An efficient formulation and implementation of the analytic energy gradient method to the single and double excitation coupled‐cluster wave function: Application to Cl2O2

1991 ◽  
Vol 94 (9) ◽  
pp. 6219-6228 ◽  
Author(s):  
Alistair P. Rendell ◽  
Timothy J. Lee
Keyword(s):  
Wave Function ◽  
Gradient Method ◽  
Coupled Cluster ◽  
Double Excitation ◽  
Energy Gradient

Analytic evaluation of energy gradients for the single and double excitation coupled cluster (CCSD) wave function: Theory and application

1987 ◽  
Vol 87 (9) ◽  
pp. 5361-5373 ◽  
Author(s):  
Andrew C. Scheiner ◽  
Gustavo E. Scuseria ◽  
Julia E. Rice ◽  
Timothy J. Lee ◽  
Henry F. Schaefer
Keyword(s):  
Wave Function ◽  
Function Theory ◽  
Coupled Cluster ◽  
Double Excitation ◽  
Analytic Evaluation

Coupled cluster energy derivatives. Analytic Hessian for the closed‐shell coupled cluster singles and doubles wave function: Theory and applications

1990 ◽  
Vol 92 (8) ◽  
pp. 4924-4940 ◽  
Author(s):  
Henrik Koch ◽  
Hans Jo/rgen Aa. Jensen ◽  
Poul Jo/rgensen ◽  
Trygve Helgaker ◽  
Gustavo E. Scuseria ◽  
...  
Keyword(s):  
Wave Function ◽  
Function Theory ◽  
Closed Shell ◽  
Coupled Cluster ◽  
Energy Derivatives ◽  
Cluster Energy

scholarly journals Calculation of dispersion interactions with the geminal-based ring Coupled Cluster Doubles method

2020 ◽  
Vol 139 (9) ◽  
Author(s):  
Á. Margócsy ◽  
Á. Szabados
Keyword(s):  
Wave Function ◽  
Asymptotic Behaviour ◽  
Noble Gas ◽  
Valence Bond ◽  
Coupled Cluster ◽  
Leading Order ◽  
Dispersion Interactions ◽  
Dispersion Energy ◽  
Generalized Valence Bond ◽  
Noble Gas Dimers

Abstract The performance of the recently developed multi-reference extension of ring coupled cluster doubles is investigated for dispersion energy calculations, applied to the generalized valence bond wave function. The leading-order contribution to the dispersion energy is shown to have the correct asymptotic behaviour. Illustrative calculations on noble gas dimers are presented.

scholarly journals Investigation of Turbulent Transition in Plane Couette Flows Using Energy Gradient Method

2011 ◽  
Vol 3 (2) ◽  
pp. 165-180 ◽  
Author(s):  
Hua-Shu Dou ◽  
Boo Cheong Khoo
Keyword(s):  
Energy Loss ◽  
Gradient Method ◽  
Poiseuille Flow ◽  
Mechanical Energy ◽  
Viscous Friction ◽  
Critical Value ◽  
Plane Couette Flow ◽  
Turbulent Transition ◽  
Energy Gradient ◽  
Total Mechanical Energy

AbstractThe energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow. In this method, it is demonstrated that the transition to turbulence depends on the relative magnitudes of the transverse gradient of the total mechanical energy which amplifies the disturbance and the energy loss from viscous friction which damps the disturbance, for given imposed disturbance. For a given flow geometry and fluid properties, when the maximum of the function K (a function standing for the ratio of the gradient of total mechanical energy in the transverse direction to the rate of energy loss due to viscous friction in the streamwise direction) in the flow field is larger than a certain critical value, it is expected that instability would occur for some initial disturbances. In this paper, using the energy gradient analysis, the equation for calculating the energy gradient function K for plane Couette flow is derived. The result indicates that K reaches the maximum at the moving walls. Thus, the fluid layer near the moving wall is the most dangerous position to generate initial oscillation at sufficient high Re for given same level of normalized perturbation in the domain. The critical value of K at turbulent transition, which is observed from experiments, is about 370 for plane Couette flow when two walls move in opposite directions (anti-symmetry). This value is about the same as that for plane Poiseuille flow and pipe Poiseuille flow (385-389). Therefore, it is concluded that the critical value of K at turbulent transition is about 370-389 for wall-bounded parallel shear flows which include both pressure (symmetrical case) and shear driven flows (anti-symmetrical case).

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