each spin state, an electron is promoted from the sp hybrid lone pair to a singly occupied 2p orbital as shown below for NH. 

The CASSCF/CASPT2 method has been designed to deal with quantum chemical situations, where the electronic structure is complex and not well described, even qualitatively, by single configurational methods. The method relies on the possibility to choose an active space of orbitals that can be used to construct a full Cl wave function that describes the system qualitatively correct. When this is possible, the method is capable of describing complex electronic structures quite accurately. Examples of such situations are found in excited states, in particular photochemical reactions that is the subject of this book, but also in transition metal, and actinide chemistry. 

This procedure suffers from a high degree of arbitrariness in the choice of just which configurations are deemed important. The calculation can be made somewhat more objective by including all excitations between a subset of occupied MOs and a subset of vacant orbitals. (These excitations are subject to certain restrictions as to multiplicity or order of excitation.) The orbitals chosen for the excitations are referred to as the active space , and the method is dubbed Complete Active Space Self Consistent Field (CASSCF) - ". Both MCSCF and CASSCF provide a certain fraction of the correlation energy, relative to a single configuration, Hartree-Fock, calculation. 

The solution to the active orbital choice and the accompanying expansion length problems may be addressed in many cases by extending the direct product definition of the orbital space. The orbitals in the full Cl expansion were partitioned into three types in the definition of the FORS/CASSCF wavefunction inactive, active and virtual. Within each orbital type, the expansion may be considered to be full. That is, subject to the occupation restrictions on each subspace, all possible orbital occupations and spin... 

In this last section we will take a short sidestep from the main subject of this chapter to look at another aspect of computational chemistry where multiconfig-urational methods, in particular CASSCF, come in very handy, i.e., the description of excited states. Indeed, one of the nice features of the CASSCF method is that it can generally be used for excited states as well as for the ground state. All it takes is to optimize a set of orbitals for the excited state in question (which is not always straightforward in cases where different roots are close in energy and may flip [10]) or, alternatively, for an average of a set of excited states. It is important to realize, however, that the calculation of excited states imposes additional demands on the active space, other than to include all near-degeneracy effects. The rule is simple and self-evident all orbitals that are either populated... 

Another striking observation was that all the Tj diradicals 1 are subject to a Jahn-Teller distortion in which one of the 7i-bonds was stretched. A final observation came from spin-orbit coupling computations that showed appreciable SOC only in diradical 2. The triplet computations on diradicals 1 and 2 were done at the CASSCF(6,6)/6-31G level, whereas the spin-orbit coupling computations were carried out with a modified Gamess i with a multiconfigurational (i.e., MCSCF) singlet interacting with the three components of the triplets. 

No experimental results on the PH ion have been published so far. The species has been the subject of a few quantum-chemical ab initio calculations. CASSCF and MRD Cl calculations of all ten electronic states correlating with the four lowest asymptotes, D, S)+ H " and p2+(2p ) + H(2S), reveal three quasi-bound and seven repulsive states. The quasi-bound states are the previously known [1 to 3] ground state X (KL (4a)2 (5a)2) correlating with the... 

It is important to emphasize from the outset that metal-metal bonds present a substantirJ challenge to electronic structure theory, particularly where diatomic overlap is weak and the electrons are highly correlated. The chromium dimer, Crj, for example, is a notoriously difficult case and has been the subject of debate for decades [13], Some progress toward a quantitative understanding of these correlation effects has been made through Complete Active Space Self Consistent Field (CASSCF) and related wavefunction-based techniques, but much of our qualitative understanding... 

One of the most challenging aspects of a CASSCF calculation is the identification of a suitable active space. Much has been written on this subject, and the reader is directed to a recent contribution by Veryazov et al. [27] on the subject. 

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