Article
Chemistry, Physical
Kyle Bystrom, Boris Kozinsky
Summary: Machine learning has gained attention for developing more accurate exchange-correlation functionals for density functional theory. This study introduces the CIDER formalism, a set of nonlocal density features, and trains a Gaussian process model to achieve exchange energy that follows the critical uniform scaling rule. The resulting CIDER exchange functional shows significantly improved accuracy compared to tested semilocal functionals, and demonstrates good transferability across main-group molecules.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2022)
Article
Chemistry, Physical
Juan Felipe Huan Lew-Yee, Mario Piris, Jorge M. del Campo
Summary: In this work, an algebraic approach named DoNOF-RI is developed to implement the resolution of the identity approximation within the Piris Natural Orbital Functional (PNOF). This implementation reduces arithmetic and memory scaling, leading to significant computational time savings. After full convergence, a restart with four-center electron repulsion integrals quickly converges to the exact result, showing improvement in numerical results and speed-ups compared to PNOF7.
JOURNAL OF CHEMICAL PHYSICS
(2021)
Article
Chemistry, Physical
Bikash Kanungo, Jeffrey Hatch, Paul M. Zimmerman, Vikram Gavini
Summary: The conventional approaches to the inverse density functional theory problem assume nondegeneracy of the Kohn-Sham eigenvalues, limiting their use in open-shell systems. This study presents a generalized approach that allows for degenerate KS eigenvalues and fractional occupancy of the orbitals, enabling the handling of noninteracting ensemble-v-representable densities. Comparison of exact and model exchange-correlation potentials shows substantial relative errors in the model potentials.
JOURNAL OF PHYSICAL CHEMISTRY LETTERS
(2023)
Article
Materials Science, Multidisciplinary
N. D. Woods, M. T. Entwistle, R. W. Godby
Summary: The study computed the exact exchange-correlation (xc) kernel f(xc) of linear response time-dependent density functional theory at different frequencies, revealing that its frequency dependence is largely influenced by its analytic structure. Despite the presence of singularities at certain frequencies, it was found that f(xc) is approximately independent within certain frequency ranges, and the key differences between the exact f(xc) and its approximations were analyzed.
Article
Chemistry, Physical
Christian Neiss, Steffen Fauser, Andreas Goerling
Summary: Recently, sigma-functionals have been introduced as new correlation functionals in Kohn-Sham (KS) methods. When used in a post-self-consistent field manner in a Gaussian basis set framework, sigma-functional methods are computationally efficient and highly accurate for main group chemistry. They can reach a chemical accuracy of 1 kcal/mol for reaction and transition state energies. Sigma-functional methods yield accurate geometries and vibrational frequencies for main group molecules superior to conventional KS methods and RPA methods.
JOURNAL OF CHEMICAL PHYSICS
(2023)
Article
Chemistry, Physical
Bikash Kanungo, Paul M. Zimmerman, Vikram Gavini
Summary: Accurate exchange-correlation potentials for three-dimensional systems can now be tested using the exact XC potential, providing a promising new direction for building more accurate XC functionals for DFT. Among the model XC functionals, SCAN0 offers the best agreement with the exact XC potential, highlighting the importance of satisfying exact conditions and including nonlocal effects in XC functionals.
JOURNAL OF PHYSICAL CHEMISTRY LETTERS
(2021)
Article
Chemistry, Physical
Jannis Erhard, Steffen Fauser, Egor Trushin, Andreas Goerling
Summary: The recently introduced sigma-functionals provide a new type of functionals for the Kohn-Sham correlation energy. They are based on the adiabatic-connection fluctuation-dissipation theorem and are computationally related to the direct random phase approximation (dRPA). However, a shortcoming of sigma-functionals is their inability to accurately describe processes involving a change in the electron number. This problem is tackled by introducing a scaling of the eigenvalues of the KS response function, resulting in scaled sigma-functionals that retain accuracy and computational efficiency.
JOURNAL OF CHEMICAL PHYSICS
(2022)
Article
Chemistry, Physical
Steffen Fauser, Egor Trushin, Christian Neiss, Andreas Goerling
Summary: The newly introduced sigma-functionals for the Kohn-Sham correlation energy show higher accuracy in energy optimization, particularly for main group chemistry. Compared to PBE-based sigma-functionals, the ones based on PBE0 and B3LYP exhibit advantages in terms of computational accuracy and efficiency.
JOURNAL OF CHEMICAL PHYSICS
(2021)
Article
Chemistry, Physical
Ashish Kumar, Manoj K. Harbola
Summary: This study demonstrates a method using random numbers to obtain the exchange-correlation potential for a given density, eliminating the need to evaluate the density functional in each iterative step. The method's effectiveness is shown through calculations of exchange-correlation potentials for atoms, clusters, and the Hookium.
CHEMICAL PHYSICS LETTERS
(2021)
Article
Computer Science, Interdisciplinary Applications
Yijin Gao, Jay Mayfield, Gang Bao, Di Liu, Songting Luo
Summary: An effective asymptotic Green's function method is presented for solving the time-dependent Schrodinger equation with scalar and vector potentials, and it is applied to the Kohn-Sham equations for electronic structure calculation within the time-dependent density functional theory. The method combines Huygens' principle or Feynman's path integral for propagating the wavefunction and semi-classical approximations for approximating the retarded Green's function. Analytic approximations of the phase and amplitudes of the asymptotic retarded Green's function are obtained through short-time Taylor series expansions, and a short-time propagator for the wavefunction is derived for evaluation using fast Fourier transform after suitable low-rank approximations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Chemistry, Physical
Lucas M. Everhart, Julio A. Derteano, Jefferson E. Bates
Summary: This study explores the connection between the adiabatic excitation energy of time-dependent density functional theory and the ground state correlation energy from the adiabatic connection fluctuation-dissipation theorem (ACFDT) in the limiting case of one excited state. The results show that there is a tension between predicting an accurate excitation energy and an accurate potential contribution to correlation, particularly in systems with strong correlation. The exact adiabatic (AE) approximation is capable of accurately predicting both quantities in weakly correlated systems, while the random phase approximation (RPA) tends to be unable to predict these properties accurately. However, the AE approximation greatly overestimates the excitation energy in strongly correlated systems.
JOURNAL OF CHEMICAL PHYSICS
(2022)
Article
Chemistry, Physical
Egor Trushin, Andreas Goerling
Summary: The numerically stable optimized effective potential (OEP) method is presented, utilizing Gaussian basis sets and preprocessing steps for auxiliary basis sets. This approach allows the use of standard Gaussian basis sets in OEP calculations and results in stable and physically reasonable exchange potentials. The inclusion of exact conditions for the KS exchange potential and application to correlation potentials are discussed, demonstrating the versatility and effectiveness of the method.
JOURNAL OF CHEMICAL PHYSICS
(2021)
Article
Chemistry, Physical
Edoardo Spadetto, Pier Herman Theodoor Philipsen, Arno Foerster, Lucas Visscher
Summary: Pair atomic density fitting (PADF) is a promising strategy to decrease the scaling of quantum chemical methods for calculating correlation energy, but it can introduce large errors. This study introduces an alternative methodology to overcome the problem associated with PADF, using regularization and projection techniques. The accuracy and efficiency of this approach are assessed numerically using different basis sets, and the results demonstrate its effectiveness and computational efficiency.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2023)
Article
Chemistry, Physical
Thomas C. Pitts, Sofia Bousiadi, Nikitas I. Gidopoulos, Nektarios N. Lathiotakis
Summary: One way to improve the accuracy of spectral properties in density functional theory is to impose constraints on the effective local potential. This study introduces an effective screening amplitude, f, as a variational quantity, which leads to a more efficient and robust minimization problem. The proposed development is found to be an accurate and robust variant of the constrained effective potential method.
JOURNAL OF CHEMICAL PHYSICS
(2023)
Article
Chemistry, Physical
Han Yang, Marco Govoni, Arpan Kundu, Giulia Galli
Summary: We propose a computational protocol based on density matrix perturbation theory to calculate non-adiabatic, frequency-dependent electron-phonon self-energies for molecules and solids. Our approach allows for the evaluation of electron-phonon interaction using hybrid functionals in spin-polarized systems, with negligible computational overhead for including dynamical and non-adiabatic terms in the self-energies calculation. We present results for molecules, pristine solids, and defective solids.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2022)