Accurateab InitioSpin Densities

Abstract

We present an approach for the calculation of spin density distributions for molecules that require very large active spaces for a qualitatively correct description of their electronic structure. Our approach is based on the density-matrix renormalization group (DMRG) algorithm to calculate the spin density matrix elements as a basic quantity for the spatially resolved spin density distribution. The spin density matrix elements are directly determined from the second-quantized elementary operators optimized by the DMRG algorithm. As an analytic convergence criterion for the spin density distribution, we employ our recently developed sampling-reconstruction scheme [J. Chem. Phys.2011, 134, 224101] to build an accurate complete-active-space configuration-interaction (CASCI) wave function from the optimized matrix product states. The spin density matrix elements can then also be determined as an expectation value employing the reconstructed wave function expansion. Furthermore, the explicit reconstruction of a CASCI-type wave function provides insight into chemically interesting features of the molecule under study such as the distribution of α and β electrons in terms of Slater determinants, CI coefficients, and natural orbitals. The methodology is applied to an iron nitrosyl complex which we have identified as a challenging system for standard approaches [J. Chem. Theory Comput.2011, 7, 2740].

Spin in density‐functional theory

“…[29][30][31][32][33][34][35][36] Moreover, the spin density-which serves as an additional fundamental quantity in the spin-DFT formalism commonly employed for open-shell systems-is qualitatively incorrect in some cases. [15,[37][38][39] To make things even worse, the treatment of low-spin states usually requires the use of a broken-symmetry description, [40][41][42][43] which provides an unphysical spin density by construction (see, e.g., Refs. [24,44] for a discussion).…”

A projected approximation to strongly contracted N-electron valence perturbation theory for DMRG wavefunctions

“…When the FOIS density is not considered during renormalization (α = 1) the energy decreases steeply and converges to within 0.1 mE h of the exact CASCI+SC-NEVPT2 value for M = 125. The curve for α = 0.5 in Figure 2 nicely demonstrates that the convergence of the total energy towards the exact value is substantially accelerated by taking the FOIS density into account according to Equation (27). Shifting the reference density weight to α = 0.3 and α = 0.7 leads to only small energy differences compared to α = 0. indistinguishable in Figure 2).…”

“…A more suitable representation of the perturber functions can be obtained by taking them into account explicitly during the renormalization step. In the presented method, the modified density matrix (27) enters the SVD. This modified density is a weighted sum of the electronic ground state density and the active part of the density of the first order interacting space (FOIS).…”

“…Introducing the density of Equation (27) to the renormalization procedure ensures that those parts of the active space that are most important for the description of the perturber functions are incorporated in the renormalized space. Of course, this improvement comes at the cost of a slightly slower convergence of the ground state energy with respect to the bond dimension M as compared to the standard renormalization procedure.…”

“…Owing to this favorable behavior DMRG is able to treat large active spaces on the order of 20-80 orbitals. [22][23][24][25][26][27][28][29] Treating dynamic electron correlation on top of largescale DMRG calculations is currently an active field of research. It is possible to straightforwardly implement direct analogues of multi-reference dynamic correlation methods on top of DMRG wavefunctions.…”