The adiabatic connection curve of density functional theory (DFT) is accurately calculated beyond the physical interaction strength for Hooke's atom, two interacting electrons in a harmonic well potential. Extrapolation of the accurate curve to the infinite coupling limit agrees well with the strictly correlated electron (SCE) hypothesis but the approach to this limit is more complex. The interaction strength interpolation is shown to be a good, but not perfect, fit to the adiabatic curve. Arguments about the locality of functionals and convexity of the adiabatic connection curve are examined in this regime.
A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to computing dynamic correlation within CASSCF and DMRG models. Practical realizations of AC have been based on two approximations: i) fixing one- and two-electron reduced density matrices (1- and 2-RDMs) at the zero-coupling constant limit and ii) extended random phase approximation (ERPA). This work investigates the the effect of removing the "fixed-RDM" approximation in AC. The analysis is carried out for two electronic Hamiltonian partitionings: the group product function- and the Dyall-Hamiltonians. Exact…
We study in detail the first three leading terms of the large coupling-strength limit of the adiabatic connection that has as weak-interaction expansion the Møller-Plesset perturbation theory. We first focus on the H atom, both in the spin-polarized and the spin-unpolarized case, reporting numerical and analytical results. In particular, we derive an asymptotic equation that turns out to have simple analytical solutions for certain channels. The asymptotic H atom solution for the spin-unpolarized case is then shown to be variationally optimal for the many-electron spin-restricted closed-shell …
The quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as one of the methods of choice for calculations of strongly correlated molecular systems. Despite its great ability to capture strong electronic correlation in large active spaces, it is not suitable for computations of dynamical electron correlation. In this work, we present a new approach to the electronic structure problem of strongly correlated molecules, in which DMRG is responsible for a proper description of the strong correlation, whereas dynamical correlation is computed via …
The adiabatic connection that has as weak-interaction expansion the Møller-Plesset perturbation series has been recently shown to have a large coupling-strength expansion in terms of functionals of the Hartree-Fock density with a clear physical meaning. In this work we accurately evaluate these density functionals and we extract second-order gradient coefficients from the data for neutral atoms, following ideas similar to the ones used in the literature for exchange, with some modifications. These new gradient expansions will be the key ingredient for performing interpolations that have alread…
Given the omnipresence of non-covalent interactions (NCIs), their accurate simulations are of crucial importance across various scientific disciplines. Here we construct accurate models for the description of NCIs by an interpolation along the Møller-Plesset adiabatic connection (MP AC). Our interpolation approximates the correlation energy, by recovering MP2 at small coupling strengths and the correct large-coupling strength expansion of the MP AC, recently shown to be a functional of the Hartree-Fock density. Our models are size consistent for fragments with non-degenerate ground states, hav…
Strong correlation can be essentially captured with multireference wavefunction methods such as complete active space self-consistent field (CASSCF) or density matrix renormalization group (DMRG). Still, an accurate description of the electronic structure of strongly correlated systems requires accounting for the dynamic electron correlation, which CASSCF and DMRG largely miss. In this work a new approach for the correlation energy based on the adiabatic connection (AC) is proposed. The AC$_{\rm n}$ method accounts for terms up to the desired order n in the coupling constant, is rigorously siz…
Adiabatic connection models (ACMs), which interpolate between the limits of weak and strong interaction, are powerful tools to build accurate exchange-correlation functionals. If the exact weak-interaction expansion from second-order perturbation theory is included, a self-consistent implementation of these functionals is challenging and still absent in the literature. In this work we fill this gap by presenting a fully self-consistent-field (SCF) implementation of some popular ACM functionals. While using second-order perturbation theory at weak interactions, we have also introduced new gener…
Finite-temperature adiabatic-connection reduced density-matrix functional theory: a unified framework for i-DMFT and TAO-DFT
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Department of Applied Physics, Nanjing University of Science and Technology（南京理工大学应用物理系）
Currently, there is a growing interest in the development of a new hierarchy of methods based on the concept of seniority, which has been introduced quite recently in quantum chemistry. Despite the enormous potential of these methods, the accurate description of both dynamical and static correlation effects within a single and in-principle-exact approach remains a challenge. In this work, we propose an alternative formulation of reduced density-matrix functional theory (RDMFT) where the (one-electron reduced) density matrix is mapped onto an ab initio seniority-zero wave function. In this theo…
Adding Temperature to the Adiabatic Connection: Hybrid Functionals for Static and Dynamic Correlation
Arnold Sommerfeld Centre for Theoretical Physics, Ludwig-Maximilians-Universität München（路德维希-马克西米利安慕尼黑大学阿诺德·索末菲理论物理中心）；Department of Computer Science, Oslo Metropolitan University（奥斯陆都市大学计算机系）；Department of Physical Chemistry, University of Geneva（日内瓦大学物理化学系）
Correcting basis-set errors due to the absence of the electron-electron cusp using an adiabatic correction
Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS（量子化学与物理实验室，图卢兹大学）；Laboratoire de Chimie Théorique, CNRS and Sorbonne University（理论化学实验室，法国国家科学研究中心和索邦大学）
