Pericyclic reactions with energies E well above the potential energy barrier B (case E>B) proceed with quantum nuclear flux densities 〈j〉 which are essentially proportional to the nuclear densities ρ in the femtosecond time domain. This corresponds to the definition of classical (cl) mechanics, j(cl)=υ(cl) ρ(cl), with almost constant velocity v(cl). For the other case E
The dissociation of N 2 and N + 2 has been studied by using the ab initio Density Matrix Renormalization Group (DMRG) method. Accurate Potential Energy Surfaces (PES) have been obtained for the electronic ground states of N 2 (X 1 Σ + g ) and N + 2 (X 2 Σ + g ) as well as for the N + 2 excited stateInherently to the DMRG approach, the eigenvalues of the reduced density matrix (ρ) and their correlation functions are at hand. Thus we can apply Quantum Information Theory (QIT) directly, and investigate how the wave function changes along the PES and depict differences between the different states. Moreover by characterizing quantum entanglement between different pairs of orbitals and analyzing the reduced density matrix, we achieved a better understanding of the multi-reference character featured by these systems. * christian.stemmle@fu-berlin.de arXiv:1711.07701v1 [physics.chem-ph]
The molecular cobalt fluorides CoF 2 , CoF 3 and CoF 4 are studied and compared by employing different basis sets as well as Quantum Information Theory (QIT) to investigate their correlation effects. These prototypical monomers may be systematically extended in size yielding a novel quasi 1-dimensional, strongly correlated model system consisting of cobalt atoms bridged by oxygen atoms and fluorine termination on both ends. Accurate correlation energies are obtained using Full Configuration Interaction (FCI) and Full Configuration Interaction Quantum Monte Carlo (FCIQMC) calculations and the results are compared to Coupled Cluster and Density Matrix Renormalization Group (DMRG) energies. The analysis indicates the cobalt atom requires a larger number of one-electron basis functions than fluorine and the use of localized molecular orbitals may facilitate calculations for the extended systems. K E Y W O R D S correlation effects, electronic structure, orbital entanglement, strong correlation
| INTRODUCTIONAccurate treatment of electron correlation is the main challenge in electronic structure theory. Electron correlation describes the difference between the Hartree-Fock (HF) solution, which represents a systematic approximation to solve the electronic Schrödinger equation, and the exact solution. HF relies on an ansatz for the wave function that is only exact for a system with noninteracting electrons, the Slater determinant. The family of wave function-based correlation methods provides an approach capable of resolving this error in the numerically exact limit of the employed one-electron basis set, known as the full configuration interaction (FCI) method. [1] Unfortunately it scales exponentially with the number of electrons and basis functions that limits practical application to very small systems with only a few electrons.One therefore tries to reduce the high computational cost by considering the largest contributions (electron configurations) only. A priori knowledge of which configurations to keep however is hard and only possible based on assumptions. As a consequence, a large number of different truncation schemes and methods have been developed, such as CCSD(T), [2,3] MRCI, [4] CASSCF, [4,5] DMRG, [6] FCIQMC, [7] and so on. An especially difficult class of problems are strongly correlated systems where partially occupied, near degenerate orbitals are present. This leads to multiple major configurations with similar weight and, due to the truncation of the FCI wave function, a balanced description of the orbitals with respect to all major configurations is required.Typical test systems to evaluate newly developed methods range from more abstract systems like the Hubbard model [8] over chains and lattices of hydrogen atoms [9,10] to small but realistic chemical systems like the dissociation of N 2 [7,11] or transition metal complexes. [12] We here propose a new system based on cobalt compounds that may be systematically extended in size. The prototypical "monomers" CoF 2 and CoF 4 (in its quadratic planar ...
Understanding electron correlation is crucial for developing new concepts in electronic structure theory, especially for strongly correlated electrons. We compare and apply two different approaches to quantify correlation contributions of orbitals: Quantum Information Theory (QIT) based on a Density Matrix Renormalization Group (DMRG) calculation and the Method of Increments (MoI). Although both approaches define very different correlation measures, we show that they exhibit very similar patterns when being applied to a polyacetelene model system. These results suggest one may deduce from one to the other, allowing the MoI to leverage from QIT results by screening correlation contributions with a cheap (“sloppy”) DMRG with a reduced number of block states. Or the other way around, one may select the active space in DMRG from cheap one‐body MoI calculations.
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