Restricted open-shell reference functions

J. Gauss, J. F. Stanton, and R. J. Bartlett,/. Chem. Phys., 95,2639 (1991). Analytic Evaluation of Energy Gradients at the Coupled-Cluster Singles and Doubles Level Using Quasi-Restricted Hartree-Fock Open-Shell Reference Functions. 

In the present chapter, we will focus on the simulation of the dynamics of photoexcited nucleobases, in particular on the investigation of radiationless decay dynamics and the determination of associated characteristic time constants. We use a nonadiabatic extension of ab initio molecular dynamics (AIMD) [15, 18, 21, 22] which is formulated entirely within the framework of density functional theory. This approach couples the restricted open-shell Kohn-Sham (ROKS) [26-28] first singlet excited state, Su to the Kohn-Sham ground state, S0, by means of the surface hopping method [15, 18, 94-97], The current implementation employs a plane-wave basis set in combination with periodic boundary conditions and is therefore ideally suited to condensed phase applications. Hence, in addition to gas phase reference simulations, we will also present nonadiabatic AIMD (na-AIMD) simulations of nucleobases and base pairs in aqueous solution. 

The choice of as the zeroth-order Hamiltonian requires the use of either a spin-restricted (closed-shell) Hartree-Fock (RHF) or spin-unrestricted Hartree-Fock (UHF) determinant as the zeroth-order (reference) wavefunction. Since spin-restricted open-shell Hartree-Fock (ROHF) reference functions are not eigenfunctions of the spin-orbital P, other partitionings are required (Refs. 127-134). 

D. Watts,. Gauss, and R.. Bartlett,/. Chem. Phys., 98, 8718 (1993). Coupled-Cluster Methods with Noniterative Triple Excitations for Restricted Open-Shell Hartree-Fock and Other General Single Determinant Reference Functions. Energies and Analytical Gradients. 

Analytic Energy Gradients for Open-Shell Coupled-Cluster Singles and Doubles Calculations Using Restricted Open-Shell Hartree-Fock (ROHE) Reference Functions. 

D. Jayatilaka and T. J. Lee, Chem. Phys. Lett., 199, 211 (1992). The Form of Spin Orbitals for Open-Shell Restricted Hartree-Fock Reference Functions. 

Watts, J.D., Gauss, J., Bartlett, R.J. Coupled-cluster methods with noniterative triple excitations for restricted open-shell Hartree-Fock and other general single determinant reference functions—energies and analytical gradients. J. Chem. Phys. 1993, 98(11), 8718-33. 

Hyperfine couplings, in particular the isotropic part which measures the spin density at the nuclei, puts special demands on spin-restricted wave-functions. For example, complete active space (CAS) approaches are designed for a correlated treatment of the valence orbitals, while the core orbitals are doubly occupied. This leaves little flexibility in the wave function for calculating properties of this kind that depend on the spin polarization near the nucleus. This is equally true for self-consistent field methods, like restricted open-shell Hartree-Fock (ROHF) or Kohn-Sham (ROKS) methods. On the other hand, unrestricted methods introduce spin contamination in the reference (ground) state resulting in overestimation of the spin-polarization. 

The calculations on Ti2He were performed (30) using a basis set of triple zeta plus polarization quality, including / functions on Ti. For the singlet states, both restricted open-shell Hartree-Fock (ROHF) and FORS MCSCF reference wavefunctions were used, while ROHF reference wavefunctions were used for the triplet states. In order to account for dynamic electron correlation and obtain... 

These two issues recently initiated interest in the development of alternative open-shell CC schemes. " " A first suggestion was to start from a restricted open-shell HF (ROHF) instead of a UHF reference function. Since the ROHF wavefunction is already a spin eigenfunction, it can be shown that energies obtained from a spin-orbital based CC treatment correspond to so-called spin-projected energies ... 

Several researchers have recently devoted considerable effort to the derivation and efficient implementation of techniques based on spin-restricted reference determinants that reduce the computational discrepancy between closed- and open-shell systems. " This emphasis on spin-restricted techniques has resulted in part from a bias toward reference wavefunctions that maintain the spin symmetry of the exact wavefunction (such as the ROHF determinant), but also because of the possible efficiency advantages of spin-restricted methods over unrestricted techniques. Thus, since the component molecular orbitals are constrained to have identical spatial parts for each spin function, it should be possible to construct the correlated wavefunction in a manner that takes advantage of this symmetry. 

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