Wave Function-based Correlation Methods Research Articles

Massively parallel implementation of gradients within the random phase approximation: Application to the polymorphs of benzene.

The Random-Phase approximation (RPA) provides an appealing framework for semi-local density functional theory. In its Resolution-of-the-Identity (RI) approach, it is a very accurate and more cost-effective method than most other wavefunction-based correlation methods. For widespread applications, efficient implementations of nuclear gradients for structure optimizations and data sampling of machine learning approaches are required. We report a well scaling implementation of RI-RPA nuclear gradients on massively parallel computers. The approach is applied to two polymorphs of the benzene crystal obtaining very good cohesive and relative energies. Different correction and extrapolation schemes are investigated for further improvement of the results and estimations of error bars.

The Ground State Electronic Energy of Benzene.

We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground-state energy of the benzene molecule in a standard correlation-consistent basis set of double-ζ quality. As a broad international endeavor, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around -863 mEH. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 mEH), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward.

BDF: A relativistic electronic structure program package.

The BDF (Beijing Density Functional) program package is in the first place a platform for theoretical and methodological developments, standing out particularly in relativistic quantum chemical methods for chemistry and physics of atoms, molecules, and periodic solids containing heavy elements. These include the whole spectrum of relativistic Hamiltonians and their combinations with density functional theory for the electronic structure of ground states as well as time-dependent and static density functional linear response theories for electronically excited states and electric/magnetic properties. However, not to be confused by its name, BDF nowadays comprises also of standard and novel wave function-based correlation methods for the ground and excited states of strongly correlated systems of electrons [e.g., multireference configuration interaction, static-dynamic-static configuration interaction, static-dynamic-static second-order perturbation theory, n-electron valence second-order perturbation theory, iterative configuration interaction (iCI), iCI with selection plus PT2, and equation-of-motion coupled-cluster]. Additional features of BDF include a maximum occupation method for finding excited states of Hartree-Fock/Kohn-Sham (HF/KS) equations, a very efficient localization of HF/KS and complete active space self-consistent field orbitals, and a unique solver for exterior and interior roots of large matrix eigenvalue problems.

Dual Basis Set Approach for Density Functional and Wave Function Embedding Schemes

A dual basis (DB) approach is proposed which is suitable for the reduction of the computational expenses of the Hartree-Fock, Kohn-Sham, and wave function-based correlation methods. The approach is closely related to the DB approximation of Head-Gordon and co-workers [ J. Chem. Phys. 2006 , 125 , 074108 ] but specifically designed for embedding calculations. The new approach is applied to our variant of the projector-based embedding theory utilizing the Huzinaga-equation, multilevel local correlation methods, and combined density functional-multilevel local correlation approximations. The performance of the resulting DB density functional and wave function embedding methods is evaluated in extensive benchmark calculations and also compared to that of the corresponding embedding schemes exploiting the mixed-basis approximation. Our results show that, with an appropriate combination of basis sets, the DB approach significantly speeds up the embedding calculations, and, for chemical processes where the electronic structure considerably changes, it is clearly superior to the mixed-basis approximation. The results also demonstrate that the DB approach, if integrated with the mixed-basis approximation, efficiently eliminates the major weakness of the latter, and the combination of the DB and mixed-basis schemes is the most efficient strategy to accelerate embedding calculations.

Communication: The failure of correlation to describe carbon=carbon bonding in out-of-plane bends.

Carbon-carbon multiply bonded systems are improperly described with standard, wave function-based correlation methods and Gaussian one-particle basis sets implying that thermochemical, spectroscopic, and potential energy surface computations are consistently erroneous. For computations of vibrational modes, the out-of-plane bends can be reported as imaginary at worst or simply too low at best. Utilizing the simplest of aromatic structures (cyclopropenylidene) and various levels of theory, this work diagnoses this known behavior as a combined one-particle and n-particle basis set effect for the first time. In essence, standard carbon basis sets do not describe equally well sp, sp2, and sp3 hybridized orbitals, and this effect is exacerbated post-Hartree-Fock by correlation methods. The latter allow for occupation of the π and π* orbitals in the expanded wave function that combine with the hydrogen s orbitals. As a result, the improperly described space is non-physically stabilized by post-Hartree-Fock correlation. This represents a fundamental problem in wavefunction theory for describing carbon.

Wavefunction-based electron correlation methods for solids

In this article we provide an overview of the most common ways of treating electron correlation effects in 3D-periodic systems with some emphasize on wavefunction-based correlation methods such as the method of increments and the local MP2 method implemented in the Cryscor program. We discuss strengths and weaknesses of the different approaches and give examples for their application. Additionally, for the method of increments we discuss recent developments for its application to open shell systems and problems related to the treatment of graphene sheets.

Accurate quantum-chemical description of gold complexes with pyridine and its derivatives

Interaction of gold with pyridine and its derivatives was studied by means of different wavefunction-based correlation methods and standar DFT functionals as well as accounting for dispersion correction. Comparison of the calculated binding energies with benchmark CCSD(T)results allows us to find an appropriate computational method, when considering the two structures reflecting the interaction of gold with the lone pair at nitrogen, on the one hand, and with the π-system of pyridine, on the other hand. Additional binding sites were evaluated, when performing potential energy surface calculations and structure optimizations. The enhancement of the interaction energy due to donor substituents in the 4-position of the pyridine molecule has been investigated.

The role of electron correlations in the binding properties of Ca, Sr, and Ba

In order to apply wavefunction-based correlation methods to solids it isnecessary to have reliable Hartree–Fock (HF) results for the infinite systemof interest. We performed Hartree–Fock calculations for the group 2 heavyalkali-earth metals Ca, Sr, and Ba. For that, basis sets of valence-double-ζ quality have been optimized for the periodic systems. In all cases small-core pseudopotentialswere used to deal with the scalar-relativistic effects. We determine the cohesive energies,the equilibrium volumes and the bulk moduli of the systems at the Hartree–Fock level andcompare them with experimental data as well as the results of density functionaltheory calculations. Relativistic effects in the case of Ba are estimated by using anon-relativistic pseudopotential. The comparative HF versus the density functionaltheory (DFT) study of the electronic structures of Ca, Sr, and Ba has been performed.

Hartree–Fock ground-state properties for the group 1 alkali metals and the group 11 noblemetals

In order to use wavefunction-based correlation methods in solids it is necessary to havereliable Hartree–Fock results for the infinite system of interest. Therefore weperformed Hartree–Fock calculations for the group 1 alkali metals (Li to Cs)and group 11 noble metals (Cu, Ag and Au). We optimized a basis set ofvalence-double-ζ quality for the periodic system. For the lighter atoms all-electron basis sets are applied,whereas for the heavier atoms small-core pseudopotentials with the corresponding basis setswere used to deal with the scalar-relativistic effects. We determine the cohesive energy, thelattice constant and the bulk modulus of the systems at the Hartree–Fock level. We use thecounterpoise correction for the free atom to minimize the basis set superposition erroroccurring for finite basis sets. The effects due to the counterpoise correction not only forthe cohesive energy but also for the lattice structure and bulk modulus are discussed indetail.

Role of face-to-face and edge-to-face aromatic interactions in the inclusion complexation of cyclobis(paraquat-p-phenylene): a theoretical study.

A B3LYP/6-31G(d,p) and MP2/6-31G(d,p)//B3LYP/6-31G(d,p) computational study of the gas-phase complexation of cyclobis(paraquat-p-phenylene) (1(4+)) with four typical aromatic guests, namely, 1,4-dimethoxybenzene (2), 1,5-dimethoxynaphthalene (3), benzidine (4), and tetrathiafulvalene (5), has been carried out. The structure of the host has been successively split into two responsible substructures, respectively, for the face-to-face and edge-to-face interactions with the guests. The sum of the two interactions calculated at the B3LYP/6-31G(d,p) and MP2/6-31G(d,p)//B3LYP/6-31G(d,p) levels for each guest proved to be in good agreement with the overall binding energy of the host calculated at the corresponding level of theory. The results show that the binding of the complexes is primarily due to London dispersion interactions which require wave function-based correlation methods for an adequate description. Face-to-face interactions are about 1 order of magnitude more important than edge-to-face interactions in determining the overall binding energy. While edge-to-face interactions essentially depend on London dispersion forces, face-to-face interactions depend about one-half on electrostatic and frontier orbital contributions (the latter being more important) and the other half on London dispersion forces.