ller-Plesset Theory Research Articles

N5-Scaling Excited-State-Specific Perturbation Theory

We show that by working in a basis similar to that of the natural transition orbitals and using a modified zeroth-order Hamiltonian, the cost of a recently introduced perturbative correction to excited-state mean field theory can be reduced from seventh to fifth order in the system size. The (occupied)2(virtual)3 asymptotic scaling matches that of ground-state second-order Møller-Plesset theory but with a significantly higher prefactor because the bottleneck is iterative: it appears in the Krylov-subspace-based solution of the linear equation that yields the first-order wave function. Here, we discuss the details of the modified zeroth-order Hamiltonian we use to reduce the cost and the automatic code generation process we used to derive and verify the cost scaling of the different terms. Overall, we find that our modifications have little impact on the method's accuracy, which remains competitive with singles and doubles equation-of-motion coupled cluster.

Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller-Plesset Perturbation Theory.

We present a systematically improvable tensor hypercontraction (THC) factorization based on interpolative separable density fitting (ISDF). We illustrate algorithmic details to achieve this within the framework of Becke's atom-centered quadrature grid. A single ISDF parameter cISDF controls the trade-off between accuracy and cost. In particular, cISDF sets the number of interpolation points used in THC, NIP = cISDF × NX with NX being the number of auxiliary basis functions. In conjunction with the resolution-of-the-identity (RI) technique, we develop and investigate the THC-RI algorithms for cubic-scaling exact exchange for Hartree-Fock and range-separated hybrids (e.g., ωB97X-V) and quartic-scaling second- and third-order Møller-Plesset theory (MP2 and MP3). These algorithms were evaluated over the W4-11 thermochemistry (atomization energy) set and A24 noncovalent interaction benchmark set with standard Dunning basis sets (cc-pVDZ, cc-pVTZ, aug-cc-pVDZ, and aug-cc-pVTZ). We demonstrate the convergence of THC-RI algorithms to numerically exact RI results using ISDF points. Based on these, we make recommendations on cISDF for each basis set and method. We also demonstrate the utility of THC-RI exact exchange and MP2 for larger systems such as water clusters and C20. We stress that more challenges await in obtaining accurate and numerically stable THC factorization for wave function amplitudes as well as for the space spanned by virtual orbitals in large basis sets and implementing sparsity-aware THC-RI algorithms.

Convergence of many-body wave-function expansions using a plane-wave basis: From homogeneous electron gas to solid state systems

Using the finite simulation-cell homogeneous electron gas (HEG) as a model, we investigate the convergence of the correlation energy to the complete-basis-set (CBS) limit in methods utilizing plane-wave wave-function expansions. Simple analytic and numerical results from second-order M\o{}ller-Plesset theory (MP2) suggest a $1/M$ decay of the basis-set incompleteness error where $M$ is the number of plane waves used in the calculation, allowing for straightforward extrapolation to the CBS limit. As we shall show, the choice of basis-set truncation when constructing many-electron wave functions is far from obvious, and here we propose several alternatives based on the momentum transfer vector, which greatly improve the rate of convergence. This is demonstrated for a variety of wave-function methods, from MP2 to coupled-cluster doubles theory and the random-phase approximation plus second-order screened exchange. Finite basis-set energies are presented for these methods and compared with exact benchmarks. A transformation can map the orbitals of a general solid state system onto the HEG plane-wave basis and thereby allow application of these methods to more realistic physical problems. We demonstrate this explicitly for solid and molecular lithium hydride.

Experimental and theoretical study of core-valence double photoionization of OCS

O $1s$, C $1s$, and S $2p$ core-valence double ionization electron spectra of the OCS molecule have been obtained experimentally by a time-of-flight photoelectron-photoelectron coincidence spectroscopy technique. In order to analyze and assign the spectral features observed, we present a protocol for computing core-valence ionization energies of such systems. The protocol is based on a restricted active space multiconfigurational self-consistent field (MCSCF) methodology with a freeze-relax procedure to guarantee a correct core-valence state root index without variational collapse. Corrections for extended dynamical correlation and core-core correlation, respectively, are made by multiconfigurational perturbation theory and by uncontracted basis set M\o{}ller-Plesset theory. Envisioning applications to larger molecules, a spin-restricted open-shell density functional method is also applied for the lowest core-valence energies. Furthermore, cross sections through a scheme for computing multiatom Auger transitions generating core-valence holes are presented. We find that the procedure outlined is capable of deriving the energy onset of core-valence ionization within a fraction of an eV and that assignments can be made of the most salient spectral features.

Empirical functionals for reduced-density-matrix-functional theory

We present fully empirical exchange-correlation functionals to be used within reduced-density-matrix-functional theory (RDMFT). These are of the popular $J\text{\ensuremath{-}}K$ form [involving only Coulomb- $(J)$ and exchange- $(K)$ type integrals over the natural orbitals], where the function of the occupation numbers that multiplies the Fock orbital term is written as a Pad\'e approximant. The coefficients of the Pad\'e approximant are optimized for a test set of eight molecules, and then refined for a larger set of $35\phantom{\rule{0.3em}{0ex}}\text{molecules}$. Two different approaches were tried, either keeping the self-interaction terms, or by removing them explicitly from the functional. The functionals thus obtained involve very few parameters, but are able to outperform other RDMFT functionals, yielding correlation energies that are, on average, even slightly better than second-order M\o{}ller-Plesset theory.

Microscopic models for self-trapped excitons in [formula omitted]-PTCDA

The three slowest radiative recombination channels observed in photoluminescence (PL) spectra of α -PTCDA single crystals can be assigned to radiative recombination between two oppositely charged molecules in different relative positions, and to an excimer in a stack geometry. For both kinds of self-trapped excitons, we construct dimer geometries involving changes of the inter-molecular distance and internal deformations of each molecule. The Stokes shift resulting from self-trapping along the inter-molecular separation is analysed with a combination of second-order M ø ller–Plesset theory (MP2) and configuration interaction of singles (CIS), and the red shift arising from the internal deformations with time-dependent density functional theory (TD-DFT). The combination of the observed PL energies with these microscopic calculations of the Stokes shift allows an assignment of the lowest charge transfer transition in the undeformed crystal. Along the stacking direction, it occurs at 2.06 eV, far below previous estimates based on micro-electrostatic calculations.

The effect of electron correlation on the structure and properties of the benzenium ion

Ab initio restricted Hartree—Fock (RHF) calculations which incorporate electron correlation via M∅ller—Plesset theory are presented for the isoelectronic species benzene and benzenium, (C 6H 7) +. Significant geometrical differences are found between this study and the results of previous studies at the RHF level. The proton affinity of benzene is predicted to be 184.6 kcal mol −1, in excellent agreement with experiment. A limited potential surface study predicts protonation at a single carbon atom site. Various one-electron properties are reported for the predicted equilibrium structures.