High-spin open-shell

The high-spin open-shell energy expression can be obtained in completely similar manner from Eq. (124),... 

We shall now follow the unrestricted Hartree-Fock (UHF) formalism to obtain a restricted high-spin open-shell functions as proposed in [34], [35]. In order to eliminate spin contamination in the UHF function f i, the following spin purity constraint is imposed on the spatial orbitals ... 

Zuchowski PS, Bussery-Honvault B, Moszynski R, Jeziorski B (2003) Dispersion interaction of high-spin open-shell complexes in the random phase approximation. J Chem Phys 119 10497-10511... 

We emphasize that the present discussion focuses only on high-spin open-shell systems to which a single-determinant reference wavefunction is applicable. Coupled cluster techniques for low-spin cases, such as open-shell singlets, have been pursued in the literature for many years, however, and provide a fertile area of research (Refs. 158, 167-170). 

T. D. Crawford and H. F. Schaefer,/. Chem. Phys., 104, 6259 (1996). A Comparison of Two Approaches to Perturbational Triple Excitation Corrections to the Coupled-Cluster Singles and Doubles Method for High-Spin Open-Shell Systems. 

P.. Knowles, C. Hampel, and H.-. Werner,/. Chem. Phys., 99, 5219 (1993). Coupled-Cluster Theory for High-Spin, Open-Shell Reference Wave Functions. 

One deficiency can be seen in the case of a high-spin open-shell wavefunction. If the condition that f should not be symmetry breaking is relaxed, by replacing D with the spin density matrix and using spin orbitals, we arrive at... 

C., and Werner, H.-J. (1993) Coupled cluster theory for high spin, open shell reference wave functions. J. Chem. Phys., 99, 5219 5227 (d) Watts, ).D., Gauss,... 

SCF, the only significant change will be that the CHF equations (33) and (34) will be different. The relevant equations for UHF have been given by Pople et for high-spin open-shell wavefunctions the theory has been examined by Saxe et and Osamura et al. have considered general open-shell... 

This includes as special cases both closed-shell and high-spin open-shell, and also cases such as open-shell singlets, symmetiy-equivalenced SCF and even some very simple types of MC-SCF wavefunction, such as two-configuration (TC-SCF) wavefunctions. The CHF equations are derived by differentiating the convergence criterion, which is... 

Orthogonality-constrained Hartree-Fock and perturbation theory for high-spin open-shell excited states... 

Cluster Theory for High Spin, Open Shell Reference Wave Functions. 

Electronic states that are amenable to a single reference starting point are either closed-shell systems or high-spin open-shell systems. Examples of the latter include B CH2,... 

The present overview is intended to give a brief introduction into CC theory, thereby focusing more on the needs of a computational chemist than on formal aspects. The basic theory of single-reference CC theory is presented together with a discussion of the computationally feasible approaches. Other important topics covered in the following are the treatment of high-spin open-shell systems, the calculation of molecular properties and the description of excited states within standard CC theory. Despite the necessarily brief presentation, emphasis will be laid on adequate discussion of recent developments in order to keep the reader informed about current research. All topics are supplemented by numerical examples which illustrate the performance and accuracy of the CC methods. 

While the treatment of closed-shell systems is rather straightforward and CC theory provides in these cases automatically spin adapted results, i.e., eigenfunctions to the spin operator the same is not true for high-spin open-shell... 

High-spin open-shell coupled-cluster theory... 

Let us consider the simultaneous solution of the Schrodinger and spin equations for high-spin open-shell states. The coupled-cluster wave function may be expressed in terms of a singledeterminant reference function with the excitation operators chosen to yield excitations from this reference state. The full coupled-cluster wave function, being equivalent to the FCI wave function in the same orbital basis, is a simultaneous eigenfunction of the Schrodinger equation and the spin equations ... 

Let us summarize the spin-restricted coupled-cluster ansatz for high-spin open-shell systems [34]. The reference wave function is an RHF state and the projection manifold consists of determinants of the same spin projection as the reference state - for example, all states obtained from the reference state by single and double spin-orbital replacements. The spin-restricted coupled-cluster energy is calculated in the usual manner... 

Normally, for the triplet state of organic molecules the ZFS parameters can be entirely determined as the SSC expectation value [48, 60]. But for the inr states in porphin the second-order SOC effect can produce an appreciable contribution to the ZFS since the FBP molecule has lone pairs at nitrogen atoms. We have therefore computed the 7i state of free-base porphin molecules taking into account both SSC and SOC perturbations. The SSC expectation values are calculated here by the singledeterminant SCF method for the high spin open shell [47] using Dalton code. 

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