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 (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle t} and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle t+1} is given by (Eq. 16):

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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)