Convergence Of Wave Functions Research Articles

Pyrene-stabilized acenes as intermolecular singlet fission candidates: importance of exciton wave-function convergence

Singlet fission (SF) is a photophysical process considered as a possible scheme to bypass the Shockley–Queisser limit by generating two triplet-state excitons from one high-energy photon. Polyacene crystals, such as tetracene and pentacene, have shown outstanding SF performance both theoretically and experimentally. However, their instability prevents them from being utilized in SF-based photovoltaic devices. In search of practical SF chromophores, we use many-body perturbation theory within the GW approximation and Bethe–Salpeter equation to study the excitonic properties of a family of pyrene-stabilized acenes. We propose a criterion to define the convergence of exciton wave-functions with respect to the fine k-point grid used in the BerkeleyGW code. An open-source Python code is presented to perform exciton wave-function convergence checks and streamline the double Bader analysis of exciton character. We find that the singlet excitons in pyrene-stabilized acenes have a higher degree of charge transfer character than in the corresponding acenes. The pyrene-fused tetracene and pentacene derivatives exhibit comparable excitation energies to their corresponding acenes, making them potential SF candidates. The pyrene-stabilized anthracene derivative is considered as a possible candidate for triplet–triplet annihilation because it yields a lower SF driving force than anthracene.

Efficient geometric integrators for nonadiabatic quantum dynamics. I. The adiabatic representation.

Geometric integrators of the Schrödinger equation conserve exactly many invariants of the exact solution. Among these integrators, the split-operator algorithm is explicit and easy to implement but, unfortunately, is restricted to systems whose Hamiltonian is separable into kinetic and potential terms. Here, we describe several implicit geometric integrators applicable to both separable and nonseparable Hamiltonians and, in particular, to the nonadiabatic molecular Hamiltonian in the adiabatic representation. These integrators combine the dynamic Fourier method with the recursive symmetric composition of the trapezoidal rule or implicit midpoint method, which results in an arbitrary order of accuracy in the time step. Moreover, these integrators are exactly unitary, symplectic, symmetric, time-reversible, and stable and, in contrast to the split-operator algorithm, conserve energy exactly, regardless of the accuracy of the solution. The order of convergence and conservation of geometric properties are proven analytically and demonstrated numerically on a two-surface NaI model in the adiabatic representation. Although each step of the higher order integrators is more costly, these algorithms become the most efficient ones if higher accuracy is desired; a thousand-fold speedup compared to the second-order trapezoidal rule (the Crank-Nicolson method) was observed for a wavefunction convergence error of 10-10. In a companion paper [J. Roulet, S. Choi, and J. Vaníček, J. Chem. Phys. 150, 204113 (2019)], we discuss analogous, arbitrary-order compositions of the split-operator algorithm and apply both types of geometric integrators to a higher-dimensional system in the diabatic representation.

Optimization of core–valence states of molecules

ABSTRACTCore–valence double-electron ionisation spectra of a few small molecules – carbon monoxide, ammonia, methyl fluoride and thiophene – are presented and analysed using the self-consistent field algorithm introduced by Hans Jørgen Jensen 30 years ago. It confirms the utility of this algorithm, frequently employed to obtain stable and sharp convergence of wave functions for the benefit of calculations of a great variety of molecular properties, thus also for optimisation of core–valence states and for the interpretation of the corresponding spectra.

On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging

We analyse a nonlinear Schrodinger equation for the time-evolution of the wave function of an electron beam, interacting selfconsistently through a Hartree–Fock nonlinearity and through the repulsive Coulomb interaction of an atomic nucleus. The electrons are supposed to move under the action of a time dependent, rapidly periodically oscillating electromagnetic potential. This can be considered a simplified effective single particle model for an X-ray free electron laser. We prove the existence and uniqueness for the Cauchy problem and the convergence of wave-functions to corresponding solutions of a Schrodinger equation with a time-averaged Coulomb potential in the high frequency limit for the oscillations of the electromagnetic potential.

Detailed Tabulation of Atomic Form Factors, Photoelectric Absorption and Scattering Cross Section, and Mass Attenuation Coefficients in the Vicinity of Absorption Edges in the Soft X-Ray (Z=30–36, Z=60–89, E=0.1 keV–10 keV), Addressing Convergence Issues of Earlier Work

Reliable knowledge of the complex x-ray form factor [Re(f ) and f″] and the photoelectric attenuation coefficient (σPE) is required for crystallography, medical diagnosis, radiation safety, and XAFS studies. Discrepancies between currently used theoretical approaches of 200% exist for numerous elements from 1 to 3 keV x-ray energies. The key discrepancies are due to the smoothing of edge structure, the use of nonrelativistic wave functions, and the lack of appropriate convergence of wave functions. This paper addresses these key discrepancies and derives new theoretical results of substantially higher accuracy in near-edge soft x-ray regions. The high-energy limitations of the current approach are also illustrated. The energy range covered is 0.1 to 10 keV. The associated figures and tabulation demonstrate the current comparison with alternate theory and with available experimental data. In general, experimental data are not sufficiently accurate to establish the errors and inadequacies of theory at this level. However, the best experimental data and the observed experimental structure as a function of energy are strong indicators of the validity of the current approach. New developments in experimental measurement hold great promise in making critical comparisons with theory in the near future.

Convergence of the coupled-cluster singles, doubles and triples method

The convergence of coupled-cluster equations for several cases, CCD, CCSD, CCSDT- n and the full CCSDT is investigated. Comparisons are made between the reduced linear equation (RLE) method for accelerating convergence and simple geometric extrapolation techniques, and between energy and wavefunction convergence criteria.