Ab initio molecular dynamics: Theory and Implementation
Ab initio molecular dynamics: Theory and Implementation
Ab initio molecular dynamics: Theory and Implementation
- No tags were found...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
determinant stems from considering the spin–unpolarized special case only. Thisreduces to the well–known gr<strong>and</strong> potential expressionΩ s (µV T) = −2k B T ln det (1 + exp [−β (H s − µ)])= −2k B T ∑ ( [ ( )])ln 1 + exp −β ɛ (i)s − µi(289)for non–interacting spin–1/2 Fermions where {ɛ (i)s } are the eigenvalues of a one–particle Hamiltonian such as Eq. (286); here the st<strong>and</strong>ard identity lndet M =Tr lnM was invoked for positive definite M.According to thermo<strong>dynamics</strong> the Helmholtz free energy F(NV T) associatedto Eq. (288) can be obtained from an appropriate Legendre transformation of thegr<strong>and</strong> free energy Ω(µV T)F s (NV T) = Ω s (µV T) + µN + ∑ I