# Modelling the adiabatic connection in H2

### Michael J. G. Peach, Andrew M. Teale, David J. Tozer, J. Chem. Phys., **126**, 244104, 2007.

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The adiabatic connection formalism is an approach to developing exchange–correlation functionals via an integral over an interaction-strength coupling parameter that connects the non-interacting DFT system with the physical interacting system. The origins of this paper lay with the Mori-Sanchez, Cohen and Yang (MCY1 and 2) functionals, which gave us the impetus to investigate the limits of the accuracy achievable from a functional based on a Padé-approximation. To achieve this, we developed a procedure involving essentially exact full configuration-interaction calculations, to derive inputs for the Padé-approximation for H_{2} for a series of bond lengths. The conclusion is that the Padé-approximation is insufficiently flexible to allow an accurate description of the full potential energy curve. The procedure has subsequently been expanded by Teale and Helgaker, who were able to calculate accurate adiabatic connection data for all values of the coupling strength parameter.

Further information, including details of subsequent work in this area, can be found on the adiabatic connection research page. For the abstract, and access to the full text, see below.

## Abstract

_{2}, within spin-restricted density functional theory (DFT). For each internuclear separation

*R*, accurate properties of the AC are determined from large basis set FCI calculations. The parameters in the approximate AC form are then determined so as to reproduce these FCI values exactly, yielding an exchange-correlation energy expressed entirely in terms of FCI-derived quantities. This is combined with other FCI-derived energy components to give the total electronic energy; comparison with the FCI energy quantifies the accuracy of the AC form. Initial calculations focus on a [1/1]-Padé-based form. The potential energy curve determined using the procedure is a notable improvement over those from existing DFT functionals. The accuracy near equilibrium is quantified by calculating the bond length and vibrational wave numbers; errors in the latter are below 0.5%. The molecule dissociates correctly, which can be traced to the use of virtual orbital eigenvalues in the slope in the noninteracting limit, capturing static correlation. At intermediate

*R*, the potential energy curve exhibits an unphysical barrier, similar to that noted previously using the random phase approximation. Alternative forms of the AC are also considered, paying attention to size extensivity and the behavior in the strong-interaction limit; none provide an accurate potential energy curve for all

*R*, although good accuracy can be achieved near equilibrium. The study demonstrates how data from correlated

*ab initio*calculations can provide valuable information about AC forms and highlight areas where further theoretical progress is required.

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