We present the all-electron scheme of calculating nonadiabatic couplings (NACs) from TDDFT using atomic orbital basis. The formal expression for calculating NAC from linear response TDDFT can be straightforwardly adapted to the all-electron TDDFT scheme. However, in contrast to the planewave basis, the nuclear coordinate dependence of atomic orbital basis needs to be considered when constructing the matrix elements of the nuclear derivative of Hamiltonian. Practical calculations show that the contribution of atomic orbital basis
“Pulay term” is significant and comparable to that of the Hellmann–Feynman term. In particular, we probe the all-electron formalism of NAC with the Hartree–Fock exact exchange, which serves as the prerequisite for hybrid functionals. It is validated that in the present framework the sum rule of NAC is rigorously satisfied, which has not been the case in the pseudopotential planewave calculations. Reasonably good results can be obtained in the vicinity of various Renner–Teller
and also Jahn–Teller intersections when the intersection point is not too closely approached.