Rigid top propagator

For a rigid three dimensional asymmetric top the kernel is given by () (Eq. 15) ):$\rho _{\mathrm {rot} }^{t,t+1}(\beta /P)=\sum _{J=0}^{\infty }\sum _{M=-J}^{J}\sum _{{\hat {K}}=-J}^{J}\left({\frac {2J+1}{8\pi ^{2}}}\right)A_{{\hat {K}}M}^{(JM)}\exp \left(-{\frac {\beta }{P}}E_{\hat {K}}^{(JM)}\right)\sum _{K=-J}^{J}A_{{\hat {K}}K}^{(JM)}d_{MK}^{J}({\tilde {\theta }}^{t+1})\cos(M{\tilde {\phi }}^{t+1}+K{\tilde {\chi }}^{t+1})$

The contribution to the rotational energy of the interactions between beads Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t+1} is given by (Eq. 16):

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e_{rot}^{t,t+1}= \frac{1}{ \rho_{\mathrm{rot}}^{t,t+1}} \sum_{JM\hat{K}} \left( \frac{2J+1}{8\pi^2} \right) A_{\hat{K}M}^{(JM)} E_{\hat{K}}^{(JM)} \exp \left( -\frac{\beta}{P} E_{\hat{K}}^{(JM)}\right) \sum_K A_{\hat{K}K}^{(JM)} d_{MK}^J (\tilde{\theta}^{t+1}) \cos( M\tilde{\phi}^{t+1}+K\tilde{\chi}^{t+1})}

References

Related reading

• Carl McBride, Eva G. Noya, and Carlos Vega "A computer program to evaluate the NVM propagator for rigid asymmetric tops for use in path integral simulations of rigid bodies", Computer Physics Communications (In Press)(2012) (computer code)