Chapter 7 - Density-Dependent Exchange–Correlation Potentials Derived From highly Accurate Ab initio Calculations

Orbital-dependent exchange-correlation functionals and potentials play an increasingly important role in Density Functional Theory (DFT). Methods which use explicit orbital-dependent functionals can be viewed as a natural extension to the standard Kohn–Sham (KS) procedure in DFT, that traditionally have used functionals with explicit density-dependence but only implicit orbital-dependence. Ab initio DFT, invented at the Quantum Theory Project, is the method which could define rigorous orbital-dependent exchange-correlation functionals and potentials in the context of KS DFT theory. The local and multiplicative exchange-correlation potentials are derived from a general theoretical framework based on the density condition in KS theory and from coupled-cluster theory and many-body perturbation theory. Ab initio DFT guarantees to converge to the right answer in the correlation and basis set limit, just as does ab initio Wave Function Theory (WFT) and solves in a rigorous way most of the shortcomings of standard density-dependent KS DFT. It is also the route toward understanding the relationships between traditional ab initio WFT and DFT. The Optimized Effective Potential ‘journey’ on the borderline of WFT and DFT was inspired and possible only because of the Quantum Theory Project where we stayed as postdocs in 1999–2001. It seems to us then we were in the right place and at the right time, and certainly with the right people. The QTP scientific melting pot and Sanibel's meetings gave us an excellent possibility to work together, learn and hopefully solve many important scientific problems.

A new approximate non-iterative procedure to obtain accurate correlation and exchange-correlation potentials of Kohn-Sham (KS) density functional theory (DFT) is presented. By carrying out only one step of the correlated optimized effective potential (OEP) iterations following the standard iterative exchange-only OEP, one can recover accurate correlation potentials corresponding to the orbital-dependent second-order many-body perturbation theory [MBPT(2)] energy functional that are hardly discernible from those obtained by the more expensive, fully iterative procedure. This new ‘one-step’ OEP-MBPT(2) algorithm reflects the non-iterative, perturbative algorithm of standard, canonical MBPT(2) of ab initio wave function theory, while it allows the correlation potentials to readjust and include the majority of the MBPT(2) correlation effect. It is also flexible in the treatment of exchange and the Hartree-Fock orbitals may be used in lieu of the exchange-only OEP orbitals, when the correlation or exchange-correlation potential is of interest.

Theoretical insights into the coordination structures, stabilities and electronic spectra of Cm3+ species at the gibbsite-water interface: A computational study combing ab initio molecular dynamics and wave function theory

Dedicated to the memory of Björn Roos (1937–2010), one of the fathers of modern multiconfigurational quantum chemistry, who also cared deeply about chemical applications, and a fun and inspiring friend to countless theoretically oriented chemists.

This chapter summarizes the recent applications of ab initio wave function theory (WFT) to a variety of properties of water ices, liquid water, and solid CO2 as well as the embedded fragmentation techniques that enable such applications at ab initio theory levels of second-order MP (MP2) and coupled-cluster with singles and doubles (CCSD). They mark the beginning of a new era of condensed matter simulations based on systematic ab initio WFT. The chapter also reviews the embedded-fragment methodology taking an application to a solid as an example. It has enabled ab initio calculations of a wide variety of properties of molecular crystals, amorphous solids, and liquids at finite temperature and pressure. Finally, the chapter addresses the different thermodynamic conditions (temperature and pressure) required to keep "MP2-water" in the liquid phase from the ambient conditions.

Mixed-ligand metallocene complexes serve as crucial precursors in organometallic actinide chemistry. However, a systematic and comprehensive understanding of how ligands influence the electronic structures and physicochemical properties of these compounds remains scarce. Hence, relativistic density functional theory (DFT) and ab initio wave function theory (WFT) calculations were carried out to elucidate the impact of auxiliary ligands on the bonding, redox properties, and electronic absorption spectra of uranium(IV) metallocene complexes, Cp*2U(NR2)X (Cp* = C5Me5, R = SiMe3, and X = F, Cl, Br, I, NCO, and OEt). The calculated redox potentials display high agreement with the available experimental values, with absolute deviations less than 0.26 V. Additionally, the simulated electronic absorption spectra show close alignment with the available experimental results, enabling the precise identification of the two primary absorption regions in the experimental spectra. This study further reveals strong linear correlations (R2 > 0.97) between ligand field parameters and the computed reduction potentials, orbital interactions, and electronic transition energies. These correlations underscore the pivotal role of ligand electron-donating or electron-withdrawing abilities in modulating the electronic structures of tetravalent uranium complexes. These findings provide a solid theoretical foundation for guiding experimental efforts to tailor the properties of organoactinide compounds via strategic ligand modification.

Assessment of the accuracy of methods including 29 DFT methods and 2 ab initio wave function theory (WFT) methods for predicting (27)Al nuclear magnetic resonance shielding tensors of aquated Al(III) species was carried out. Among all of the tested methods, HF and MP2 methods give the best performance for the calculations of chemical shifts. Among all of the DFT methods with GIAO calculations, O3LYP and MPWKCIS1K are the most accurate models for calculations of chemical shifts, followed in order by BHandHLYP, B98, B97-1, mPW1PW91, PBE1PBE, and MPW1KCIS. Among all of the DFT methods with CSGT calculations, VSXC is the best method for the prediction of chemical shifts, followed in order by TPSSh, B97-2, O3LYP, TPSS, TPSS1KCIS, MPWKCIS1K, BHandHLYP, B97-1, and B98. The popular B3LYP method overestimates largely the chemical shifts with both GIAO and CSGT methods. The calculated results indicate that the predictions of (27)Al chemical shifts on the base of the model that includes both explicit solvent effect and bulk solvent effect are most accurate for aquated Al(III) species.

The tetraoxo pertechnetate anion (TcO4(-)) is of great interest for nuclear waste management and radiopharmceuticals. To elucidate its electronic structure and to compare with that of its lighter congener MnO4(-), the photoelectron and electronic absorption spectra of MnO4(-) and TcO4(-) are investigated with density functional theory (DFT) and ab initio wave function theory (WFT). The vertical electron detachment energies (VDEs) of MnO4(-) obtained with the CR-EOM-CCSD(T) method are in good agreement with the lowest two experimental VDEs; the differences are less than 0.1 eV, representing a significant improvement over the IP-EOM-CCSD(T) result in the literature. Combining our CCSD(T) and CR-EOM-CCSD(T) results, the first five VDEs of TcO4(-) are estimated between 5 and 10 eV with an estimated accuracy of about ±0.2 eV. The vertical excitation energies are determined by using TD-DFT, CR-EOM-CCSD(T), and RAS-PT2 methods. The excitation energies and the assignments of the spectra are analyzed and partly improved. They are compared with reported SAC-CI results and available experimental data. Both dynamic and nondynamic electron correlations are important in the ground and excited states of MnO4(-) and TcO4(-). Nondynamical correlations are particularly relevant in TcO4(-) for reliable prediction of excitation energies. In TcO4(-) one Rydberg state interlaces but does not mix with the valence excited states, and it disappears in the condensed phase.

In many cases, the dynamic correlation can be calculated quite accurately and at a fairly low computational cost in Kohn-Sham density-functional theory (KS-DFT), using current standard approximate functionals. However, in general, KS-DFT does not treat static correlation effects (near degeneracy) adequately which, on the other hand, can be described in wave-function theory (WFT), for example, with a multiconfigurational self-consistent field (MCSCF) model. It is therefore of high interest to develop a hybrid model which combines the best of both WFT and DFT approaches. The merge of WFT and DFT can be achieved by splitting the two-electron interaction into long-range and short-range parts. The long-range part is then treated by WFT and the short-range part by DFT. In this work the authors consider the so-called "erf" long-range interaction erf(micror12)/r12, which is based on the standard error function, and where mu is a free parameter which controls the range of the long-/short-range decomposition. In order to formulate a general method, they propose a recipe for the definition of an optimal microopt parameter, which is independent of the approximate short-range functional and the approximate wave function, and they discuss its universality. Calculations on a test set consisting of He, Be, Ne, Mg, H2, N2, and H2O yield microopt approximately 0.4 a.u.. A similar analysis on other types of test systems such as actinide compounds is currently in progress. Using the value of 0.4 a.u. for micro, encouraging results are obtained with the hybrid MCSCF-DFT method for the dissociation energies of H2, N2, and H2O, with both short-range local-density approximation and PBE-type functionals.

Theoretical investigations using density functional theory (DFT) and ab initio wavefunction theory (WFT) have been performed to understand the geometric and electronic structures, chemical bonding, and structural transformation of 5dx6s2-metal doped triboron clusters MB3 (M = La, Ta, Re, Ir; x = 1, 3, 5, 7). Global-minimum structural searches find that early-metal doped MB3 (M = La, Ta) clusters adopt a two-dimensional (2D) planar structure, with σ- and π-type delocalized molecular orbitals (MOs) consisting of M-5d and B-2p atomic orbitals (AOs) identified by chemical bonding analysis. In contrast, late-metal doped MB3 (M = Re, Ir) clusters prefer three-dimensional (3D) structures of near-pyramidal and triangular pyramid geometries, respectively, which exhibit enhanced stability involving σ- and δ-type M(5d)-B(2p) interactions. The M-B bonding in the Re and Ir borides is more covalent than the La and Ta ones due to less charge transfer and similar orbital energies of late 5d-metals and boron. Moreover, the Jahn-Teller effect leads to MO mixing and electron redistribution, thus enlarging the HOMO-LUMO gaps. This work provides insights into the nature of the structural stability in triboron clusters induced by metal doping.

A benchmark database of forward and reverse barrier heights for 19 non-hydrogen-transfer reactions has been developed by using Weizmann 1 calculations, and 29 DFT methods and 6 ab initio wave-function theory (WFT) methods have been tested against the new database as well as against an older database for hydrogen atom transfer reactions. Among the tested hybrid DFT methods without kinetic energy density, MPW1K is the most accurate model for calculations of barrier heights. Among the tested hybrid meta DFT methods, BB1K and MPWB1K are the two most accurate models for the calculations of barrier heights. Overall, the results show that BB1K and MPWB1K are the two best DFT methods for calculating barrier heights, followed in order by MPW1K, MPWKCIS1K, B1B95, MPW1B95, BH and HLYP, B97-2, mPW1PW91, and B98. The popular B3LYP method has a mean unsigned error four times larger than that of BB1K. Of the methods tested, QCISD(T) is the best ab initio WFT method for barrier height calculations, and QCISD is second best, but QCISD is outperformed by the BB1K, MPWB1K, MPWKCIS1K, and MPW1K methods.

The ground- and excited-state geometries and electronic structures of the isoelectronic series of molecules UN2, NUO+, and UO22+ are investigated by using relativistic density functional theory (DFT) and ab initio wavefunction theory (WFT). Scalar relativistic and spin–orbit-coupled quantum chemical methods at the CASPT2, RASPT2, CCSD(T), DFT and TDDFT levels are applied. Relativistic effects as elucidated by Pekka Pyykko play an important role in these uranium compounds, in particular for the excited states. The three molecular species exhibit significantly different spectroscopic properties, concerning their excitation energies, bond lengths and vibrations. Density functional approaches yield qualitatively correct results for the ground states and the valence → U.7s,6d excited states. However, the performance of TDDFT for valence → U.5f type excitations (in particular of UN2 and NUO+) is less satisfactory, indicating the importance of the self-interaction correction for such excitations.

Kohn-Sham density functional theory has been tremendously successful in chemistry and physics. Yet, it is unable to describe the energy degeneracy of spin-multiplet components with any approximate functional. This work features two contributions. (1) We present a multistate density functional theory (MSDFT) to represent spin-multiplet components and to determine multiplet energies. MSDFT is a hybrid approach, taking advantage of both wave function theory and density functional theory. Thus, the wave functions, electron densities and energy density-functionals for ground and excited states and for different components are treated on the same footing. The method is illustrated on valence excitations of atoms and molecules. (2) Importantly, a key result is that for cases in which the high-spin components can be determined separately by Kohn-Sham density functional theory, the transition density functional in MSDFT (which describes electronic coupling) can be defined rigorously. The numerical results may be explored to design and optimize transition density functionals for configuration coupling in multiconfigurational DFT.

Transition states for Diels-Alder reactions are strongly correlated, as evidenced by high-to-very-high M diagnostics, and therefore they require treatment by multireference methods. Multiconfiguration pair-density functional theory (MC-PDFT) combines a multiconfiguration wave function with a functional of the electron density and the on-top pair density to calculate the electronic energy for strongly correlated systems at a much lower cost than wave function methods that do not employ density functionals. Here we apply MC-PDFT to the Diels-Alder cycloaddition reaction of 1,3-butadiene with ethylene, where two kinds of reaction paths have been widely studied: concerted synchronous paths and diradical stepwise paths. The lowest-energy reaction path is now known to be a concerted synchronous one, and a method's ability to predict this is an important test. By comparison to the best available theoretical results in the literature, we test the accuracy of MC-PDFT with several choices of on-top functional for geometries and enthalpies of stable structures along both paths and for the transition state geometries. We also calculate the Arrhenius activation energies for both paths and compare these to experiment. We also compare to Kohn-Sham density functional theory (KS-DFT) with selected exchange-correlation functionals. CAS-PDFT gives consistently good energies and geometries for both the concerted and stepwise mechanisms, but none of the KS-DFT functionals gives accurate activation energies for both. The stepwise transition state is very strongly correlated, and MC-PDFT can treat it, but KS-DFT (which involves a single-configuration treatment) has larger errors. The results confirm that using a multiconfigurational reference function for strongly correlated transition states can significantly improve the reliability and that MC-PDFT can provide good accuracy at a much lower computational cost than competing multireference methods.

The high computational cost of correlated wavefunction theory (WFT) calculations has motivated the development of numerous methods to partition the description of large chemical systems into smaller subsystem calculations. For example, WFT-in-DFT embedding methods facilitate the partitioning of a system into two subsystems: a subsystem A that is treated using an accurate WFT method, and a subsystem B that is treated using a more efficient Kohn-Sham density functional theory (KS-DFT) method. Representation of the interactions between subsystems is non-trivial, and often requires the use of approximate kinetic energy functionals or computationally challenging optimized effective potential calculations; however, it has recently been shown that these challenges can be eliminated through the use of a projection operator. This dissertation describes the development and application of embedding methods that enable accurate and efficient calculation of the properties of large chemical systems. Chapter 1 introduces a method for efficiently performing projection-based WFT-in-DFT embedding calculations on large systems. This is accomplished by using a truncated basis set representation of the subsystem A wavefunction. We show that naive truncation of the basis set associated with subsystem A can lead to large numerical artifacts, and present an approach for systematically controlling these artifacts. Chapter 2 describes the application of the projection-based embedding method to investigate the oxidative stability of lithium-ion batteries. We study the oxidation potentials of mixtures of ethylene carbonate (EC) and dimethyl carbonate (DMC) by using the projection-based embedding method to calculate the vertical ionization energy (IE) of individual molecules at the CCSD(T) level of theory, while explicitly accounting for the solvent using DFT. Interestingly, we reveal that large contributions to the solvation properties of DMC originate from quadrupolar interactions, resulting in a much larger solvent reorganization energy than that predicted using simple dielectric continuum models. Demonstration that the solvation properties of EC and DMC are governed by fundamentally different intermolecular interactions provides insight into key aspects of lithium-ion batteries, with relevance to electrolyte decomposition processes, solid-electrolyte interphase formation, and the local solvation environment of lithium cations.