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Investigating short-range behavior of wave function by comparing projected Hartree-Fock spectra using basis functions having harmonic oscillator and Wood-Saxon radial dependence
We report charge order is commonly believed to compete with superconducting order. An intertwined form of a superconducting wave function, known as pair density wave (PDW) order, has been proposed; however, direct evidence, theoretical or experimental, that it forms the ground state of any cuprate superconductor is lacking. As a test case, we consider La 2-x Ba x CuO 4 with x = 1/8, where charge and spin stripe orders within the CuO 2 planes compete with three-dimensional superconducting order. We report measurements of the superconducting critical current perpendicular to the planes in the presence of an in-plane magnetic field. The variation of the critical current with orientation of the field is inconsistent with a theoretical prediction specific to the PDW model. It appears, instead, that the orientation dependence of the critical-current density might be determined by a minority phase of d-wave superconductivity that is present as a consequence of doped-charge inhomogeneity.
We report that graphene bilayers exhibit zero-energy flatbands at a discrete series of magic twist angles. In the absence of intrasublattice interlayer hopping, zero-energy states satisfy a Dirac equation with a non-Abelian SU(2) gauge potential that cannot be diagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Planck’s constant proportional to the twist angle, solving the linearized Dirac equation around AB and BA turning points, and connecting Airy function solutions via bulk WKB wave functions. We find zero-energy solutions at a discrete set of values of the dimensionless Planck’s constant, which we obtain analytically. Our analytic flatband twist angles correspond closely to those determined numerically in previous work.
Perturbation-like theory for case when available starting wave function is not eigenfunction of unperturbed Hamiltonian
Electron capture cross section by protons in hydrogen atom obtained, using perturbed wave functions due to electric field
Geometry of diatomic molecular wave functions - molecular spectroscopy
Energy states of helium isoelectronic series investigated by 50-term variational wave function with two nonlinear parameters
Vibrational energy transfer in high energy molecular collisions - time-dependent wave function evaluation of transition probabilities for forced harmonic oscillator
Perturbation treatment of diatomic hydrogen ion, improving polarized hydrogen-atom treatment by using zero-order wave function
Zeeman effect of germanium I and II, discussing configuration-interaction, deriving intermediate- coupling wave functions
Generalization of Sternheimer potential to include wave functions with spin
Energy minimization for trial wave function constrained to give expectation value of operator
By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal density functional theory (DFT) and thereby furnish a more accurate and reliable description of the underlying electronic structure in systems throughout biology, chemistry, physics, and materials science. However, the high computational cost associated with the evaluation of all required EXX quantities has limited the applicability of hybrid DFT in the treatment of large molecules and complex condensed-phase materials. To overcome this limitation, we describe a linear-scaling approach that utilizes a local representation of the occupied orbitals (e.g., maximally localized Wannier functions (MLWFs)) to exploit the sparsity in the real-space evaluation of the quantum mechanical exchange interaction in finite-gap systems. In this work, we present a detailed description of the theoretical and algorithmic advances required to perform MLWF-based ab initio molecular dynamics (AIMD) simulations of large-scale condensed-phase systems of interest at the hybrid DFT level. We focus our theoretical discussion on the integration of this approach into the framework of Car–Parrinello AIMD, and highlight the central role played by the MLWF-product potential (i.e., the solution of Poisson’s equation for each corresponding MLWF-product density) in the evaluation of the EXX energy and wave function forces. We then provide a comprehensive description of the exx algorithm implemented in the open-source Quantum ESPRESSO program, which employs a hybrid MPI/OpenMP parallelization scheme to efficiently utilize the high-performance computing (HPC) resources available on current- and next-generation supercomputer architectures. Furthermore, this is followed by a critical assessment of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach when AIMD simulations of liquid water are performed in the canonical (NVT) ensemble. With access to HPC resources, we demonstrate that exx enables hybrid DFT-based AIMD simulations of condensed-phase systems containing 500–1000 atoms (e.g., (H₂O)₂₅₆) with a wall time cost that is comparable to that of semilocal DFT. In doing so, exx takes us one step closer to routinely performing AIMD simulations of complex and large-scale condensed-phase systems for sufficiently long time scales at the hybrid DFT level of theory.
The recently developed ab-initio multiple cloning (AIMC) approach based on the multicongurational Ehrenfest (MCE) method provides a powerful and accurate way of describing the excited-state dynamics of molecular systems. The AIMC method is a controlled approximation to non-adiabatic dynamics with a particular strength in the proper description of decoherence effects due to branching of vibrational wavepackets at a level crossing. In this work, we report a new implementation of the AIMC algorithm in the open source NWChem computational chemistry program. The framework combines linear-response time-dependent density functional theory with Ehrenfest mean-eld theory to determine the equations of motion for classical trajectories. The multi-dimensional wave function is decomposed into a superposition of Gaussian coherent states guided by Ehrenfest trajectories (i.e., MCE approach), which can clone with fully quantum mechanical amplitudes and phases. By using an efficient time-derivative based non-adiabatic coupling approach within the AIMC method, all observable are calculated on-the-y in the non-adiabatic molecular dynamics process. As a representative example, we apply our implementation to study the ultrafast photoinduced electronic and vibrational energy transfer in a pyridine molecule. The effects of the cloning procedure on electronic and vibrational coherence, relaxation and unidirectional energy transfer are discussed. This new AIMC implementation provides a high-level non-adiabatic molecular dynamics framework for simulating photoexcited dynamics in complex molecular systems and experimentally relevant ultrafast spectroscopic probes, such as nonlinear coherent optical and X-ray signals.
Wave function of multivalent atom from linear determinants formulated from laplace theorem
Approximate ground state wave function used in variational principle for second order energy
Vector model for wave functions of atomic energy levels
The computation of two-electron repulsion integrals (ERIs) is often the most expensive step of integral-direct self-consistent field methods. Formally it scales as O(N 4 ), where N is the number of Gaussian basis functions used to represent the molecular wave function. In practice, this scaling can be reduced to O(N 2 ) or less by neglecting small integrals with screening methods. The contributions of the ERIs to the Fock matrix are of Coulomb (J) and exchange (K) type and require separate algorithms to compute matrix elements efficiently. We previously implemented highly efficient GPU-accelerated J-matrix and K-matrix algorithms in the electronic structure code TeraChem. Although these implementations supported the use of multiple GPUs on a node, they did not support the use of multiple nodes. This presents a key bottleneck to cutting-edge ab initio simulations of large systems, e.g., excited state dynamics of photoactive proteins. We present our implementation of multinode multi-GPU J- and K-matrix algorithms in TeraChem using the Regent programming language. Regent directly supports distributed computation in a task-based model and can generate code for a variety of architectures, including NVIDIA GPUs. We demonstrate multinode scaling up to 45 GPUs (3 nodes) and benchmark against hand-coded TeraChem integral code. Finally, we also outline our metaprogrammed Regent implementation, which enables flexible code generation for integrals of different angular momenta.