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Register a new userKoopmans-compliant functionals and potentials and their application to the GW100 test-set
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Koopmans-compliant (KC) functionals have been shown to provide accurate spectral properties through a generalized condition of piece-wise linearity of the total energy as a function of the fractional addition/removal of an electron to/from any orbital. We analyze the performance of different KC functionals on the GW100 test-set, comparing the ionization potentials (as opposite of the energy of the highest occupied orbital) of these 100 molecules to those obtained from CCSD(T) total energy differences, and experimental results, finding excellent agreement with a mean absolute error of 0.20 eV for the KIPZ functional, that is state-of-the-art for both DFT-based calculations and many-body perturbation theory. We highlight similarities and differences between KC functionals and other electronic-structure approaches, such as dielectric-dependent hybrid functionals and G$_0$W$_0$, both from a theoretical and from a practical point of view, arguing that Koopmans-compliant potentials can be considered as a local and orbital-dependent counterpart to the electronic GW self-energy, albeit already including approximate vertex corrections.
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Obtaining a precise theoretical description of the spectral properties of liquid water poses challenges for both molecular dynamics (MD) and electronic structure methods. The lower computational cost of the Koopmans-compliant functionals with respect to Greens function methods allows the simulations of many MD trajectories, with a description close to the state-of-art quasi-particle self-consistent GW plus vertex corrections method (QSGW+f$_{xc}$). Thus, we explore water spectral properties when different MD approaches are used, ranging from classical MD to first-principles MD, and including nuclear quantum effects. We have observed that the different MD approaches lead to up to 1 eV change in the average band gap, thus, we focused on the band gap dependence with the geometrical properties of the system to explain such spread. We have evaluated the changes in the band gap due to variations in the intramolecular O-H bond distance, and HOH angle, as well as the intermolecular hydrogen bond O$cdotcdotcdot$O distance, and the OHO angles. We have observed that the dominant contribution comes from the O-H bond length; the O$cdotcdotcdot$O distance plays a secondary role, and the other geometrical properties do not significantly influence the gap. Furthermore, we analyze the electronic density of states (DOS), where the KIPZ functional shows a good agreement with the DOS obtained with state-of-art approaches employing quasi-particle self-consistent GW plus vertex corrections. The O-H bond length also significantly influences the DOS. When nuclear quantum effects are considered, a broadening of the peaks driven by the broader distribution of the O-H bond lengths is observed, leading to a closer agreement with the experimental photoemission spectra.
We present an implementation of range separated functionals utilizing the Slater-function on grids in real space in the projector augmented waves method. The screened Poisson equation is solved to evaluate the necessary screened exchange integrals on Cartesian grids. The implementation is verified against existing literature and applied to the description of charge transfer excitations. We find very slow convergence for calculations within linear response time-dependent density functional theory and unoccupied orbitals of the canonical Fock operator. Convergence can be severely improved by using Huzinagas virtual orbitals instead. This combination furthermore enables an accurate determination of long-range charge transfer excitations by means of ground-state calculations.
The performance of density functional theory depends largely on the approximation applied for the exchange functional. We propose here a novel screened exchange potential for semiconductors, with parameters based on the physical properties of the underlying microscopic screening and obeying the requirements for proper asymptotic behavior. We demonstrate that this functional is Koopmans-compliant and reproduces a wide range of band gaps. We also show, that the only tunable parameter of the functional can be kept constant upon changing the cation or the anion isovalently, making the approach suitable for treating alloys.
Configuration-interaction-type calculations on electronic and vibrational structure are often the method of choice for the reliable approximation of many-particle wave functions and energies. The exponential scaling, however, limits their application range. An efficient approximation to the full configuration interaction solution can be obtained with the density matrix renormalization group (DMRG) algorithm without a restriction to a predefined excitation level. In a standard DMRG implementation, however, excited states are calculated with a ground-state optimization in the space orthogonal to all lower lying wave function solutions. A trivial parallelization is therefore not possible and the calculation of highly excited states becomes prohibitively expensive, especially in regions with a high density of states. Here, we introduce two variants of the density matrix renormalization group algorithm that allow us to target directly specific energy regions and therefore highly excited states. The first one, based on shift-and-invert techniques, is particularly efficient for low-lying states, but is not stable in regions with a high density of states. The second one, based on the folded auxiliary operator, is less efficient, but more accurate in targeting high-energy states. We apply the algorithm to the solution of the nuclear Schroedinger equation, but emphasize that it can be applied to the diagonalization of general Hamiltonians as well, such as the electronic Coulomb Hamiltonian to address X-ray spectra. In combination with several root-homing algorithms and a stochastic sampling of the determinant space, excited states of interest can be adequately tracked and analyzed during the optimization. We demonstrate that we can accurately calculate prominent spectral features of large molecules such as the sarcosyn-glycine dipeptide.
We develop a neuroevolution-potential (NEP) framework for generating neural network based machine-learning potentials. They are trained using an evolutionary strategy for performing large-scale molecular dynamics (MD) simulations. A descriptor of the atomic environment is constructed based on Chebyshev and Legendre polynomials. The method is implemented in graphic processing units within the open-source GPUMD package, which can attain a computational speed over $10^7$ atom-step per second using one Nvidia Tesla V100. Furthermore, per-atom heat current is available in NEP, which paves the way for efficient and accurate MD simulations of heat transport in materials with strong phonon anharmonicity or spatial disorder, which usually cannot be accurately treated either with traditional empirical potentials or with perturbative methods.
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