Subsystem Density-Functional Theory (DFT) is an emerging technique for calculating the electronic structure of complex molecular and condensed phase systems. In this topical review, we focus on some recent advances in this field related to the computation of condensed phase systems, their excited states, and the evaluation of many-body interactions between the subsystems. As subsystem DFT is in principle an exact theory, any advance in this field can have a dual role. One is the possible applicability of a resulting method in practical calculations. The other is the possibility of shedding light on some quantummechanical phenomenon which is more easily treated by subdividing a supersystem into subsystems. An example of the latter is many-body interactions. In the discussion, we present some recent work from our research group as well as some new results, casting them in the current state-of-the-art in this review as comprehensively as possible.2

We present the formulation and the implementation of a spin-free state-specific multi-reference coupled cluster (SSMRCC) theory, realized via the unitary group adapted (UGA) approach, using a multi-exponential type of cluster expansion of the wave-operator Ω. The cluster operators are defined in terms of spin-free unitary generators, and normal ordered exponential parametrization is utilized for cluster expansion instead of pure exponentials. Our Ansatz for Ω is a natural spin-free extension of the spinorbital based Jeziorski-Monkhorst (JM) Ansatz. The normal ordered cluster Ansatz for Ω results in a terminating series of the direct term of the MRCC equations, and it uses ordinary Wick algebra to generate the working equations in a straightforward manner. We call our formulation as UGA-SSMRCC theory. Just as in the case of the spinorbital based SSMRCC theory, there are redundancies in the cluster operators, which are exploited to ensure size-extensivity and avoidance of intruders via suitable sufficiency conditions. Although there already exists in the literature a spin-free JM-like Ansatz, introduced by Datta and Mukherjee, its structure is considerably more complex than ours. The UGA-SSMRCC offers an easier access to spin-free MRCC formulation as compared to the Datta-Mukherjee Ansatz, which at the same time provides with quite accurate description of electron correlation. We will demonstrate the efficacy of the UGA-SSMRCC formulation with a set of numerical results. For non-singlet cases, there is pronounced M(s) dependence of the energy for the spinorbital based SSMRCC results. Although M(s) = 1 results are closer to full configuration interaction (FCI), the extent of spin-contamination is more. In most of the cases, our UGA-SSMRCC results are closer to FCI than the spinorbital M(s) = 0 results.

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The correlation energy of interaction is an elusive and sought-after interaction between molecular systems. By partitioning the response function of the system into subsystem contributions, the Frozen Density Embedding (FDE)-vdW method provides a computationally amenable nonlocal correlation functional based on the adiabatic connection fluctuation dissipation theorem applied to subsystem density functional theory. In reproducing potential energy surfaces of weakly interacting dimers, we show that FDE-vdW, either employing semilocal or exact nonadditive kinetic energy functionals, is in quantitative agreement with high-accuracy coupled cluster calculations (overall mean unsigned error of 0.5 kcal/mol). When employing the exact kinetic energy (which we term the Kohn-Sham (KS)-vdW method), the binding energies are generally closer to the benchmark, and the energy surfaces are also smoother.

A coupled cluster theory with iterative inclusion of triple excitations and associated equation of motion formulation for excitation energy and ionization potential The Journal of Chemical Physics 147, 074103 (2017); 10.1063/1.4985916 A quantum dynamics method for excited electrons in molecular aggregate system using a group diabatic Fock