Capturing static and dynamic electron correlation simultaneously at manageable computational cost remains a key challenge in electronic structure theory. Motivated by the recurring role of effective temperature in self-consistent field methods we extend the adiabatic connection mechanism from density functional theory to include a temperature dimension. This gives rise to thermally enhanced hybrid functionals, in which static correlation is captured via fractional occupations generated by an effective "correlation temperature" within thermal Hartree-Fock, while dynamic correlation is described by established density functional approximations. The framework formally unifies information-density matrix functional theory (i-DMFT) and thermally-assisted-occupation (TAO-)DFT as special cases, clarifying their theoretical basis and the respective prescriptions for the temperature parameter. We assess the performance of several thermally enhanced hybrids for different cases where i-DMFT was previously shown to fail. Furthermore, we discuss and test different schemes for determining the correlation temperature and investigate the accuracy of different such choices for a benchmark set derived from biphenyl. The results help to clarify the achievable balance of accuracy, generality, and efficiency, establishing thermally enhanced hybrids as a systematic route toward low-cost treatment of both correlation types.
Capturing static and dynamic electron correlation simultaneously at manageable computational cost remains a key challenge in electronic structure theory. Motivated by the recurring role of effective temperature in self-consistent field methods we extend the adiabatic connection mechanism from density functional theory to include a temperature dimension. This gives rise to thermally enhanced hybrid functionals, in which static correlation is captured via fractional occupations generated by an effective "correlation temperature" within thermal Hartree-Fock, while dynamic correlation is described by established density functional approximations. The framework formally unifies information-density matrix functional theory (i-DMFT) and thermally-assisted-occupation (TAO-)DFT as special cases, clarifying their theoretical basis and the respective prescriptions for the temperature parameter. We assess the performance of several thermally enhanced hybrids for different cases where i-DMFT was previously shown to fail. Furthermore, we discuss and test different schemes for determining the correlation temperature and investigate the accuracy of different such choices for a benchmark set derived from biphenyl. The results help to clarify the achievable balance of accuracy, generality, and efficiency, establishing thermally enhanced hybrids as a systematic route toward low-cost treatment of both correlation types.
Accurately describing chemical bond breaking requires capturing strong/static electron correlation, a major challenge for single-reference self-consistent-field methods such as Hartree--Fock and Kohn--Sham density-functional theory (DFT). Fractional occupations substantially improve this situation, as demonstrated by information-density-matrix-functional theory (i-DMFT) and thermally-assisted-occupation DFT (TAO-DFT). Although useful, they are formulated within rather different theoretical frameworks, are somewhat semi-empirical, and their relationship remains unclear. Here we introduce finite-temperature adiabatic-connection reduced density-matrix functional theory (FT-AC-RDMFT), in which i-DMFT and TAO-DFT emerge as different reductions of a unified framework. The effective eigenvalue equation for natural orbitals and the Fermi--Dirac occupation numbers follow directly from the variational principle, while a thermal adiabatic connection relates the empirical entropy coefficient of i-DMFT to a characteristic temperature of the auxiliary non-interacting system. Within this framework, i-DMFT is the exact-exchange-based reduction, whereas TAO-DFT results when exact exchange is replaced by a density-based exchange-correlation functional. Numerical calculations confirm that i-DMFT, apart from a constant, coincides with the exact-exchange realization of the framework, and show that the improved dissociation behavior from finite-temperature occupations extends beyond exact exchange to hybrid and semilocal density functionals. For strongly correlated V2O3, finite-temperature occupations substantially reduce the severely overestimated non-magnetic LDA bulk modulus, bringing it close to experiment. These results establish FT-AC-RDMFT as a common theoretical foundation for finite-temperature occupation-based electronic-structure methods in molecular and solid-state systems.
Recently, thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] has been demonstrated to be an efficient and accurate electronic structure method for studying the ground-state properties of large multi-reference (MR) systems at absolute zero. To explore the thermal equilibrium properties of large MR systems at finite electronic temperatures, in the present work, we propose the finite-temperature (FT) extension of TAO-DFT, denoted as FT-TAO-DFT. Besides, to unlock the dynamical information of large MR systems at finite temperatures, FT-TAO-DFT is combined with ab initio molecular dynamics, leading to FT-TAO-AIMD. In addition, we also develop FT-TAO-DFT-based quantum mechanics/molecular mechanics (QM/MM), denoted as FT-TAO-QM/MM, to provide a cost-effective description of the thermal equilibrium properties of a QM subsystem with MR character embedded in an MM environment at finite temperatures. Moreover, the FT-TAO-DFT, FT-TAO-AIMD, and FT-TAO-QM/MM methods are employed to explore the radical nature and infrared (IR) spectra of n-acenes (n = 2--6), consisting of n linearly fused benzene rings, in vacuum and in an argon (Ar) matrix at finite temperatures. According to our calculations, for n-acenes at 1000 K or below, the electronic temperature effects on the radical nature and IR spectra are very minor, while the nuclear temperature effects on these properties are noticeable. For n-acene in an Ar matrx at absolute zero, the Ar matrix has minimal impact on the radical nature of n-acene, while the co-deposition procedure of n-acene and Ar atoms may affect the IR spectrum of n-acene.
It is common wisdom that a better understanding of how to quantify electron correlation should lead to more efficient treatments of the correlation problem. Here, we not only substantiate this view but turn it into a concrete, systematic framework for ground states. Since prominent correlation measures such as the nonfreeness depend only on the one-particle reduced density matrix, modeling the correlation energy as a function of such a measure naturally places the framework within reduced density matrix functional theory, while keeping the cost at mean-field level. Strikingly, the variable conjugate to the measure emerges as a ``correlation temperature'', thereby connecting correlation measures, functional theory, and effective temperatures. The framework rationalizes methods such as i-DMFT, and we illustrate its key concepts analytically for the Hubbard dimer and numerically for small molecular systems. This brings a fundamental question within reach: how much of the correlation problem can be solved at mean-field cost?
Over the years, several schemes have been proposed to describe multireference systems with Kohn-Sham Density Functional Theory. Problematic is the combination of two aspects: the Kohn-Sham reference wavefunction is usually taken to be a single Slater determinant, and approximate exchange-correlation functionals are typically derived form the local density approximation. In this work, we develop a theoretical framework that foregoes the single Slater determinant and instead employs thermal states as reference states for zero-temperature interacting systems. We provide convenient definitions of static and dynamic correlation functionals via an adiabatic connection approach. The formalism and computational results indicate that the entropic term of the thermal reference state is a good approximation to the static correlation functional. Hence, this work validates several reported results in the literature and motivates additional developments of static correlation density functionals.
Recent progress in materials synthesis combined with advances in computational science have opened up an opportunity to design new materials with specific properties. Semiconductors, heterostructures, and thin layered films are used for energy harvesting and solar cells. Transition metal oxides and metallic surfaces with deposited magnetic molecules are used for signal conversion, nonvolatile memory modules and spintronics. Due to growing complexity of the new materials the most efficient approach to their design requires combined experimental and theoretical effort. In order to advance our understanding of the complicated physics of the modern materials new theoretical methods based on controlled, reliable, computationally efficient and systematically improvable approximations describing correlation and finite-temperature effects are needed. Density functional theory (DFT) remains a method of choice for materials science calculations due to its low computational cost. However, despite all recent efforts, the majority DFT applications are limited to weakly correlated systems and zero temperature. The lack of systematic improvability, inaccurate treatment of strongly correlated systems will continue to restrict the domain of DFT applications. The multi-reference wave-function methods can provide an accurate description of the strongly correlated systems. Unfortunately, these methods are computationally expensive. In spite of recent improvement the computational complexity will likely to hinder the applications of wave-function based methods to materials science in foreseeable future. Finite-temperature Green's function methods offer several advantages such as systematic improvability, access to the excitation spectrum, thermodynamic properties and straightforward implementation of embedding frameworks. It has been realized long time ago and has been successfully used in condensed matter physics to study model systems. The applications of such methods to realistic systems are impeded due to lack of theoretical approaches providing chemical accuracy and efficient computational algorithms. In this dissertation, these shortcomings are addressed by developing self-energy embedding theory and its extensive comparison to established quantum chemistry methods. New numerical algorithms for efficient application of the finite-temperature Green's function methods to molecular and extended systems were developed. Properties of the second-order Green's function theory (GF2) in the context of quantum chemistry were investigated. Additionally, a new range-separated hybrid functional combining GF2 and DFT was developed and benchmarked.
The central problem in the modern electronic structure theory is the calculation of cor- relation energy, possibly by an approach that would account for both static and dynamic correlation in an efficient, balanced and accurate way. In this thesis, I present a collection of methods that combine the effective treatment of dynamic correlation by the coupled cluster theory with density matrix renormalization group, a well-established technique for calculations of strongly correlated systems. The connection between them is achieved via the tailored coupled clusters (TCC) ansatz, which conveniently does not impose any ad- ditional computational costs. After the successful initial assessment, we developed more efficient implementations of these methods by employing the local approaches based on pair natural orbitals. This way, we extended the range of possible applications to larger systems with thousands of basis functions. To assess the accuracy of TCC as well as its local counterparts, we performed a variety of benchmark calculations ranging from small, yet challenging systems such as the nitrogen molecule or tetramethyleneethane diradical, to larger molecules like oxo-Mn(Salen) or Fe(II)-porphyrin model. 1