Generalized perturbative singles corrections to the random phase approximation method: Impact on noncovalent interaction energies of closed- and open-shell dimers.

The post-Kohn-Sham (KS) random phase approximation (RPA) method may provide a poor description of interaction energies of weakly bonded molecules due to inherent density errors in approximate KS functionals. To overcome these errors, we develop a generalized formalism to incorporate perturbative singles (pS) corrections to the RPA method using orbital rotations as a perturbation parameter. The pS schemes differ in the choice of orbital-rotation gradient and Hessian. We propose a pS scheme termed RPA singles (RPAS)[Hartree-Fock (HF)] that uses the RPA orbital-rotation gradient and time-dependent HF Hessian. This correction reduces the errors in noncovalent interaction energies of closed- and open-shell dimers. For the open-shell dimers, the RPAS(HF) method leads to a consistent error reduction by 50% or more compared to the RPA method for the cases of hydrogen-bonding, metal-solvent, carbene-solvent, and dispersion interactions. We also find that the pS corrections are more important in error reduction compared to higher-order exchange corrections to the RPA method. Overall, for open shells, the RPAS(HF)-corrected RPA method provides chemical accuracy for noncovalent interactions and is more reliable than other perturbative schemes and dispersion-corrected density functional approximations, highlighting its importance as a reliable beyond-RPA correction.

Quantifying the Impact of Halogenation on Intermolecular Interactions and Binding Modes of Aromatic Molecules.

Halogenation of aromatic molecules is frequently used to modulate intermolecular interactions with ramifications for optoelectronic and mechanical properties. In this work, we accurately quantify and understand the nature of intermolecular interactions in perhalogenated benzene (PHB) clusters. Using benchmark binding energies from the fixed-node diffusion Monte Carlo (FN-DMC) method, we show that generalized Kohn-Sham semicanonical projected random phase approximation (GKS-spRPA) plus approximate exchange kernel (AKX) provides reliable interaction energies with mean absolute error (MAE) of 0.23 kcal/mol. Using the GKS-spRPA+AXK method, we quantify the interaction energies of several binding modes of PHB clusters ((C6X6)n; X = F, Cl, Br, I; n = 2, 3). For a given binding mode, the interaction energies increase 3-4 times from X = F to X = I; the X-X binding modes have energies in the range of 2-4 kcal/mol, while the π-π binding mode has interaction energies in the range of 4-12 kcal/mol. SAPT-DFT-based energy decomposition analysis is then used to show that the equilibrium geometries are dictated primarily by the dispersion and exchange interactions. Finally, we test the accuracy of several dispersion-corrected density functional approximations and show that only the r2SCAN-D4 method has a low MAE and correct long-range behavior, which makes it suitable for large-scale simulations and for developing structure-function relationships of halogenated aromatic systems.

Excited state dynamics of a spontaneously generated TTF radical cation inside a water-soluble nanocage.

Supramolecular cavities have been traditionally used to stabilize reactive redox intermediates. Recently with the success of multiple new photoredox catalytic strategies that use supramolecular cages, there is a growing demand for photogeneration strategies of diverse reactive intermediates inside confined spaces, which will drive enzyme-like catalysis in real time. Here we report the excited state dynamics of a redox-active TTF radical cation and its corresponding dimethyl-derivative DiMeTTF inside a confined supramolecular cavity. We prepare the radical cation by spontaneous oxidation of neutral TTF upon incarceration inside a water-soluble nanocage Pd6L412+, and characterize it with a combination of resonance Raman and electron paramagnetic resonance spectroscopy. Using broadband transient absorption spectroscopy, we demonstrate that the confined native TTF radical cation and its dimethyl derivative upon photoexcitation rapidly de-excite to form the hot ground state, thereby inhibiting further oxidation to a TTF+2 dication. We discuss our results in the context of excited state crossings of the radical cation potentials as well as modifying the cage energetics to generate a stable dication. Our work has important implications for the usage of such radical cations for photoactivated catalysis.

Static polarizabilities within the generalized Kohn-Sham semicanonical projected random phase approximation (GKS-spRPA).

An analytical implementation of static dipole polarizabilities within the generalized Kohn-Sham semicanonical projected random phase approximation (GKS-spRPA) method for spin-restricted closed-shell and spin-unrestricted open-shell references is presented. General second-order analytical derivatives of the GKS-spRPA energy functional are derived using a Lagrangian approach. By resolution-of-the-identity and complex frequency integration methods, an asymptotic O(N4⁡log(N)) scaling of operation count and O(N3) scaling of storage is realized, i.e., the computational requirements are comparable to those for GKS-spRPA ground state energies. GKS-spRPA polarizabilities are assessed for small molecules, conjugated long-chain hydrocarbons, metallocenes, and metal clusters, by comparison against Hartree-Fock (HF), semilocal density functional approximations (DFAs), second-order Møller-Plesset perturbation theory, range-separated hybrids, and experimental data. For conjugated polydiacetylene and polybutatriene oligomers, GKS-spRPA effectively addresses the "overpolarization" problem of semilocal DFAs and the somewhat erratic behavior of post-PBE RPA polarizabilities without empirical adjustments. The ensemble averaged GKS-spRPA polarizabilities of sodium clusters (Nan for n = 2, 3, …, 10) exhibit a mean absolute deviation comparable to PBE with significantly fewer outliers than HF. In conclusion, analytical second-order derivatives of GKS-spRPA energies provide a computationally viable and consistent approach to molecular polarizabilities, including systems prohibitive for other methods due to their size and/or electronic structure.

Understanding the role of intermolecular interactions between lissoclimides and the eukaryotic ribosome.

Natural products that target the eukaryotic ribosome are promising therapeutics to treat a variety of cancers. It is therefore essential to determine their molecular mechanism of action to fully understand their mode of interaction with the target and to inform the development of new synthetic compounds with improved potency and reduced cytotoxicity. Toward this goal, we have previously established a short synthesis pathway that grants access to multiple congeners of the lissoclimide family. Here we present the X-ray co-crystal structure at 3.1 Å resolution of C45, a potent congener with two A-ring chlorine-bearing stereogenic centers with 'unnatural' configurations, with the yeast 80S ribosome, intermolecular interaction energies of the C45/ribosome complex, and single-molecule FRET data quantifying the impact of C45 on both human and yeast ribosomes. Together, these data provide new insights into the role of unusual non-covalent halogen bonding interactions involved in the binding of this synthetic compound to the 80S ribosome.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations.

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

Effective one-particle energies from generalized Kohn-Sham random phase approximation: A direct approach for computing and analyzing core ionization energies.

Generalized-Kohn-Sham (GKS) orbital energies obtained self-consistently from the random phase approximation energy functional with a semicanonical projection (spRPA) were recently shown to rival the accuracy of GW quasiparticle energies for valence ionization potentials. Here, we extend the scope of GKS-spRPA correlated one-particle energies from frontier-orbital ionization to core orbital ionization energies, which are notoriously difficult for GW and other response methods due to strong orbital relaxation effects. For a benchmark consisting of 23 1s core electron binding energies (CEBEs) of second-row elements, chemical shifts estimated from GKS-spRPA one-particle energies yield mean absolute deviations from experiment of 0.2 eV, which are significantly more accurate than the standard GW and comparable to Δ self-consistent field theory without semiempirical adjustment of the energy functional. For small ammonia clusters and cytosine tautomers, GKS-spRPA based chemical shifts capture subtle variations in covalent and noncovalent bonding environments; GKS-spRPA 1s CEBEs for these systems agree with equation-of-motion coupled cluster singles and doubles and ADC(4) results within 0.2-0.3 eV. Two perturbative approximations to GKS-spRPA orbital energies, which reduce the scaling from O(N6) to O(N5) and O(N4), are introduced and tested. We illustrate the application of GKS-spRPA orbital energies to larger systems by using oxygen 1s CEBEs to probe solvation and packing effects in condensed phases of water. GKS-spRPA predicts a lowering of the oxygen 1s CEBE of approximately 1.6-1.7 eV in solid and liquid phases, consistent with liquid-jet X-ray photoelectron spectroscopy and gas phase cluster experiments. The results are rationalized by partitioning GKS-spRPA electron binding energies into static, relaxation, and correlation parts.

Random-Phase Approximation Methods.

Random-phase approximation (RPA) methods are rapidly emerging as cost-effective validation tools for semilocal density functional computations. We present the theoretical background of RPA in an intuitive rather than formal fashion, focusing on the physical picture of screening and simple diagrammatic analysis. A new decomposition of the RPA correlation energy into plasmonic modes leads to an appealing visualization of electron correlation in terms of charge density fluctuations. Recent developments in the areas of beyond-RPA methods, RPA correlation potentials, and efficient algorithms for RPA energy and property calculations are reviewed. The ability of RPA to approximately capture static correlation in molecules is quantified by an analysis of RPA natural occupation numbers. We illustrate the use of RPA methods in applications to small-gap systems such as open-shell d- and f-element compounds, radicals, and weakly bound complexes, where semilocal density functional results exhibit strong functional dependence.

Using Diamagnetic Yttrium and Lanthanum Complexes to Explore Ligand Reduction and C-H Bond Activation in a Tris(aryloxide)mesitylene Ligand System.

[Y(N(SiMe3)2)3] reacts with (Ad,MeArOH)3mes to form the Y3+ complex [((Ad,MeArO)3mes)Y], 1-Y. This complex reacts with potassium metal in the presence of 2.2.2-cryptand to give a cocrystallized mixture of [K(2.2.2-cryptand)][((Ad,MeArO)3mes)Y], 2-Y, and [K(2.2.2-cryptand)][((Ad,MeArO)3mes)YH], 3-Y. The electron paramagnetic resonance spectrum of this crystalline mixture exhibits an isotropic signal at 77 K ( giso = 2.000, Wiso = 1.8 mT), suggesting that 2-Y is best described as a Y3+ complex of the tris(aryloxide)mesitylene radical ((Ad,MeArO)3mes)4-. Evidence of the hydride ligand in 3-Y was obtained by 89Y-1H heteronuclear multiple quantum coherence NMR spectroscopy, and a coupling constant of JYH = 93 Hz was observed. A single crystal of 3-Y was also obtained in pure form and structurally characterized for comparison with the crystal data on the mixed component 2-Ln/3-Ln crystals. The origin of the hydride in 3-Ln is unknown, but further studies of the reduction of 1-La, previously found to form 2-La, revealed a possible source. Ligand-based C-H bond activation and loss of hydrogen can occur under reducing conditions to form a tetraanionic ligand derived from ((Ad,MeArO)3mes)3-, as observed in [K(2.2.2-cryptand)][((Ad,MeArO)3(C6Me3(CH2)2CH)La], 4-La.

Metal versus Ligand Reduction in Ln3+ Complexes of a Mesitylene-Anchored Tris(Aryloxide) Ligand.

The synthesis of 4f n Ln3+ complexes of the tris(aryloxide) mesitylene ligand, ((Ad,MeArO)3mes)3-, with Ln = La, Ce, Pr, Sm, and Yb, and their reduction with potassium have revealed that this ligand system can be redox active with some metals. Protonolysis of [Ln(N(SiMe3)2)3] (Ln = La, Ce, Pr, Sm, Yb) with the tris(phenol) (Ad,MeArOH)3mes yielded the Ln3+ complexes [((Ad,MeArO)3mes)Ln] (Ln = La, Ce, Pr, Sm, Yb), 1-Ln. Single electron reduction of each 4f n complex, 1-Ln, using potassium yielded the reduced products, [K(2.2.2-cryptand)][((Ad,MeArO)3mes)Ln] (Ln = La, Ce, Pr, Sm, Yb), 2-Ln. The Sm and Yb complexes have properties consistent with the presence of Ln2+ ions with traditional 4f n+1 electron configurations. However, the La, Ce, and Pr complexes appear to formally contain Ln3+ ions and ((Ad,MeArO)3mes)4- ligands. Structural comparisons of the [((Ad,MeArO)3mes)Ln] and [((Ad,MeOAr)3mes)Ln]1- complexes along with UV-vis absorption and EPR spectroscopy as well as density functional theory calculations support these ground state assignments.

Theoretical approaches for treating non-valence correlation-bound anions.

In this work, we use a model (H2O)4 cluster, the bent CO2 molecule, and tetracyanoethylene as systems to explore the applicability of various electronic structure methods for characterizing non-valence correlation-bound anion states. The methods examined include the algebraic diagrammatic construction, various equation-of-motion coupled cluster methods, orbital-optimized MP2, and Brueckner coupled cluster doubles with perturbative triples. We demonstrate that the key to treating this challenging class of anions is the use of methods that include adequate orbital relaxation in response to long-range dispersion-like correlation effects.

Nonvalence correlation-bound anion states of spherical fullerenes.

We present a one-electron model Hamiltonian for characterizing nonvalence correlation-bound anion states of fullerene molecules. These states are the finite system analogs of image potential states of metallic surfaces. The model potential accounts for both atomic and charge-flow polarization and is used to characterize the nonvalence correlation-bound anion states of the C60, (C60)2, C240, and C60@C240 fullerene systems. Although C60 is found to have a single (s-type) nonvalence correlation-bound anion state, the larger fullerenes are demonstrated to have multiple nonvalence correlation-bound anion states.

Nonvalence correlation-bound anion state of C6F6: doorway to low-energy electron capture.

The ground-state anion of perfluorobenzene is investigated by means of equation-of-motion (EOM) methods. It is found that at the geometry of the neutral, the excess electron is bound by 0.135 eV. This anion state is nonvalence in nature with the excess electron bound in a very diffuse orbital with dispersion-type interactions between the excess electron and the valence electrons being pivotal to the binding. The diffuse correlation-bound state is shown to evolve into a more stable compact valence-bound anion state with a buckled structure having an adiabatic EA of 0.5 eV. Results are also presented for the bound anion states of the C6F6 dimer.

Single-Pole Polarization Models: Rapid Evaluation of Electron Affinities of Solvated-Electron and Superatomic Molecular Anionic States.

We propose a single-parameter effective one-particle potential, termed the single-pole exchange-correlation (1p-XC), to rapidly evaluate electron affinities (EAs) of nonvalence electronic states of molecular clusters and nanoassemblies. The model combines exact-exchange and the random phase approximation (RPA) correlation potential with a single-pole approximation to model the frequency-dependent polarization function. It captures long-range static and dynamic-frequency effects in the correlation potential, with mean absolute errors of 0.06 eV for EAs of hydrated- and ammoniated-electron clusters with EA values in the range 0.24-1.77 eV. The 1p-XC approximation enables EA estimation with a computational wall-time similar to that of hybrid functionals. The model also provides a compressed-basis, which significantly reduces the rank of higher-level parameter-free one-particle Hamiltonians and further simplifies the computation of EAs. The compressed-basis approach is used to model the hybridization of superatomic molecular states of (C60)2- and (C60)3-, thereby verifying previous model Hamiltonian studies.

Taming Negative Ion Resonances Using Nonlocal Exchange-Correlation Functionals.

The characterization of negative ion resonances poses a fundamental challenge to density functional methods due to the unbound nature of resonances. To overcome this challenge, we propose one-particle nonlocal exchange-correlation (xc) potentials combining the exact-exchange (EXX) and the random phase approximation (RPA) correlation potentials. The negative ion resonances are identified by perturbing the real Hermitian nonlocal xc potentials using complex absorbing local potentials. Our studies show that the nonlocal EXX+RPA potential significantly enhances the description of positions and widths of negative ion resonance states compared to potentials that exclude dynamic polarization in RPA or include only EXX. The use of low-scaling algorithms simplifies the computation of the RPA potential, thereby providing a practical solution for resonance-state characterization within the density functional framework. A theoretical framework and the underlying assumptions required for combining real Hermitian nonlocal xc potentials with complex local potentials are discussed.

Bottom-up view of water network-mediated CO2 reduction using cryogenic cluster ion spectroscopy and direct dynamics simulations.

The transition states of a chemical reaction in solution are generally accessed through exchange of thermal energy between the solvent and the reactants. As such, an ensemble of reacting systems approaches the transition state configuration of reactant and surrounding solvent in an incoherent manner that does not lend itself to direct experimental observation. Here we describe how gas-phase cluster chemistry can provide a detailed picture of the microscopic mechanics at play when a network of six water molecules mediates the trapping of a highly reactive "hydrated electron" onto a neutral CO(2) molecule to form a radical anion. The exothermic reaction is triggered from a metastable intermediate by selective excitation of either the reactant CO(2) or the water network, which is evidenced by the evaporative decomposition of the product cluster. Ab initio molecular dynamics simulations of energized CO(2)·(H(2)O)(6)(-) clusters are used to elucidate the nature of the network deformations that mediate intracluster electron capture, thus revealing the detailed solvent fluctuations implicit in the Marcus theory for electron-transfer kinetics in solution.

Modeling Nonresonant X-ray Emission of Second- and Third-Period Elements without Core-Hole Reference States and Empirical Parameters.

Nonresonant X-ray emission (XE) energies and oscillator strengths are obtained using the effective potential of the generalized Kohn-Sham semi-canonical projected random phase approximation (GKS-spRPA) method. XE energies are estimated as a difference between the valence and core ionization eigenvalues, while the oscillator strengths are obtained within a frozen orbital approximation. This straightforward approach provides accurate XE energies without any need for core-hole reference states, empirical shifting parameters, or tuning of density functionals. To account for relativistic corrections to the core orbitals, we have formulated a scalar relativistic (sr) GKS-spRPA approach based on the spin-free X2C one-electron Hamiltonian. The sr-GKS-spRPA method provides highly reliable XE energies using uncontracted basis-sets on atoms where the core-hole is created prior to emission. For the largest basis-sets used in our study, using completely uncontracted polarized core-valence Dunning basis-sets, the mean absolute errors (MAEs) are within 0.7 eV compared to experimental reference values for a test-set consisting of 27 valence-to-core XE energies of molecules with second- and third-period elements. Considering a balance of accuracy and computational effort, we recommend the use of s-uncontracted def2-TZVP for second-period and all-uncontracted def2-TZVP for third-period elements. For this recommended basis-set, the MAE is 0.2 eV. The analytically continued sr-GKS-spRPA approach, with an O(N4) computational cost, enables efficient computation of XE spectra of molecules such as S8 and C60 with several core-hole states.

Density functional theory study of pyrophyllite and M-montmorillonites (M = Li, Na, K, Mg, and Ca): role of dispersion interactions.

The stacking parameters, lattice constants, bond lengths, and bulk moduli of pyrophyllite and montmorillonites (MMTs), with alkali and alkali earth metal ions, are investigated using density functional theory with and without dispersion corrections. For pyrophyllite, it is found that the inclusion of the dispersion corrections significantly improves the agreement of the calculated values of the lattice parameters and bulk modulus with the experimental values. For the MMTs, the calculations predict that the interlayer spacing varies approximately linearly with the cation radius. The inclusion of dispersion corrections leads to sizable shifts of the interlayer spacings to shorter values. In Li-MMT, compaction of the interlayer distance triggers migration of the Li ion into the tetrahedral sheet and close coordination with basal oxygen atoms. Analysis of electron density distributions shows that the isomorphic octahedral Al(3+)/Mg(2+) substitution in MMT causes an increase of electron density on the basal oxygen atoms of the tetrahedral sheets.

Molecular Electron Affinities Using the Generalized Kohn-Sham Semicanonical Projected Random Phase Approximation.

The suitability of one-particle energies from the generalized Kohn-Sham semicanonical projected random phase approximation (GKS-spRPA) method for electron affinities of molecules is investigated. It is shown that the GKS-spPRA effective potential includes exact exchange and polarizability-dependent correlation terms that are necessary for the correct description of anionic systems. An O(N4) implementation that enables fast computation of electron affinities is presented. For model systems, I show that the GKS-spRPA approach is applicable for valence and nonvalence type anions with a maximum error of 0.13 eV for valence anionic states and 0.03 eV for nonvalence anionic states compared to equation of motion coupled cluster methods. For a series of perhalobenzene molecules, C6X6 (X= F, Cl, Br, and I), GKS-spRPA predicts that the ground-state character changes from a nonvalence-σ* type in C6F6- to valence-π* in C6Cl6- and valence-σ* in C6Br6- and C6I6-. Experimental implications of these findings are discussed.

Exploring the Solvation of Acetic Acid in Water Using Liquid Jet X-ray Photoelectron Spectroscopy and Core Level Electron Binding Energy Calculations.

Liquid jet X-ray photoelectron spectroscopy was used to investigate changes in the local electronic structure of acetic acid in the bulk of aqueous solutions induced by solvation effects. These effects manifest themselves as shifts in the difference in the carbon 1s binding energy (ΔBE) between the methyl and carboxyl carbons of acetic acid. Furthermore, molecular dynamics simulations, coupled with correlated electronic structure calculations of the first solvation sphere, provide insight into the number of water molecules directly interacting with the carboxyl group that are required to match the ΔBE from the photoelectron spectroscopy experiments. This comparison shows that a single water molecule in the first solvation shell describes the photoelectron ΔBE of acetic acid while at least 20 water molecules are required for the conjugate base, acetate, in aqueous solutions.