A new form of transcorrelated Hamiltonian inspired by range-separated DFT

Abstract

The present work introduces a new form of explicitly correlated factor in the context of the transcorrelated methods. The new correlation factor is obtained from the r 12 $\approx$ 0 mathematical analysis of the transcorrelated Hamiltonian, and its analytical form is obtained such that the leading order in 1/r 12 of the scalar part of the effective two-electron potential reproduces the long-range interaction of the range-separated density functional theory. The resulting correlation factor exactly imposes the cusp and is tuned by a unique parameter $\mu$ which controls both the depth of the coulomb hole and its typical range in r 12. The transcorrelated Hamiltonian obtained with such a new correlation factor has a straightforward analytical expression depending on the same parameter $\mu$, and its physical contents continuously change by varying $\mu$ : one can change from a non divergent repulsive Hamiltonian at large $\mu$ to a purely attractive one at small $\mu$. We investigate the convergence of the ground state eigenvalues and right-eigenvectors of such new transcorrelated Hamiltonian as a function of the basis set and as a function of $\mu$ on a series of two-electron systems. We found that the convergence towards the complete basis set is much faster for a quite wide range values of $\mu$. We also propose a specific value of $\mu$ which essentially reproduce the results obtained with the frozen Gaussian geminal introduced by Ten-No [CPL-330,169 (2000)].

References in corpus (23)

• Long-range/short-range separation of the electron-electron interaction in density functional theory
• Semistochastic Heat-bath Configuration Interaction method: selected configuration interaction with semistochastic perturbation theory
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• Van der Waals forces in density functional theory: perturbational long-range electron interaction corrections
• Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation
• Long-range-corrected hybrids including RPA correlation
• Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs
• Short-range exchange and correlation energy density functionals: beyond the local density approximation
• Density Matrix Renormalization Group with Efficient Dynamical Electron Correlation Through Range Separation
• Fixed-Node Diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions
• Closed-shell ring coupled cluster doubles theory with range separation applied on weak intermolecular interactions
• Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence
• Unbiasing the initiator approximation in Full Configuration Interaction Quantum Monte Carlo
• Quantum simulation of electronic structure with a transcorrelated Hamiltonian: improved accuracy with a smaller footprint on the quantum computer
• Compact numerical solutions to the two-dimensional repulsive Hubbard model obtained via non-unitary similarity transformations
• Similarity transformation of the electronic Schrödinger equation via Jastrow factorisation
• A general range-separated double-hybrid density-functional theory
• Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density
• Basis convergence of range-separated density-functional theory
• Spin-unrestricted random-phase approximation with range separation: Benchmark on atomization energies and reaction barrier heights
• Fractional-charge and fractional-spin errors in range-separated density-functional theory
• Range-separated double-hybrid density-functional theory with coupled-cluster and random-phase approximations
• Iterative diagonalization of the non-Hermitian transcorrelated Hamiltonian using a plane-wave basis set: Application to $sp$-electron systems with deep core states

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