Clusters open-shell

J. Gauss, J. F. Stanton, and R. J. Bartlett, ]. Chem. Phys., 95, 2623 (1991). Coupled-Cluster Open-Shell Analytic Gradients Implementation of the Direct Product Decomposition Approach in Energy Gradient Calculations. 

VIsser O, Vlssoher L, Aerts P J C and NIeuwpoort W C 1992 Moleoular open shell oonflguratlon Interaotlon oaloulatlons using the Dlrao-Coulomb Flamlltonlan the f -manlfold of an embedded cluster J. Chem. Phys. 96 2910-19... 

The spherical shell model can only account for tire major shell closings. For open shell clusters, ellipsoidal distortions occur [47], leading to subshell closings which account for the fine stmctures in figure C1.1.2(a ). The electron shell model is one of tire most successful models emerging from cluster physics. The electron shell effects are observed in many physical properties of tire simple metal clusters, including tlieir ionization potentials, electron affinities, polarizabilities and collective excitations [34]. 

Since the singly excited determinants effectively relax the orbitals in a CCSD calculation, non-canonical HF orbitals can also be used in coupled cluster methods. This allows for example the use of open-shell singlet states (which require two Slater determinants) as reference for a coupled cluster calculation. 

If the focus of interest is on the carbon clusters themselves, then of course no substitute system can be used. However, for studying the convergence of properties towards bulk values one can minimize the termination effects by saturating the dangling bonds in the simplest possible way, i.e. with hydrogen. By that approach one can both avoid the problem of handling an excessive number of open shells, and obtain a series of molecules that converge towards bulk properties more smoothly than the bare carbon clusters. 

The representation of an essentially infinite framework by a finite SCF treated cluster of atoms, (with or without point-ions), inevitably leads to the problem of how to truncate the model-molecule . Previous attempts at this have included using hydrogen atoms l and ghost atoms . Other possibilities include leaving the electron from the broken bond in an open shell, or closing this shell to form an ionic cluster. A series of calculations were performed to test which was the host physically realistic, and computationally viable, solution to this problem for this system. 

Eliav, E., Kaldor, U. and Ishikawa, Y. (1994) Open-shell relativistic coupled-cluster method with Dirac-Breit wave functions Energies of the gold atom and its cation. Physical Review Letters, 49, 1724—1729 Including newer unpublished results from this group. 

Nakatsuji H, Hirao K (1978) Cluster expansion of the wavefunction. symmetry-adapted-cluster expansion, its variational determination, and extension of open-shell orbital theory. J Chem Phys 68 2053... 

Uneven open shell Pn clusters are easier to ionize than even closed shell ones and the stability of the closed shell uneven P cluster cations is higher. For very large Pn+ cations with n = 25 + 8x (x — 0.1.2. 8) islands of stability were observed in the time of flight mass spectrum (TOF-MS) obtained by laser ablation of red phosphorus, suggesting that the more stable P clusters have connections with units of eight P atoms [71d]. A lot of effort has been put into the calculation of the most stable Pn+ cation structures. The respective global minimum structures of the more stable uneven P3+, Ps+, P71 and P<)h cluster cations are shown in Figure 2.6-10 [73, 74],... 

Fig. 12.1 An ultra-fast heating of a cluster containing both N2 and 02 molecules upon impact at a surface. [9] Shown is the instantaneous configuration of 14 N atoms (dark) and 14 O atoms (light) 50 fsec after a cluster of 7 N2 and 7 02 molecules embedded in 97 Ne atoms impacts a surface at a velocity of 20 Mach. The potential used allows for alii 25 atoms of the cluster to interact with one another and with the atoms of the surface. In addition, each atom-atom chemical interaction is influenced by the presence or absence of other open-shell atoms nearby.

The yttrium monocarbide molecule was only recently observed under high resolution by Simard et al. (37) using Jet-cooled optical spectroscopy. The ground electronic state was determined to be an 0=5/2 state, which was consistent with the ab initio calculations of Shim et al. (38) who predicted a 11 ground state for YC in CASSCF calculations. The experimental work of Simard et al. yielded estimates for both the bond length and harmonic frequency of YC. In addition to their CASSCF calculations. Shim et al. (38) also reported results from mass spectrometric equilibrium experiments, which resulted in a bond dissociation energy of Do = 99.0 3.3 kcal/mol. The results from the present work are shown in Table I. An open-shell coupled cluster singles and doubles... 

The coupled cluster calculations involved in Wlc theory were carried out using MOLPRO 2002.3. (7P) (For the open-shell calculations on the constituent atoms, the definition of the open-shell CCSD and CCSD(T) energies in Ref. (20) was employed.) The density functional calculations were carried out using a modified version of Gaussian 98 rev. All (27), as were the Gn theory (22-24) and CBS-n (25) calculations. 

By adopting the no-pair approximation, a natural and straightforward extension of the nonrelativistic open-shell CC theory emerges. The multireference valence-universal Fock-space coupled-cluster approach is employed [25], which defines and calculates an effective Hamiltonian in a low-dimensional model (or P) space, with eigenvalues approximating some desirable eigenvalues of the physical Hamiltonian. The effective Hamiltonian has the form [26]... 

Noga, J., Valiron, P. Explicitly correlated R12 coupled cluster calculations for open shell systems. Chem. Phys. Lett. 2000, 324, 166-74. 

M. Urban, P. Neogrady, and I. Hubac, Spin Adaptation in the Open-Shell Coupled-Cluster Theory with a Single Determinant Restricted Hartree-Fock Reference. In R. J. Bartlett (Ed.) Recent Advances in Coupled-Cluster Methods. Recent Advances in Computational Chemistry, Vol. 3. (World Scientific, Singapore, 1997), pp. 275-306. 

---