Quasipinning and selection rules for excitations in atoms and molecules

Abstract

Postulated by Pauli to explain the electronic structure of atoms and molecules, the exclusion principle establishes an upper bound of 1 for fermionic natural occupation numbers {n i }. A recent analysis of the pure N -representability problem provides a wide set of inequalities for the {n i }, leading to constraints on these numbers. This has a strong potential impact on reduced density matrix functional theory as we know it. In this work we continue our study of the nature of these inequalities for some atomic and molecular systems. The results indicate that (quasi)saturation of some of them leads to selection rules for the dominant configurations in configuration interaction expansions, in favorable cases providing means for significantly reducing their computational requirements.

Optimal Slater-determinant approximation of fermionic wave functions

“…, φ N } can then be obtained by extending φ 1 into a full orthonormal basis of V . It is readily seen that such chosen basis vectors satisfy condition (18).…”

“…Only recently has the problem in the simplest case of m = 1 been solved [10], generalizing the equalities and inequalities in (1) systematically. This has led to a burst of studies of the relevance and implications of the so-called generalized Pauli constraints like (1) in atoms, molecules, and model systems [11][12][13][14][15][16][17][18][19][20]. As for the next case of m = 2 (which is possibly of more interest from the point of view of calculating the * wdlang06@163.com † mauser@courant.nyu.edu ground state energy of a multi-electron system), a systematic procedure for generating the N -representability conditions on the two-particle reduced density matrix has been derived by Mazziotti [21].…”

Spectral properties of reduced fermionic density operators and parity superselection rule

“…Eigenvalues of 1-RDM are called natural occupation numbers. In general case, natural occupation numbers cannot be arbitrary ones within [0, 1] (simple Pauli's exclusion principle) and must satisfy generalized Pauli constraints [32][33][34][35].…”

“…In quantum chemistry, a particle reduction is realized by integrating over irrelevant particles' coordinates [28][29][30], which results in the so-called p-particle reduced density matrix (see, e.g., [31]). Such an approach provides new inequalities for fermionic occupation numbers and leads to the generalized Pauli constraints [32][33][34][35]. As far as systems with a varying number of particles are concerned, the construction of p-particle reduced density matrices is non-trivial and we discuss it in this paper.…”

Conditions for Describing Triplet States in Reduced Density Matrix Functional Theory

“…The class of spin-compensated systems with time-reversal symmetry is a notable exception, since, in that case, the conditions for pure-state N -representability collapse to the ensemble conditions [32]. The necessary and sufficient conditions for pure-state N -representability, also called generalized Pauli constraints, have only recently been discussed and explicitly expressed for systems with a small number of particles and specific finite sizes of the Hilbert space [33][34][35][36][37][38][39]. Recently, it has been demonstrated that with enforcing only the ensemble conditions in a RDMFT calculation for open-shell systems, the pure-state conditions will be violated for many functionals of the 1RDM [40].…”