Johannes T. Margraf

Does the ionization potential condition employed in QTP functionals mitigate the self-interaction error?

Though contrary to conventional wisdom, the interpretation of all occupied Kohn-Sham eigenvalues as vertical ionization potentials is justified by several formal and numerical arguments. Similarly, the performance of density functional approximations (DFAs) for fractionally charged systems has been extensively studied as a measure of one- and many-electron self-interaction errors (MSIEs). These complementary perspectives (initially recognized in ab initio dft) are shown to lead to the unifying concept that satisfying Bartletts IP theorem in DFAs mitigates self-interaction errors. In this contribution, we show that the IP-optimized QTP functionals (reparameterization of CAM-B3LYP where all eigenvalues are approximately equal to vertical IPs) display reduced self-interaction errors in a variety of tests including the He2+ potential curve. Conversely, the MSIE-optimized rCAM-B3LYP functional also displays accurate orbital eigenvalues. It is shown that the CAM-QTP and rCAM-B3LYP functionals show improved dissociation limits, fundamental gaps and thermochemical accuracy compared to their parent functional CAM-B3LYP.

Ionization potential optimized double-hybrid density functional approximations

Double-hybrid density functional approximations (DH-DFAs) provide an accurate description of the electronic structure of molecules by semiempirically mixing density functional and wavefunction theory. In this paper, we investigate the properties of the potential used in such approximations. By using the optimized effective potential approach, the consistent Kohn-Sham (KS) potential for a double-hybrid functional (including the second-order perturbational contribution) can be generated. This potential is shown to provide an improved description of orbital energies as vertical ionization potentials (IPs), relative to the perturbation-free KS potential typically used. Based on this observation, we suggest that DH-DFAs should be constructed in such a way that the potential provides accurate orbital energies. As a proof of principle, the B2-PLYP functional is reparameterized to obtain the IP-optimized B2IP-PLYP functional, using a small set of vertical IPs and atomization energies as reference data. This functional is shown to outperform B2-PLYP in a wide range of benchmarks and is en par with the related B2GP-PLYP. In particular, it is shown to be the most reliable choice in electronically difficult and multireference cases.

Theoretical investigation of interactions between palladium and fullerene in polymer

Applying density functional theory (DFT) calculations, we predict the structural and electronic properties of different types of palladium–fullerene polymers. We examine the structures of one- (1-D), two- (2-D), and three-dimensional (3-D) polymers. We find that the most stable polymer is that represented by bonding via the [6,6] position of the fullerene molecules with Pd in a distorted tetrahedral coordination. Special attention is paid to the electronic structure. We demonstrate clearly that changes in the Pd coordination geometry strongly affect the projected density-of-states picture of the 4d orbitals. The energy band gaps in the 1-D and 2-D systems obviously differ from that in the 3-D one; thus, we can directly modify the electronic properties of polymers. The results at the AM1* level of theory for the reduced 1-D polymer show that isolated polarons are the preferred electronic states.

Determination of consistent semiempirical one-centre integrals based on coupled-cluster theory

ABSTRACT We examine the one-centre integrals used in semiempirical molecular orbital theory, for the elements H–Ne. The currently used parameters do not provide good estimates for the relative energies of ionised states of atoms. Directly calculating the one-electron integrals U ss and U pp with coupled-cluster theory and fitting the two-electron repulsion integrals G ss and G pp to accurate coupled-cluster ionisation curves improves this behaviour. Since all the remaining parameters can be derived from these, the number of fitted variables is reduced from seven to two. The two-parameter model provides qualitative agreement with coupled-cluster theory for all ionisation potentials (IPs) and the principal electron affinity (EA). To obtain quantitative agreement for the principal IP and EA, U ss and U pp are included as variables in a four-parameter model. We discuss the new parameters and implications for the development of new, consistent semiempirical Hamiltonians. GRAPHICAL ABSTRACT

Communication: Coupled cluster and many-body perturbation theory for fractional charges and spins

The study of systems with fractional charges and spins has become an extremely important tool to understand errors in approximate electronic structure methods, particularly in the context of density functional theory. Meanwhile, similar studies with wavefunction (WF)-based methods beyond second-order perturbation theory have been lacking. In this contribution, we study the performance of different coupled cluster (CC) and many-body perturbation theory (MBPT)-based methods for fractional charges. The use of the conventional and renormalized formulations of fractional-charge MBPT is discussed. The fractional spin behavior of the coupled cluster doubles (CCD) method is also investigated. Overall, all tested WF methods show very promising performance for the fractional charge problem. CCD is also quite accurate for the fractional spin problem in He+ across most of the range, although it breaks down to near Hartree-Fock quality in the strongly correlated limit. Beyond the study of fractional charge and spin curves, the implementation of CC methods with fractional occupation numbers offers a promising route to treating problems with multi-reference character in a single-reference framework.

Rigorous and Empirical Approaches to Correlated Single-Particle Theories

In this contribution, we will discuss how electron correlation is described in different types of single-particle approaches, namely those based on many-body theory, density functional theory, and semiempirical approximations. Our goal is to provide some insight into how the term “correlation” is used in different communities and what the physical and computational advantages and drawbacks of the different approaches are. This interdisciplinary perspective will illuminate how researchers with different backgrounds think about electron correlation in single-particle methods. In this context, the main focus lies on MO-like theories such as KS-DFT and semiempirical methods, since these are the most common “general-purpose” approaches in quantum chemistry, which allow predicting ground state and excited state energies and properties.

Valence and charge-transfer optical properties for some SinCm (m, n ≤ 12) clusters: Comparing TD-DFT, complete-basis-limit EOMCC, and benchmarks from spectroscopy

Accurate optical characterization of the closo-Si12C12 molecule is important to guide experimental efforts toward the synthesis of nano-wires, cyclic nano-arrays, and related array structures, which are anticipated to be robust and efficient exciton materials for opto-electronic devices. Working toward calibrated methods for the description of closo-Si12C12 oligomers, various electronic structure approaches are evaluated for their ability to reproduce measured optical transitions of the SiC2, Si2Cn (n = 1-3), and Si3Cn (n = 1, 2) clusters reported earlier by Steglich and Maier [Astrophys. J. 801, 119 (2015)]. Complete-basis-limit equation-of-motion coupled-cluster (EOMCC) results are presented and a comparison is made between perturbative and renormalized non-iterative triples corrections. The effect of adding a renormalized correction for quadruples is also tested. Benchmark test sets derived from both measurement and high-level EOMCC calculations are then used to evaluate the performance of a variety of density functionals within the time-dependent density functional theory (TD-DFT) framework. The best-performing functionals are subsequently applied to predict valence TD-DFT excitation energies for the lowest-energy isomers of SinC and Sin-1C7-n (n = 4-6). TD-DFT approaches are then applied to the SinCn (n = 4-12) clusters and unique spectroscopic signatures of closo-Si12C12 are discussed. Finally, various long-range corrected density functionals, including those from the CAM-QTP family, are applied to a charge-transfer excitation in a cyclic (Si4C4)4 oligomer. Approaches for gauging the extent of charge-transfer character are also tested and EOMCC results are used to benchmark functionals and make recommendations.