ABSTRACT:The problems arising in the density functional theory when it is applied to the spin-and space-degenerate states are discussed. It is rigorously proved that in the case of orthonormal orbital set, the electron density of an arbitrary Nelectron system does not depend upon the total spin S and for all values of S has the same form as it has for a single-determinantal wave function. From this follows that the conventional Kohn-Sham equations cannot distinguish the states with different total spin values. A critical survey of the existing DFT methods of taking into account the total spin is performed. It is shown that all these methods, including state-and orbitaldependent functional method, modify only the expression for the exchange energy and use the correlation functionals not corresponding to the total spin of the state. It is also proved that the diagonal element of the density matrix is invariant with respect to the symmetry of the state, hence in this respect there is no difference between degenerate and nondegenerate states. On the other hand, for the degenerate states, the Born-Oppenheimer approximation fails, so that makes it impossible to apply the density functional formalism.
We have examined the electronic structure and bonding of the Mn(2) molecule through multireference variational calculations coupled with augmented quadruple correlation consistent basis sets. The Mn atom has a (6)S(4s(2)3d(5)) ground state with its first excited state, (6)D(4s(1)3d(6)), located 2.145 eV higher. For all six molecular states (1)Sigma(g)(+), (3)Sigma(u)(+), (5)Sigma(g)(+), (7)Sigma(u)(+), (9)Sigma(g)(+), and (11)Sigma(u)(+)(1) correlating to Mn((6)S)+Mn((6)S), and for six undecets, i.e., (11)Pi(u), (11)Sigma(g)(+), (11)Delta(g), (11)Delta(u), (11)Sigma(u)(+)(2), and (11)Pi(g) with end fragments Mn((6)S)+Mn((6)D), complete potential energy curves have been constructed for the first time. We prove that the bonding in Mn(2) dimer is of van der Waals type. The interaction of two Mn (6)S atoms is hardly influenced by the total spin, as a result the six Sigma states, singlet ((1)Sigma(g)(+)) to undecet ((11)Sigma(u)(+)(1)), are in essence degenerate packed within an energy interval of about 70 cm(-1). Their ordering follows the spin multiplicity, the ground state being a singlet, X (1)Sigma(g)(+), with binding energy D(e) (D(0)) approximately 600 (550)cm(-1) at r(e) approximately 3.60 A. The six undecet states related to the Mn((6)S)+Mn((6)D) manifold, are chemically bound with binding energies ranging from 3 ((11)Pi(g)) to 25 ((11)Pi(u))kcal/mol and bond distances about 1 A shorter than the states of the lower manifold, Mn((6)S)+Mn((6)S). The lowest of the undecets is of Pi(u) symmetry located 30 kcal/mol above the X (1)Sigma(g)(+) state.
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