Electronic correlation

Electronic correlation is the interaction between electrons in the electronic structure of a quantum system. The correlation energy is a measure of how much the movement of one electron is influenced by the presence of all other electrons. Atomic and molecular systems Within the Hartree–Fock method of quantum chemistry, the antisymmetric wave function is approximated by a single Slater determinant. Exact wave functions, however, cannot generally be expressed as single determinants. The single-determinant approximation does not take into account Coulomb correlation, leading to a total electronic energy different from the exact solution of the non-relativistic Schrödinger equation within the Born–Oppenheimer approximation. Therefore, the Hartree–Fock limit is always above this exact energy. The difference is called the correlation energy, a term coined by Löwdin. The concept of the correlation energy was studied earlier by Wigner. A certain amount of electron correlation

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Towards a Composite Benchmark Method for the Aqueous Solvation Free Energies of Organic Compounds

Daniel David Sadowsky

Water is ubiquitous in the biosphere, and the difficulty of rigorously treating the effects of aqueous solvation currently limits the widespread use of computational methods in many areas of environmental chemistry. We propose an approach to benchmark calculations of aqueous free energies of solvation based on molecular dynamics simulation which is derived from first principles, statistical mechanically complete, and systematically improvable. The approach partitions the solvation free energy into the free energies of solvent density change, solvent cavity organization, and solvent-solute interaction, each of which is computed from first principles. A composite approach is considered for the calculation of the contributions of quantum nuclear effects to solvation free energies and the contributions of electron correlation and relativistic effects to solvent-solute interactions.

2015

Influence of static correlation on the magnon dynamics of an itinerant ferromagnet with competing exchange interactions: First-principles study of MnBi

Henrik Moodysson Rønnow, Thorbjørn Skovhus

We present first-principles calculations of the dynamic susceptibility in strained and doped ferromagnetic MnBi using time-dependent density functional theory. In spite of being a metal, MnBi exhibits signatures of strong correlation and a proper description in the framework of density functional theory requires Hubbard corrections to the Mn d orbitals. To permit calculations of the dynamic susceptibility with Hubbard corrections applied to the ground-state electronic structure, we use a consistent rescaling of the exchange-correlation kernel maintaining the delicate balance between the magnon dispersion and the Stoner continuum. We find excellent agreement with the experimentally observed magnon dispersion for pristine MnBi and show that the material undergoes a phase transition to helical order under application of either doping or strain. The presented methodology paves the way for future linear response time-dependent density functional theory studies of magnetic phase transitions, also for the wide range of materials with pronounced static correlation effects that are not accounted for at the local density approximation level.

AMER PHYSICAL SOC2022

Efficient Treatment of Correlation Energies at the Basis-Set Limit by Monte Carlo Summation of Continuum States

Martin Peter Bircher, Ursula Röthlisberger, Justin Villard

The calculation of electron correlation is vital for the description of atomistic phenomena in physics, chemistry, and biology. However, accurate wavefunction-based methods exhibit steep scaling and often sluggish convergence with respect to the basis set at hand. Because of their delocalization and ease of extrapolation to the basis-set limit, plane waves would be ideally suited for the calculation of basis-set limit correlation energies. However, the routine use of correlated wavefunction approaches in a plane-wave basis set is hampered by prohibitive scaling due to a large number of virtual continuum states and has not been feasible for all but the smallest systems, even if substantial computational resources are available and methods with comparably beneficial scaling, such as the Moller-Plesset perturbation theory to second order (MP2), are used. Here, we introduce a stochastic sampling of the MP2 integrand based on Monte Carlo summation over continuum orbitals, which allows for speedups of up to a factor of 1000. Given a fixed number of sampling points, the resulting algorithm is dominated by a flat scaling of similar to O(N-2). Absolute correlation energies are accurate to

AMER CHEMICAL SOC2020

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