We present the MCSCF version of density functional theory. Two sets of equations, which correspond to the CI and orbital relaxation respectively, are derived. An important feature is that the correlation potential of DFT for CI wavefunction and that for orbitals are different to each other. These relations ensure that a density yielded by a effective MCSCF solution also satisfies the Euler equation of DFT
We present an improved approach for generating a set of optimized frontier orbitals (HOMO and LUMO) that minimizes the energy of one double configuration. We further benchmark the effect of including such a double within a CIS or TD-DFT configuration interaction Hamiltonian for a set of test cases. We find that, although we cannot achieve quantitative accuracy, the algorithm is quite robust and routinely delivers an enormous qualitative improvement to standard single-reference electronic structure calculations.
Off-diagonal hypervirial relationships, combined with quantum mechanical sum rules of charge-current conservation, offer a way for testing electronic excited-state transition energies and moments, which does not need any external reference. A number of fundamental relations were recast into absolute deviations from zero, which have been used to assess the performance of some popular DFT functionals. Extended TD-DFT calculations have been carried out for a pool of molecules chosen to the purpose, adopting a large basis set to ensure high quality results. A general agreement with previous benchm…
In this work we propose a chemically-informed data-driven approach to benchmark the approximate density-functional tight-binding (DFTB) excited state (ES) methods that are currently available within the DFTB+ suite. By taking advantage of the large volume of low-detail ES-data in the machine learning (ML) dataset, QM8, we were able to extract valuable insights regarding the limitations of the benchmarked methods in terms of the approximations made to the parent formalism, density-functional theory (DFT), while providing recommendations on how to overcome them. For this benchmark, we compared t…
Diagrammatic Multiplet-Sum Method (MSM) Density-Functional Theory (DFT): Investigation of the Transferability of Integrals in "Simple" DFT-Based Approaches to Multi-Determinantal Problems
Nuclear Magnetic Resonance (NMR) shielding constants of transition metals in solvated complexes are computed at the relativistic density functional theory (DFT) level. The solvent effects evaluated with subsystem-DFT approaches are compared with the reference solvent shifts predicted from supermolecular calculations. Two subsystem-DFT approaches are analyzed -- in the standard frozen density embedding (FDE) scheme the transition metal complexes are embedded in an environment of solvent molecules whose density is kept frozen, in the second approach the densities of the complex and of its enviro…
While CCSD(T) with spin-restricted Hartree-Fock (RHF) orbitals has long been lauded for its ability to accurately describe closed-shell interactions, the performance of CCSD(T) on open-shell species is much more erratic, especially when using a spin-unrestricted HF (UHF) reference. Previous studies have shown improved treatment of open-shell systems when a non-HF set of molecular orbitals, like Brueckner or Kohn-Sham density functional theory (DFT) orbitals, is used as a reference. Inspired by the success of regularized orbital-optimized second-order Møller-Plesset perturbation theory ($κ$-OOM…
Development of the electronic kinetic-energy density functional is a subject of major interest in theoretical physics and chemistry. In this work, the nonlocal kinetic-energy functional is developed in terms of the response function for the molecular system to realize the orbital free density-functional theory(OF-DFT) to be utilized in the hybrid QM/MM(quantum mechanical/molecular mechanical) method. The present approach shows a clear contrast to the previous functionals where the homogeneous electron gas serves as a reference to build the response function. As a benchmark test we apply the me…
The lytic polysaccharide monooxygenase (LPMO) enzymes boost polysaccharide depolymerization through oxidative chemistry, which has fueled the hope for more energy-efficient production of biofuel. We have recently proposed a mechanism for the oxidation of the polysaccharide substrate (Hedegård & Ryde, Chem. Sci. 2018, 9, 3866). In this mechanism, complexes with superoxide, oxyl, as well as hydroxyl (i.e. [CuO2]+, [CuO]+ and [CuOH]2+) cores were involved. These complexes can have both singlet and triplet spin states, and both spin-states may be important for how LPMOs function during catalytic t…
The accurate resolution of the chemical properties of strongly correlated systems, such as biradicals, requires the use of electronic structure theories that account for both multi-reference as well as dynamic correlation effects. A variety of methods exist that aim to resolve the dynamic correlation in multi-reference problems, commonly relying on an exponentially scaling complete-active-space self-consistent-field (CASSCF) calculation to generate reference molecular orbitals (MOs). However, while CASSCF orbitals provide the optimal solution for a selected set of correlated (active) orbitals,…
The self-consistent charge density functional tight-binding (DFTB) theory study of carbon adatoms using tuned Hubbard U parameters
Institute of Atomic and Molecular Physics, Jilin University（吉林大学原子与分子物理研究所）；Jilin Provincial Key Laboratory of Applied Atomic and Molecular Spectroscopy (Jilin University)（吉林大学应用原子分子光谱学吉林省重点实验室）
This work presents a theory to unify the two independent theoretical frameworks of Kohn-Sham (KS) density functional theory (DFT) and reduced density matrix functional theory (RDMFT). The generalization of the KS orbitals to hypercomplex number systems leads to the hypercomplex KS (HCKS) theory, which extends the search space for the density in KS-DFT to a space that is equivalent to natural spin orbitals with fractional occupations in RDMFT. Thereby, HCKS is able to capture the multi-reference nature of strong correlation by dynamically varying fractional occupations. Moreover, the potential …
Herein, we present a new method to efficiently calculate electronically excited states in large molecular assemblies, consisting of hundreds of molecules. For this purpose, we combine the long-range corrected tight-binding density-functional fragment molecular orbital method (FMO-LC-DFTB) with an excitonic Hamiltonian, which is constructed in the basis of locally excited and charge-transfer configuration state functions calculated for embedded monomers and dimers and accounts explicitly for the electronic coupling between all types of excitons. We first evaluate both the accuracy and efficienc…
How Good Is DFT for Solid-Liquid Interfaces? A Comparison With the Random-Phase Approximation for Water on Graphene
University of Cambridge（剑桥大学）；Max Planck Institute for Polymer Research（马克斯·普朗克聚合物研究所）；Max Planck Initiative for Liquid Research（马克斯·普朗克液体研究倡议）；Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）
Force correcting atom centered potentials for generalized gradient approximated density functional theory: Approaching hybrid functional accuracy for geometries and harmonic frequencies in small chlorofluorocarbons
The practical utility of Møller-Plesset (MP) perturbation theory is severely constrained by the use of Hartree-Fock (HF) orbitals. It has recently been shown that use of regularized orbital-optimized MP2 orbitals and scaling of MP3 energy could lead to a significant reduction in MP3 error (J. Phys. Chem. Lett. 10, 4170, 2019). In this work we examine whether density functional theory (DFT) optimized orbitals can be similarly employed to improve the performance of MP theory at both the MP2 and MP3 levels. We find that use of DFT orbitals leads to significantly improved performance for predictio…
Using a set of oscillator strengths and excited-state dipole moments of near full configuration interaction (FCI) quality determined for small compounds, we benchmark the performances of several single-reference wave function methods (CC2, CCSD, CC3, CCSDT, ADC(2), and ADC(3/2)) and time-dependent density-functional theory (TD-DFT) with various functionals (B3LYP, PBE0, M06-2X, CAM-B3LYP, and $ω$B97X-D). We consider the impact of various gauges (length, velocity, and mixed) and formalisms: equation of motion (EOM) \emph{vs} linear response (LR), relaxed \emph{vs} unrelaxed orbitals, etc. Beyon…
The energy landscape of silicon systems and its description by force fields, tight binding schemes, density functional methods and Quantum Monte Carlo methods
We have studied the correlation potentials produced by various adiabatic connection models (ACM) for several atoms and molecules. The results have been compared to accurate reference potentials (coupled cluster and quantum Monte Carlo results) as well as to state-of-the-art ab initio DFT approaches. We have found that all the ACMs yield correlation potentials that exhibit a correct behavior, quite resembling scaled second-order Görling-Levy (GL2) potentials, and including most of the physically meaningful features of the accurate reference data. The behavior and contribution of the strong-inte…
Defect states in 2D materials present many possible uses but both experimental and computational characterization of their spectroscopic properties is difficult. We provide and compare results from 13 DFT and ab initio computational methods for up to 25 excited states of a paradigm system, the VNCB defect in hexagonal boron nitride (h-BN). Studied include include: (i) potentially catastrophic effects for computational methods arising from the multi-reference nature of the closed-shell and open-shell states of the defect, which intrinsically involves broken chemical bonds, (ii) differing result…
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）
Efficient first-principles modeling of complex molecular crystals at sub-chemical accuracy
Flatiron Institute（平顿研究所）；University of Chicago（芝加哥大学）；University of Washington（华盛顿大学）；University of Cambridge（剑桥大学）；University College London（伦敦大学学院）；Università di Napoli Federico II（那不勒斯费德里科二世大学）；Budapest University of Technology and Economics（布达佩斯技术与经济大学）
The interaction between electronic and nuclear spins in the presence of external magnetic fields can be described by a spin Hamiltonian, with parameters obtained from first principles, electronic structure calculations. We describe an approach to compute these parameters, applicable to both molecules and solids, which is based on Density Functional Theory (DFT) and real-space, all-electron calculations using finite elements (FE). We report results for hyperfine tensors, zero field splitting tensors (spin-spin component) and nuclear quadrupole tensors of a series of molecules and of the nitroge…
How reproducible are first-principles simulations of liquid water?
Max Planck Institute for Polymer Research（马克斯·普朗克聚合物研究所）；Flatiron Institute（平顿研究所）；University of Cambridge（剑桥大学）；University of Warwick（华威大学）；Tohoku University（东北大学）
Finite-Temperature Thermally-Assisted-Occupation Density Functional Theory, Ab Initio Molecular Dynamics, and Quantum Mechanics/Molecular Mechanics Methods
National Taiwan University（台湾大学）；Department of Physics, National Taiwan University（台湾大学物理系）；Center for Theoretical Physics and Center for Quantum Science and Engineering, National Taiwan University（台湾大学理论物理中心与量子科学与工程中心）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）
