Augmented phase space

Figure 10 Augmented phase space illustrated for a one-dimensional system. The arc length of the curve in the augmented space x, a is z. The solution is detennined at a reference point, here denoted Oq, and continued along the curve by determining the slope (here shown via the tangent line to the curve).

In well-known papers [22,23] Nose showed how a deterministic canonical ensemble N, V, T) MD simulation scheme could be constructed. Again the system phase space variables were augmented with an additional degree of freedom s. The physical system variables (qiiP ) were related to virtual variables (q,-,p,-,f) by a non-canonical transformation q, - = q,-, p = p,/i and = J df/i. The Hamiltonian of the extended system is... 

In this case, the term in dH jdu vanishes identically it is the augmented switching function that is to be zero for an optimum trajectory on the boundary in the continuum regime. Now dN may be arbitrary save that it must not cross into the forbidden region of the phase space ... 

AUGMENTED SPACE RECURSION APPROACH FOR ALLOY PHASE STABILITY... 

Our results demonstrate that the augmented space recursion and the orbital peeling method in conjunction with the LMTO formalism, constitute a viable and computationally feasible approach to the calculation of phase stability in binary substitutionally disordered alloys. ... 

Fig. 6 Schematic of orbital doubling procedure for multi-configurational wavefunctions as applied to transition metal photochemistry. On the left a predominately orbital is shown (in phase combination of smaller and larger exponent metal centred basis functions). To account for the dative nature of the M-CO bond any active space needs to be augmented with further orbitals containing extra nodes in the M-L region, here a orbital is shown (out of phase combination of smaller and larger exponent metal centred basis functions). In the subsequent configuration interaction this 3d-4d dynamic correlation generates qualitatively reliable wavefunctions...

Augmented Space Recursive Approach for Alloy Phase... 

As an illustration of the performance of TDDFT, we compare various density functionals and wave function methods for the first singlet excited states of naphthalene in Tables 4, 5, and 6. All calculations were performed using the aug-TZVP basis set, while the complete active space self-consistent field (SCF) with second-order perturbation theory (CASPT2) results from Ref. 200 were obtained in a smaller double-zeta valence basis set with some diffuse augmentation. The experimental results correspond to band maxima from gas-phase experiments however, the position of the band maximum does not necessarily coincide with the vertical excitation energy, especially if... 

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