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Register a new userA general range-separated double-hybrid density-functional theory
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Authors
Cairedine Kalai
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A range-separated double-hybrid (RSDH) scheme which generalizes the usual range-separated hybrids and double hybrids is developed. This scheme consistently uses a two-parameter Coulomb-attenuating-method (CAM)-like decomposition of the electron-electron interaction for both exchange and correlation in order to combine Hartree-Fock exchange and second-order M{{o}}ller-Plesset (MP2) correlation with a density functional. The RSDH scheme relies on an exact theory which is presented in some detail. Several semi-local approximations are developed for the short-range exchange-correlation density functional involved in this scheme. After finding optimal values for the two parameters of the CAM-like decomposition, the RSDH scheme is shown to have a relatively small basis dependence and to provide atomization energies, reaction barrier heights, and weak intermolecular interactions globally more accurate or comparable to range-separated MP2 or standard MP2. The RSDH scheme represents a new family of double hybrids with minimal empiricism which could be useful for general chemical applications.
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We construct range-separated double-hybrid schemes which combine coupled-cluster or random-phase approximations with a density functional based on a two-parameter Coulomb-attenuating-method-like decomposition of the electron-electron interaction. We find that the addition of a fraction of short-range electron-electron interaction in the wave-function part of the calculation is globally beneficial for the range-separated double-hybrid scheme involving a variant of the random-phase approximation with exchange terms. Even though the latter scheme is globally as accurate as the corresponding scheme employing only second-order M{{o}}ller-Plesset perturbation theory for atomization energies, reaction barrier heights, and weak intermolecular interactions of small molecules, it is more accurate for the more complicated case of the benzene dimer in the stacked configuration. The present range-separated double-hybrid scheme employing a random-phase approximation thus represents a new member in the family of double hybrids with minimal empiricism which could be useful for general chemical applications.
We introduce an approximation to the short-range correlation energy functional with multide-terminantal reference involved in a variant of range-separated density-functional theory. This approximation is a local functional of the density, the density gradient, and the on-top pair density, which locally interpolates between the standard Perdew-Burke-Ernzerhof correlation functional at vanishing range-separation parameter and the known exact asymptotic expansion at large range-separation parameter. When combined with (selected) configuration-interaction calculations for the long-range wave function, this approximation gives accurate dissociation energy curves of the H2, Li2, and Be2 molecules, and thus appears as a promising way to accurately account for static correlation in range-separated density-functional theory.
We provide a rationale for a new class of double-hybrid approximations introduced by Bremond and Adamo [J. Chem. Phys. 135, 024106 (2011)] which combine an exchange-correlation density functional with Hartree-Fock exchange weighted by $l$ and second-order M{o}ller-Plesset (MP2) correlation weighted by $l^3$. We show that this double-hybrid model can be understood in the context of the density-scaled double-hybrid model proposed by Sharkas et al. [J. Chem. Phys. 134, 064113 (2011)], as approximating the density-scaled correlation functional $E_c[n_{1/l}]$ by a linear function of $l$, interpolating between MP2 at $l=0$ and a density-functional approximation at $l=1$. Numerical results obtained with the Perdew-Burke-Ernzerhof density functional confirms the relevance of this double-hybrid model.
We present a rigorous framework that combines single-particle Greens function theory with density functional theory based on a separation of electron-electron interactions into short-range and long-range components. Short-range contributions to the total energy and exchange-correlation potential are provided by a density functional approximation, while the long-range contribution is calculated using an explicit many-body Greens function method. Such a hybrid results in a nonlocal, dynamic, and orbital-dependent exchange-correlation functional of a single-particle Greens function. In particular, we present a range-separated hybrid functional called srSVWN5-lrGF2 which combines the local-density approximation and the second-order Greens function theory. We illustrate that similarly to density functional approximations the new functional is weakly basis-set dependent. Furthermore, it offers an improved description of the short-range dynamical correlation. The many-body contribution to the functional allows us to mitigate the many-electron self-interaction error present in most of density functional approximations and provides a better description of molecular properties. Additionally, the new functional can be used to scale down the self-energy and, therefore, introduce an additional sparsity to the self-energy matrix that in the future can be exploited in calculations for large molecules or periodic systems.
We extend the range-separated double-hybrid RSH+MP2 method [J. G. Angyan et al., Phys. Rev. A 72, 012510 (2005)], combining long-range HF exchange and MP2 correlation with a short-range density functional, to a fully self-consistent version using the optimized-effective-potential technique in which the orbitals are obtained from a local potential including the long-range HF and MP2 contributions. We test this approach, that we name RS-OEP2, on a set of small closed-shell atoms and molecules. For the commonly used value of the range-separation parameter $mu=0.5$ bohr$^{-1}$, we find that self-consistency does not seem to bring any improvement for total energies, ionization potentials, and electronic affinities. However, contrary to the non-self-consistent RSH+MP2 method, the present RS-OEP2 method gives a LUMO energy which physically corresponds to a neutral excitation energy and gives local exchange-correlation potentials which are reasonably good approximations to the corresponding Kohn-Sham quantities. At a finer scale, we find that RS-OEP2 gives largely inaccurate correlation potentials and correlated densities, which points to the need of further improvement of this type of range-separated double hybrids.
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