Gaussian basis sets for use in correlated molecular calculations. VII. Valence, core-valence, and scalar relativistic basis sets for Li, Be, Na, and Mg

Range-separated density functional theory using multiresolution analysis and quantum computing

Quantum computers are expected to outperform classical computers for specific problems in quantum chemistry. Such calculations remain expensive, but costs can be lowered through the partition of the molecular system. In the present study, partition was achieved with range-separated density functional theory (RS-DFT). The use of RS-DFT reduces both the basis set size and the active space size dependence of the ground state energy in comparison with the use of wave function theory (WFT) alone. The utilization of pair natural orbitals (PNOs) in place of canonical molecular orbitals (MOs) results in more compact qubit Hamiltonians. To test this strategy, a basis-set independent framework, known as multiresolution analysis (MRA), was employed to generate PNOs. Tests were conducted with the variational quantum eigensolver for a number of molecules. The results show that the proposed approach reduces the number of qubits needed to reach a target energy accuracy.

Alignment transport between ultracold polar molecules

We propose an array of ultracold polar molecules as a platform to study alignment transport between molecules. We envision a polar molecule being aligned with an intense off-resonant laser field whose alignment migrates to a nearby molecule due to dipole-dipole interactions. Our results show that the transport of the alignment is due to a complex interplay between electric field-driven excitations and dipole-dipole interactions. All mechanisms for alignment transfer are elucidated and analyzed. Using NaCs as a prototype molecule, we find that the time for alignment transfer is (10 μs), which makes the phenomena readily observable in the lab.

Targeting spectroscopic accuracy for dispersion bound systems from ab initio techniques: Translational eigenstates of Ne@C70

We investigate the endofullerene system Ne@C70 by constructing a three-dimensional Potential Energy Surface (PES) describing the translational motion of the Ne atom. This is constructed from electronic structure calculations from a plethora of methods, including MP2, SCS-MP2, SOS-MP2, RPA@PBE, and C(HF)-RPA, which were previously used for He@C60 in Panchagnula et al. [J. Chem. Phys. 160, 104303 (2024)], alongside B86bPBE-25X-XDM and B86bPBE-50X-XDM. The reduction in symmetry moving from C60 to C70 introduces a double well potential along the anisotropic direction, which forms a test of the sensitivity and effectiveness of the electronic structure methods. The nuclear Hamiltonian is diagonalized using a symmetrized double minimum basis set outlined in Panchagnula and Thom [J. Chem. Phys. 159, 164308 (2023)], with translational energies having error bars ±1 and ±2 cm-1. We find no consistency between electronic structure methods as they find a range of barrier heights and minima positions of the double well and different translational eigenspectra, which also differ from the Lennard-Jones (LJ) PES given in Mandziuk and Bačić [J. Chem. Phys. 101, 2126-2140 (1994)]. We find that generating effective LJ parameters for each electronic structure method cannot reproduce the full PES nor recreate the eigenstates, and this suggests that the LJ form of the PES, while simple, may not be best suited to describe these systems. Even though MP2 and RPA@PBE performed best for He@C60, due to the lack of concordance between all electronic structure methods, we require more experimental data in order to properly validate the choice.

Scalable Ab Initio Electronic Structure Methods with Near Chemical Accuracy for Main Group Chemistry

This study evaluates the precision of widely recognized quantum chemical methodologies, CCSD(T), DLPNO-CCSD(T), and localized ph-AFQMC, for determining the thermochemistry of main group elements. DLPNO-CCSD(T) and localized ph-AFQMC, which offer greater scalability compared to canonical CCSD(T), have emerged over the past decade as pivotal in producing precise benchmark chemical data. Our investigation includes closed-shell, neutral molecules, focusing on their heat of formation and atomization energy sourced from four specific small molecule data sets. First, we selected molecules from the G2 and G3 data sets, noted for their reliable experimental heat of formation data. Additionally, we incorporate molecules from the W4-11 and W4-17 sets, which provide high-level theoretical reference values for atomization energy at 0 K. Our findings reveal that both DLPNO-CCSD(T) and ph-AFQMC methods are capable of achieving a root-mean-square deviation of less than 1 kcal/mol across the combined data set, aligning with the threshold for chemical accuracy. Moreover, we make efforts to confine the maximum deviations within 2 kcal/mol, a degree of precision that significantly broadens the applicability of these methods in fields such as biology and materials science.

Prediction of the pKa's of Hydrated Metal Carbonates and Bicarbonates for Mg, Ca, Mn, Fe, Co, Ni, Cu, and Zn Dications

The gas- and aqueous-phase acidities of hydrated metal dication carbonates, bicarbonates, and hydroxide complexes M(CO3)(H2O)n for n = 1 to 3, M(HCO3)2, M(HCO3)2(H2O)2, M(HCO3)(OH), and M(HCO3)(H2O)2(OH) for M = Mg, Ca, Mn, Fe, Co, Ni, Cu, and Zn were calculated at the CCSD(T)/aug-cc-pwCVDZ/cc-pwCVDZ level in the gas phase and at the B3LYP/aug-cc-pVTZ/cc-pVTZ(-PP) level with the COSMO self-consistent reaction field (SCRF) method in the aqueous phase. The composite correlated molecular orbital theory G3(MP2) and G3(MP2)B3 methods were used to predict the pKa's of the Mg structures and cis-cis carbonic acid to provide additional benchmarks. Using values scaled to experiment for H2CO3, the pKa's of bicarbonate ligands in group 2 and transition-metal complexes were compared to carbonic acid to gauge the effect of the metal complex on the bicarbonate. The group 2 metal complexes M(HCO3)2 and M(HCO3)(OH) decreased the acidity of the bicarbonate ligands, whereas their dihydrates were even less acidic. The transition-metal di-bicarbonate and bicarbonate hydroxide complexes generally made the bicarbonate more acidic especially when reduction of the metal occurs consistent with electron donation from the ligands; this is accompanied by spin transfer which typically increases in the order Mn < Fe < Co < Ni < Cu. The transition-metal dihydrates were less acidic than carbonic acid. Using values scaled to experiment for hydrated metal dications, the pKa's of water coordinated to group 2 and transition-metal complexes were generally more acidic than the hydrated metal dications, with the exception of Ca bicarbonate dihydrate, Co carbonate, Ni di-bicarbonate dihydrate, and Cu bicarbonate hydroxide di-bicarbonate.

Electron superhalogens as positronium superhalogens

Positronium (Ps) exhibits the ability to form energetically stable complexes with atoms and molecules before annihilation occurs. In particular, F, a halogen, shows the highest reported positronium binding energy (2.95 eV) in the periodic table. Superhalogens are defined as molecules with electron affinities exceeding that of Cl (3.61 eV), the atom with the highest electron affinity. Building upon the concept of superhalogens, we can define Ps-superhalogens as molecules with Ps binding energies surpassing that of F. This study explores structural and energetic aspects of positronium and positron binding to neutral and anionic superhalogen molecules of the MXk+1 family (M = Li, Na, Be, Mg, B, Al, Si, P; X = F, Cl, Br), respectively and where k represents the highest formal valence of M. We perform multicomponent MP2 calculations for positron systems, which reveal how positron affinities vary with the type and number of halogen atoms present. The analysis of the results emphasizes the predominant role of electrostatic interactions in determining the positron affinity, with negligible effects of electronic and geometric relaxation upon positron attachment. We predict the energetic stability of 22 of the 24 PsMXk+1 complexes with respect to the chemically relevant dissociation channels: e+ emission, Ps emission and M-X bond breaking. Our findings reveal six MFk+1 systems that qualify as Ps-superhalogens, showing a positronium binding energy exceeding 2.95 eV. Of these, AlF4 stands out by setting a new record for the highest positronium binding energy among neutral molecules, reaching 4.36 eV.

Norcaradiene-Cycloheptatriene Equilibrium: A Heavy-Atom Quantum Tunneling Case

The equilibrium between norcaradiene and cycloheptatriene, which has captivated chemists for more than half a century, is revisited by state-of-the-art quantum chemical calculations. Our theoretical data significantly deviate from the experimental results (J. Am. Chem. Soc., 1981, 26, 7791-7792), especially at low temperatures, where isomerization is dominated by heavy-atom tunneling. This effect results in an extremely short half-life for norcaradiene, rendering it undetectable. This work sheds light on this equilibrium, updating the kinetic and thermodynamic data while also expanding the repertoire of organic reactions controlled by this exotic quantum effect.

Quadruple bonds in MoC: Accurate calculations and precise measurement of the dissociation energy of low-lying states of MoC

In the present work, the electronic structure and chemical bonding of the MoC X3Σ- ground state and the six lowest excited states, A3Δ, a1Γ, b5Σ-, c1Δ, d1Σ+, and e5Π, have been investigated in detail using multireference configuration interaction methods and basis sets, including relativistic effective core potentials. In addition, scalar relativistic effects have been considered in the second order Douglas-Kroll-Hess approximation, while spin-orbit coupling has also been calculated. Five of the investigated states, X3Σ-, A3Δ, a1Γ, c1Δ, and d1Σ+, present quadruple σ2σ2π2π2 bonds. Experimentally, the predissociation threshold of MoC was measured using resonant two-photon ionization spectroscopy, allowing for a precise measurement of the dissociation energy of the ground state. Theoretically, the complete basis set limit of the calculated dissociation energy with respect to the atomic ground state products, including corrections for scalar relativistic effects, De(D0), is computed as 5.13(5.06) eV, in excellent agreement with our measured value of D0(MoC) of 5.136(5) eV. Furthermore, the calculated dissociation energies of the states having quadruple bonds with respect to their adiabatic atomic products range from 6.22 to 7.23 eV. The excited electronic states A3Δ2 and c1Δ2 are calculated to lie at 3899 and 8057 cm-1, also in excellent agreement with the experimental values of DaBell et al., 4002.5 and 7834 cm-1, respectively.

Theoretical study of the spin-orbit coupled molecular states of the Mg-He dimer

The primary objective of this study is to conduct precise ab initio calculations of the spin-orbit interaction between Mg and He atoms. Our investigation centers on identifying the first low-lying electronic states of the Mg-He molecule through high-level theoretical methods such as CCSD(T) and RCCSD(T) and SA-CASSCF/MRCI, while also integrating Davidson and BSSE corrections to refine our findings further. Additionally, we employ the state-interacting method to comprehensively account for the influence of spin-orbit coupling (SO) on molecular states. We carefully characterize the potential energy curves (PECs) of these molecular states by deriving crucial spectroscopic parameters including Re, De, Be and Te, which are then compared against data from prior studies. Moreover, our analysis extends to evaluating vibrational levels, radiative lifetimes, and transition dipole moments (TDMs), offering a comprehensive understanding of the system's dynamics. Notably, we locate the positions of satellite features within the absorption spectra of brown and white dwarfs. To validate the precision and reliability of our findings, extensive comparisons are made with both theoretical predictions and experimental observations, ensuring robustness and accuracy in our conclusions.

Electronic structure analysis and DFT benchmarking of Rydberg-type alkali-metal-crown ether, -cryptand, and -adamanzane complexes

Density functional theory (DFT) and electron propagator theory (EPT) calculations were performed to study ground and excited electronic structures of alkali-metal (M) coordinated 9-crown-3, 24-crown-8, [2.1.1]cryptand, o-Me2-1.1.1, and 36Adamanzane complexes. Each complex bears an expanded electron in the periphery and occupies diffuse 1p-, 1d-, 1f-type molecular orbitals (or superatomic 1P, 1D, 1F orbitals) in excited electronic states. The calculated superatomic shell model of the M(9-crown-3)2 is 1S, 1P, 1D, 1F, 2S, 2P, 2D, 1G and it is held by all other complexes up to the studied 1F level. Due to the highly diffuse nature of the electron, the ionization energies of these complexes are significantly lower (1.6-2.0 eV) and hence these complexes belong to the superalkali category. The ab initio EPT ionization energy and the excitation energies of the Li(9-crown-3)2 were used to evaluate DFT errors associated with a series of exchange correlation functionals that span multiple rungs of Jacob's ladder (i.e., GGA, meta-GGA, global GGA hybrid, meta-GGA hybrid, range-separated hybrid, double-hybrid). Among these, the best performing functional is the range-separated hybrid CAM-B3LYP and the errors are within 6% of high-level ab initio EPT results. The accuracy of CAM-B3LYP is indeed transferable to similar complexes and hence the findings are expected to accelerate the progression of studies of Rydberg-type systems.

Reference Energies for Valence Ionizations and Satellite Transitions

Upon ionization of an atom or a molecule, another electron (or more) can be simultaneously excited. These concurrently generated states are called "satellites" (or shakeup transitions) as they appear in ionization spectra as higher-energy peaks with weaker intensity and larger width than the main peaks associated with single-particle ionizations. Satellites, which correspond to electronically excited states of the cationic species, are notoriously challenging to model using conventional single-reference methods due to their high excitation degree compared to the neutral reference state. This work reports 42 satellite transition energies and 58 valence ionization potentials (IPs) of full configuration interaction quality computed in small molecular systems. Following the protocol developed for the quest database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; and Loos, P.-F. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517], these reference energies are computed using the configuration interaction using a perturbative selection made iteratively (CIPSI) method. In addition, the accuracy of the well-known coupled-cluster (CC) hierarchy (CC2, CCSD, CC3, CCSDT, CC4, and CCSDTQ) is gauged against these new accurate references. The performances of various approximations based on many-body Green's functions (GW, GF2, and T-matrix) for IPs are also analyzed. Their limitations in correctly modeling satellite transitions are discussed.

New Diabatic Potential Energy Surfaces for the Li + H2 Reaction and Time-Dependent Quantum Wave Packet Studies

New global diabatic potential energy surfaces (DPESs) for the ground (12A') and first excited (22A') states for the Li + H2 system were developed, with more than 30,000 energy points at the IC-MRCI+Q level of theory, utilizing the aug-cc-pV5Z basis set for the H atoms and the cc-pCV5Z basis set for the Li atom, fitted by a single neural network (NN) with symmetry. Product state-resolved quantum dynamics calculations of the nonadiabatic reaction Li (2P) + H2 (X 1 ∑g+, v0 = 0, j0 = 0) → LiH (X 1∑+) + H(2S) were carried out using these new DPESs and also the previous HYLC-DPESs. The numerical results suggested that our newly constructed DPESs provided an accurate description of the LiH2 system.

Potential of Molecular Catalysts with Electron-Rich Transition Metal Centers for Addressing Long-Standing Chemistry Enigmas

Molecular complexes with electron-rich metal centers are highlighted as potential catalysts for the following five important chemical transformations: selective conversion of methane to methanol, capture and utilization of carbon dioxide, fixation of molecular nitrogen, water splitting, and recycling of perfluorochemicals. Our initial focus lies on negatively charged metal centers and ligands that can stabilize anionic metal atoms. Catalysts with electron-rich metal atoms (CERMAs) can sustain catalytic cycles with a "ping-pong" mechanism, where one or more electrons are transferred from the metal center to the substrate and back. The donated electrons can activate the chemical bonds of the substrate by populating its antibonding orbitals. At the last step of the catalytic cycle, the electrons return to the metal and the product interacts only weakly with the formed anion, which enables the solvent molecules to remove the product fast from the catalytic cycle and prevent subsequent unfavorable reactions. This process resembles electrocatalysis, but the metal serves as both an anode and a cathode (molecular electrocatalysis). We also analyze the usage of CERMAs as the base of Frustrated Lewis pairs proposing a new type of bimetallic catalysts. This Featured Article aspires to initiate systematic experimental and theoretical studies on CERMAs and their reactivity, the potential of which has probably been underestimated in the literature.

Performance assessment of the effective core potentials under the fermionic neural network: First and second row elements

The rapid development of deep learning techniques has driven the emergence of a neural network-based variational Monte Carlo (VMC) method (referred to as FermiNet), which has manifested high accuracy and strong predictive power in the electronic structure calculations of atoms, molecules, and some periodic systems. Recently, the implementation of the effective core potential (ECP) scheme has further facilitated more efficient calculations in practice. However, there is still a lack of comprehensive assessments of the ECP's performance under the FermiNet. In this work, we set sail to fill this gap by conducting extensive tests on the first two row elements regarding their atomic, spectral, and molecular properties. Our major finding is that, in general, the qualities of ECPs have been correctly reflected under FermiNet. Two recently built ECP tables, namely, correlation consistent ECP (ccECP) and energy consistent correlated electron pseudopotential (eCEPP), seem to prevail in terms of overall performance. In particular, ccECP performs slightly better on spectral precision and covers more elements, while eCEPP is more systematically built from both shape and energy consistency and better treats the core polarization. On the other hand, the high accuracy of the all-electron calculations is hindered by the absence of relativistic effects as well as the numerical instabilities in some heavier elements. Finally, with further in-depth discussions, we generate possible directions for developing and improving FermiNet in the near future.

Ab Initio Ground-State Potential Energy Function and Vibration-Rotation Energy Levels of Magnesium Monohydride

The accurate potential energy function of magnesium monohydride in its X2Σ+ state has been determined from ab initio calculations. The vibration-rotation energy levels of the main isotopologue 24MgH were predicted to near the "spectroscopic" accuracy. The scalar relativistic, adiabatic, and nonadiabatic effects were discussed.

Which Options Exist for NISQ-Friendly Linear Response Formulations?

Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photoinduced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced [Kumar et al., J. Chem. Theory Comput. 2023, 19, 9136-9150]. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resource-efficient qLR theory, using a truncated active-space version of the multiconfigurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates, dubbed "proj LRSD" and "all-proj LRSD".

Search for Chirality in Hydrogenated Magnesium Nanosilicates: A DFT and TD-DFT Investigation

The formation of silicate grains in the interstellar medium (ISM), especially those containing chiral surfaces such as clinopyroxenes, is poorly understood. Moreover, silicate interactions with various forms of hydrogen-proton (H+), neutral H (HI), and molecular hydrogen (H2) are of high importance as hydrogen comprises >90% of the ISM gas budget, and these species play important roles in the formation of new molecules in space. Furthermore, silicate surfaces catalyze the formation of H2 in the interstellar medium formed on dust grain surfaces by H-H association. The technical difficulty of in situ laboratory investigations of nanosilicate nucleation using astrophysically relevant environmental conditions makes computational chemistry a useful tool for studying potential nanosilicate structures. Furthermore, chiral surfaces interacting with chiral organic molecules could serve as templates that lead to the enantiomeric excess of l-amino acids and d-polyols detected in carbonaceous meteorites. However, in order for this effect to take place, an excess of one chiral form of a mineral is required to break the symmetry. This symmetry-breaking event could have been due to the asymmetric absorption of circularly polarized light by the nanosilicate as it traverses star-forming regions. We investigate this possibility using a metastable chiral form of an enstatite dimer as an input for density functional theory (DFT) and time-dependent (TD)-DFT calculations to obtain various properties and circular dichroism spectra. All in all, twenty-six magnesium nanosilicate structures were studied using varying degrees of hydrogenation: none, with HI, with H+, and with H2. The HSE06/aug-cc-pVQZ level of theory was used for the DFT calculations. TD-DFT calculations utilized the CAM-B3LYP/cc-pVQZ and ωB97X-D3/cc-pVQZ functional and basic set pairings. Results show that (1) all twenty-six structures have absorption bands that fall within the 0.6-28.3 μm range available with the newly launched James Webb Space Telescope and (2) there is a small enantioselective effect by UV-CPL on the eight chiral enstatite dimers (predicted g-values of up to 0.007). While the observed effect is small, it opens up the possibility that it is the inorganic material that becomes enantiomerically biased by UV-CPL, driving chiral enhancements in meteoric organic molecules.

High-Resolution Rovibronic Cross Sections of the MgH+ Molecular Cation

The high-resolution rovibronic line lists of the MgH+ molecular cation are presented in our work. The potential energy curves are calculated by the method of multireference configuration interaction and Davidson correction (MRCI+Q) with the spin-orbit coupling (SOC) effect. Spectroscopy constants are fitted and the results are in good agreement with experiments, ensuring the accuracy of the electronic structure. On account of potential energy curves and transition dipole moments, the Franck-Condon factors and Einstein coefficients of transition are obtained. These calculations are used to obtain an accurate partition functions and line lists for molecules. Using the partition functions and line lists, the absorption cross-sections under different temperatures and pressures were simulated. Our work could provide some theoretical insights into solar and cold planet spectrum.

The impact of solvation on the structure and electric field strength in Li+GlyGly complexes

To scrutinise the impact of electric fields on the structure and vibrations of biomolecules in the presence of water, we study the sequential solvation of lithium diglycine up to three water molecules with cryogenic infrared action spectroscopy. Conformer-specific IR-IR spectroscopy and H2O/D2O isotopic substitution experiments provide most of the information required to decipher the structure of the observed conformers. Additional confirmation is provided by scaled harmonic vibrational frequency calculations using MP2 and DFT. The first water molecule is shown to bind to the Li+ ion, which weakens the electric field experienced by the peptide and as a consequence, also the strength of an internal NH⋯NH2 hydrogen bond in the diglycine backbone. The strength of this hydrogen bond decreases approximately linearly with the number of water molecules as a result of the decreasing electric field strength and coincides with an increase in the number of conformers observed in our spectra. The addition of two water molecules is already sufficient to change the preferred conformation of the peptide backbone, allowing for Li+ coordination to the lone pair of the terminal amine group.

Ground and excited electronic structures of electride and alkalide units: The cases of Metal-Tren, -Azacryptand, and -TriPip222 complexes

A systematic electronic structure analysis was conducted for M(L)n molecular electrides and their corresponding alkalide units M(L)n @M' (M/M' = Na, K; L = Tren, Azacryptand, TriPip222; n = 1, 2). All complexes belong to the "superalkali" category due to their low ionization potentials. The saturated molecular electrides display M+ (L)n - form with a greatly diffuse quasispherical electron cloud. They were identified as "superatoms" considering the contours of populating atomic-type molecular orbitals. The observed superatomic Aufbau order of M(Tren)2 is 1S, 1P, 1D, 1F, 2S, 2P, and 1G and it is consistent with those of M(Azacryptand) and M(TriPip222) up to the analyzed 1F level. Their excitation energies decrease gradually moving from M(Tren)2 to M(Azacryptand) and to M(TriPip222). The studied alkalide complexes carry [M(L)n ]+ @M'- ionic structure and their dissociation energies vary in the sequence of K(L)n @Na > Na(L)n @Na > K(L)n @K > Na(L)n @K. Similar to molecular electrides, the anions of alkalide units occupy electrons in diffuse Rydberg-like orbitals. In this work, excited states of [M(L)n @M']0/+/- and their trends are also analyzed.

From the Iron Pentacarbonyl Cation to Heteroleptic η6-arene Carbonyls and bis-η6-arene Cations

Partial ligand substitution at the iron pentacarbonyl radical cation generates novel half-sandwich complexes of the type [Fe(η6-arene)(CO)2]⋅+ (arene=1,3,5-tri-tert-butylbenzene, 1,3,5-trimethylbenzene, benzene and fluorobenzene). Of those, the bulkier 1,3,5-tri-tert-butylbenzene (mes*) derivative [Fe(mes*)(CO)2]⋅+ was fully characterized by XRD analysis, IR, NMR, cw-EPR, Mössbauer spectroscopy and cyclic voltammetry as the [Al(ORF)4]- (RF=C(CF3)3) salt. Chemical electronation, i. e., the single electron reduction, with decamethylferrocene generates neutral [Fe(mes*)(CO)2], whereas further deelectronation under CO-pressure leads to a dicationic three-legged [Fe(mes*)(CO)3]2+ salt with [Al(ORF)4]- counterion. The full substitution of the carbonyl ligands in [Fe(CO)5]⋅+[Al(ORF)4]- mainly resulted in disproportionation reactions, giving solid Fe(0) and the dicationic bis-arene salts [Fe(η6-arene)2]2+([Al(ORF)4]-)2 (arene=1,3,5-trimethylbenzene, benzene and fluorobenzene). Only by employing the very large fluoride bridged anion [F-{Al(ORF)3}2]-, it was possible to isolate an open shell bis-arene cation salt [Fe(C6H6)2]⋅+[F-{Al(ORF)3}2]-. The highly reactive cation was characterized by XRD analysis, cw-EPR, Mössbauer spectroscopy and cyclic voltammetry. The disproportionation of [Fe(C6H6)2]⋅+ salts to give solid Fe(0) and [Fe(C6H6)2]2+ salts was analyzed by a suitable cycle, revealing that the thermodynamic driving force for the disproportionation is a function of the size of the anion used and the polarity of the solvent.

Relative cooperativity in neutral and charged molecular clusters using QM/MM calculations

QM/MM methods have been used to study electronic structure properties and chemical reactivity in complex molecular systems where direct electronic structure calculations are not feasible. In our previous work, we showed that non-polarizable force fields, by design, describe intermolecular interactions through pairwise interactions, overlooking many-body interactions involving three or more particles. In contrast, polarizable force fields account partially for many-body effects through polarization, but still handle van der Waals and permanent electrostatic interactions pairwise. We showed that despite those limitations, polarizable and non-polarizable force fields can reproduce relative cooperativity achieved using density functional theory due to error compensation mechanisms. In this contribution, we assess the performance of QM/MM methods in reproducing these phenomena. Our study highlights the significance of the QM region size and force field choice in QM/MM calculations, emphasizing the importance of parameter validation to obtain accurate interaction energy predictions.

Variational Pair-Density Functional Theory: Dealing with Strong Correlation at the Protein Scale

Multiconfigurational pair-density functional theory (MC-PDFT) offers a promising solution to the challenges faced by traditional density functional theory (DFT) in addressing molecular systems containing transition metals, open-shells, or strong correlations in general. By utilizing both the density and on-top pair-density, MC-PDFT can make use of a more flexible multiconfigurational wave function to capture the necessary static correlation, while the pair-density functional also includes the effect of dynamic correlation. So far, MC-PDFT has been used after a multiconfigurational self-consistent field (MCSCF) step, using the orbitals and configuration interaction coefficients from the converged MCSCF wave function to compute PDFT energies and properties. Here, instead, we propose to perform a direct optimization of the wave function using the pair-density functionals, resulting in a variational formulation of MC-PDFT. We derive the expressions for the wave function gradient and illustrate their similarity to standard MCSCF equations. Furthermore, we illustrate the accuracy on a set of singlet-triplet gaps as well as dissociation curves. Our findings highlight one of MC-PDFT's standout features: a reduced dependency on the active space size compared to conventional multiconfigurational wave function methodologies. Additionally, we show that the computational cost of MC-PDFT is potentially lower than MCSCF and often on-par with standard Kohn-Sham DFT, which is demonstrated by performing a MC-PDFT calculation of the entire ferredoxin protein with 1447 atoms and nearly 12 000 basis functions.

Electronic structure of Li1,2,3 +,0,- and nature of the bonding in Li2,3 +,0,

The current study of the small lithium molecules Li2 +,0,- and Li3 +,0,- focuses on the nature of the bonding in these molecules as well as their structures and energetics (bond energies, ionization energies, and electron affinities). Valence CASSCF (2s,2p) calculations incorporate nondynamical electron correlation in the calculations, while the corresponding multireference configuration interaction and coupled cluster calculations incorporate dynamical electron correlation. Treatment of nondynamical correlation is critical for properly describing the Li2,3 +,0,- molecules as well as the Li- anion with dynamical correlation, in general, only fine-tuning the predictions. All lithium molecules and ions are bound, with the Li3 + and Li2 + ions being the most strongly bound, followed by Li3 - , Li2 , Li2 - and Li3 . The minimum energy structures of Li3 +,0,- are, respectively, an equilateral triangle, an isosceles triangle, and a linear structure. The results of SCGVB calculations are analyzed to obtain insights into the nature of the bonding in these molecules. An important finding of this work is that interstitial orbitals, a concept first put forward by McAdon and Goddard in 1985, play an essential role in the bonding of all lithium molecules considered here except for Li2 . The interstitial orbitals found in the Li3 +,0 molecules likely give rise to the non-nuclear attractors/maxima observed in these molecules.

Theoretical electronic structure with spin-orbit coupling effect of the molecules SrAt and BaAt for laser cooling studies

Ab initio CASSCF/MRCI + Q calculations have been used to investigate the electronic structure and transition properties of the alkaline earth astatine molecules SrAt and BaAt. The adiabatic potential energy curves have been computed and plotted for the low-lying electronic states in the representations 2S+1Λ+/- and Ω(±) (with and without spin-orbit coupling effect). The spectroscopic and vibrational constants have been deduced for the corresponding bound states. An analysis of the Franck-Condon factors, the Einstein Coefficients, and the branching ratios among different vibrational levels has shown that both SrAt and BaAt molecules are suitable candidates for Doppler and Sysphus laser cooling. Experimental laser cooling schemes and conditions for these two molecules have been proposed. These results may pave the way for new spectroscopic and laser cooling experiments of alkaline earth astatine molecules.

Translational eigenstates of He@C60 from four-dimensional ab initio potential energy surfaces interpolated using Gaussian process regression

We investigate the endofullerene system 3He@C60 with a four-dimensional potential energy surface (PES) to include the three He translational degrees of freedom and C60 cage radius. We compare second order Møller-Plesset perturbation theory (MP2), spin component scaled-MP2, scaled opposite spin-MP2, random phase approximation (RPA)@Perdew, Burke, and Ernzerhof (PBE), and corrected Hartree-Fock-RPA to calibrate and gain confidence in the choice of electronic structure method. Due to the high cost of these calculations, the PES is interpolated using Gaussian Process Regression (GPR), owing to its effectiveness with sparse training data. The PES is split into a two-dimensional radial surface, to which corrections are applied to achieve an overall four-dimensional surface. The nuclear Hamiltonian is diagonalized to generate the in-cage translational/vibrational eigenstates. The degeneracy of the three-dimensional harmonic oscillator energies with principal quantum number n is lifted due to the anharmonicity in the radial potential. The (2l + 1)-fold degeneracy of the angular momentum states is also weakly lifted, due to the angular dependence in the potential. We calculate the fundamental frequency to range between 96 and 110 cm-1 depending on the electronic structure method used. Error bars of the eigenstate energies were calculated from the GPR and are on the order of ∼±1.5 cm-1. Wavefunctions are also compared by considering their overlap and Hellinger distance to the one-dimensional empirical potential. As with the energies, the two ab initio methods MP2 and RPA@PBE show the best agreement. While MP2 has better agreement than RPA@PBE, due to its higher computational efficiency and comparable performance, we recommend RPA as an alternative electronic structure method of choice to MP2 for these systems.

Sonification of molecular electronic energy density and its dynamics

A method is proposed for sonification of the molecular electronic energy density. The characteristic energetic structures of the individual complicated electronic wavefunctions are extracted in terms of the Energy Natural Orbitals (ENO), which are the eigenfunctions of the electronic energy density operator [K. Takatsuka and Y. Arasaki, J. Chem. Phys., 2021, 154, 094103]. Then, the frequency corresponding to each ENO energy is linearly transformed to the audible range. The time-variation of the population of the ENO serves as the volume (amplitude) of the sound. We demonstrate the sonification and associated voiceprints for a couple of very basic chemical bondings, from across an avoided crossing, and from the bond dissociation of a cluster.

Electron transfer-mediated synergistic nonlinear optical response in the Agn@C18 (n = 4-6) complexes: A DFT study on the electronic structures and optical characteristics

Seeking highly efficient and stable non-linear optical (NLO) materials is crucial yet challenging, given their promising applications in laser diodes and photovoltaics. In this study, we employ the excess electron and charge transfer strategies to theoretically design three novel complexes, namely Agn@C18 (n = 4-6), by adsorbing silver clusters onto the cyclo[18]carbon ring (C18). Our aim is to investigate the NLO characteristics of these complexes using density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations. The results reveal that the adsorption of Ag clusters onto C18 leads to a decrease in excitation energy and an increase in dipole moment and oscillator strengths, thereby significantly enhancing the hyperpolarizability of the complexes. Strikingly, among all these complexes, Ag6@C18 exhibits the highest first hyperpolarizability value of approximately 109496.2620 au calculated at the B3LYP/cc-PVDZ-pp level of theory, which is about 1.3 × 106 times higher than that of pure C18. This finding validates the effectiveness of the proposed strategies in enhancing the NLO response of the species. Moreover, the calculated UV-Vis absorption spectrum demonstrates that the Agn@C18 complexes with excess electrons exhibit absorption at longer wavelengths (ranging from 385 to 731 nm) compared to C18. In addition, the stability, chemical bonding, and charge transfer characteristics of the Agn@C18 (n = 4-6) complexes were also discussed. These findings highlight the potential of these complexes for the development of highly efficient NLO devices.

Spectroscopic Study of [Mg, H, N, C, O] Species: Implications for the Astrochemical Magnesium Chemistry

Magnesium is an abundant metal element in space, and magnesium chemistry has vital importance in the evolution of interstellar medium (ISM) and circumstellar regions, such as the asymptotic giant branch star IRC+10216 where a variety of Mg compounds bearing H, C, N, and O have been detected and proposed as the important components in the gas-phase molecular clouds and solid-state dust grains. Herein, we report the formation and infrared spectroscopic characterization of the Mg-bearing molecules HMg, [Mg, N, C], [Mg, H, N, C], [Mg, N, C, O], and [Mg, H, N, C, O] from the reactions of Mg/Mg+ and the prebiotic isocyanic acid (HNCO) in the solid neon matrix. Based on their thermal diffusion and photochemical behavior, a complex reactivity landscape involving association, decomposition, and isomerization reactions of these Mg-bearing molecules is developed, which can not only help understand the chemical processes of the magnesium (iso)cyanides in astrochemistry but also provide implications on the presence of magnesium (iso)cyanates in the ISM and the chemical model for the dust grain surface reactions. It also provides a new paradigm of the key intermediate nature of the cationic complexes in the formation of neutral interstellar species.

Global minimum and a heap of low-lying isomers with planar tetracoordinate carbon in the CAl3MgH2- system

A global minimum and a heap of low-lying isomers with planar tetracoordinate carbon (ptC) are identified in the CAl3MgH2- system by computational quantum chemical investigations. The nature of the chemical bonding in the global minimum ptC isomer is examined using the conceptual quantum chemical tools. The atoms in molecule (AIM) analysis reveals that the global minimum isomer possesses a ptC geometry. Additionally, the adaptive natural density partitioning (AdNDP), electron localization function (ELF), and nucleus-independent chemical shifts (NICS) analysis corroborate the presence of delocalization in the ptC isomer. The delocalization of electron density in the global minimum ptC isomer contributes to attaining structural stability. The results also suggest that the bridging hydrogen plays a crucial role in stabilizing the ptC system. Furthermore, the ab initio molecular dynamics study supports the structural stability of the ptC isomer.

Second quantization-based symmetry-adapted perturbation theory: Generalizing exchange beyond single electron pair approximation

This paper presents a general second-quantized form of a permutation operator interchanging n pairs of electrons between interacting subsystems in the framework of the symmetry-adapted perturbation theory (SAPT). We detail the procedure for constructing this operator through the consecutive multiplication of single-pair permutation operators. This generalized form of the permutation operator has enabled the derivation of universal formulas for S2n approximations of the exchange energies in the first and second order of the interaction operator. We present expressions for corrections of S4 approximations and assess its efficacy on a selection of systems anticipated to exhibit a slowly converging overlap expansion. Additionally, we outline a method to sum the overlap expansion series to infinity in second-quantization, up to the second order in V. This new approach offers an alternative to the existing formalism based on density-matrix formulations. When combined with a symbolic algebra program for automated derivations, it paves the way for advancements in SAPT theory, particularly for intricate wavefunction theories.

Insights into the Effect of Charges on Hydrogen Bonds

Previous computational and experimental studies showed that charges located at the surroundings of hydrogen bonds can exert two opposite effects on them: rupture or strengthening of the hydrogen bond. This work aims to generalize the effect of charges in different hydrogen-bonded systems and to propose a coherent explanation of this effect. For these purposes, 19 systems with intra- and intermolecular hydrogen bonds were studied computationally with DFT. The FT-IR spectra of the systems were simulated, and two energy components of the hydrogen bond were studied separately to determine their variation upon the presence of a charge: charge transfer and molecular overlap. It was determined that either the breaking or strengthening of the hydrogen bond can be favored one over the other, for instance, depending on the heteroatom involved in the hydrogen bond. In addition, it is showed that the strengthening of the hydrogen bond by the presence of a charge is directly related to the decrease in charge transfer between the monomers, which is explained by an increase in molecular overlapping, suggesting a more covalent character of the interaction. The understanding of how hydrogen bonds are affected by charges is important, as it is a key towards a strategy to manipulate hydrogen bonds at convenience.

Formulation and Implementation of Frequency-Dependent Linear Response Properties with Relativistic Coupled Cluster Theory for GPU-Accelerated Computer Architectures

We present the development and implementation of relativistic coupled cluster linear response theory (CC-LR), which allows the determination of molecular properties arising from time-dependent or time-independent electric, magnetic, or mixed electric-magnetic perturbations (within a common gauge origin for the magnetic properties) as well as taking into account the finite lifetime of excited states in the framework of damped response theory. We showcase our implementation, which is capable to offload the computationally intensive tensor contractions characteristic of coupled cluster theory onto graphical processing units, in the calculation of (a) frequency-(in)dependent dipole-dipole polarizabilities of IIB atoms and selected diatomic molecules, with a particular emphasis on the calculation of valence absorption cross sections for the I2 molecule; (b) indirect spin-spin coupling constants for benchmark systems such as the hydrogen halides (HX, X = F-I) as well the H2Se-H2O dimer as a prototypical system containing hydrogen bonds; and (c) optical rotations at the sodium D line for hydrogen peroxide analogues (H2Y2, Y = O, S, Se, Te). Thanks to this implementation, we are able to show the similarities in performance, but often the significant discrepancies, between CC-LR and approximate methods such as density functional theory. Comparing standard CC response theory with the flavor based upon the equation of motion formalism, we find that for valence properties such as polarizabilities, the two frameworks yield very similar results across the periodic table as found elsewhere in the literature; for properties that probe the core region, such as spin-spin couplings, on the other hand, we show a progressive differentiation between the two as relativistic effects become more important. Our results also suggest that as one goes down the periodic table, it may become increasingly difficult to measure pure optical rotation at the sodium D line due to the appearance of absorbing states.

Polarizable AMOEBA Model for Simulating Mg2+·Protein·Nucleotide Complexes

Molecular mechanics (MM) simulations have the potential to provide detailed insights into the mechanisms of enzymes that utilize nucleotides as cofactors. In most cases, the activities of these enzymes also require the binding of divalent cations to catalytic sites. However, modeling divalent cations in MM simulations has been challenging. The inclusion of explicit polarization was considered promising, but despite improvements over nonpolarizable force fields and despite the inclusion of "Nonbonded-fix (NB-fix)" corrections, errors in interaction energies of divalent cations with proteins remain large. Importantly, the application of these models fails to reproduce the experimental structural data on Mg2+·Protein·ATP complexes. Focusing on these complexes, here we provide a systematic assessment of the polarizable AMOEBA model and recommend critical changes that substantially improve its predictive performance. Our key results are as follows. We first show that our recent revision of the AMOEBA protein model (AMOEBABIO18-HFC), which contains high field corrections (HFCs) to induced dipoles, dramatically improves Mg2+-protein interaction energies, reducing the mean absolute error (MAE) from 17 to 10 kcal/mol. This further supports the general applicability of AMOEBABIO18-HFC. The inclusion of many-body NB-fix corrections further reduces MAE to 6 kcal/mol, which amounts to less than 2% error. The errors are estimated with respect to vdW-inclusive density functional theory that we benchmark against CCSD(T) calculations and experiments. We also present a new model of ATP with revised polarization parameters to better capture its high field response, as well as new vdW and dihedral parameters. The ATP model accurately predicts experimental Mg2+-ATP binding free energy in the aqueous phase and provides new insights into how Mg2+ associates with ATP. Finally, we show that molecular dynamics (MD) simulations of Mg2+·Kinase·ATP complexes carried out with these improvements lead to a better agreement in global and local catalytic site structures between MD and X-ray crystallography.

Trapping and thermal migration of the first- and second-row atoms in Ar, Kr and Xe crystals

Trapping and temperature-induced migration (TIM) of the first- and second-row atoms A from H to Ne in the face-centered cubic rare gas RG = Ar, Kr and Xe crystals are investigated within the classical crystal model parameterized by the empirically modified pairwise potentials. New ab initio coupled cluster A-RG potentials computed in a uniform way for all the atoms A are used to represent the atom-crystal interactions. Absolute and relative stabilities of the substitutional and interstitial trapping sites, their structures, interstitial migration pathways, related activation energies and rough estimates of the TIM rates are obtained. The isotropic model, which neglects non-zero atomic electronic orbital momentum, reveals that migration of interstitial atoms along the network of conjugated fcc octahedral voids is the generic case for atomic mobility. Anisotropic interactions with a crystal inherent to P-state atoms B, C, O and F are accounted for using the non-relativistic diatomics-in-molecule method. Depending on its sign, interaction anisotropy can alter the structures of interstitial trapping sites and transition states remarkably. This, in turn, can dramatically affect the TIM rates. Comparison with reliable experimental data available for oxygen and hydrogen indicates a systematic overestimation of the measured activation energies, by 30% at worst. A comprehensive literature review accomplished for other atoms reveals a lack of information on the TIM processes and rates, though makes it possible to verify a part of the present results on the trapping site energies and structures.

Revisiting Gauge-Independent Kinetic Energy Densities in Meta-GGAs and Local Hybrid Calculations of Magnetizabilities

In a recent study [J. Chem. Theory Comput. 2021, 17, 1457-1468], some of us examined the accuracy of magnetizabilities calculated with density functionals representing the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA (mGGA), as well as global hybrid (GH) and range-separated (RS) hybrid functionals by assessment against accurate reference values obtained with coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)]. Our study was later extended to local hybrid (LH) functionals by Holzer et al. [J. Chem. Theory Comput. 2021, 17, 2928-2947]; in this work, we examine a larger selection of LH functionals, also including range-separated LH (RSLH) functionals and strong-correlation LH (scLH) functionals. Holzer et al. also studied the importance of the physically correct handling of the magnetic gauge dependence of the kinetic energy density (τ) in mGGA calculations by comparing the Maximoff-Scuseria formulation of τ used in our aforementioned study to the more physical current-density extension derived by Dobson. In this work, we also revisit this comparison with a larger selection of mGGA functionals. We find that the newly tested LH, RSLH, and scLH functionals outperform all of the functionals considered in the previous studies. The various LH functionals afford the seven lowest mean absolute errors while also showing remarkably small standard deviations and mean errors. Most strikingly, the best two functionals are scLHs that also perform remarkably well in cases with significant multiconfigurational character, such as the ozone molecule, which is traditionally excluded from statistical error evaluations due to its large errors with common density functionals.

DAPD Set of Pd-Containing Diatomic Molecules: Accurate Molecular Properties and the Great Lengths to Obtain Them

In the present study, we obtained reliable bond energy, bond length, and zero-point vibrational frequency for a set of diatomic Pd species (the DAPD set). It includes PdH, Pd2, and PdX (X = B, C, N, O, F, Al, Si, P, S, and Cl). Our highest-level protocol (W4X-L) represents scalar and spin-orbit relativistic, valence- and inner-valence correlated, extrapolated CCSDTQ(5) energy. The DAPD set of molecules is challenging for computational chemistry methods in different manners; for Pd2, the spin-orbit contribution to the bond energy is fairly large, whereas for PdC and PdSi, the post-CCSD(T) correlation components are considerable. The diverse range of requirements represents a significant challenge for lower-level methods. While density functional theory (DFT) methods generally yield good agreements for bond lengths and vibrational frequencies, large deviations are found for bond energies. In general, hybrid DFT methods are more accurate than nonhybrid functionals, but the agreement in individual cases varies. This illustrates the critical role that new high-quality reference data would play in the continual development of lower-cost methods.

Nested gausslet basis sets

We introduce nested gausslet bases, an improvement on previous gausslet bases that can treat systems containing atoms with much larger atomic numbers. We also introduce pure Gaussian distorted gausslet bases, which allow the Hamiltonian integrals to be performed analytically, as well as hybrid bases in which the gausslets are combined with standard Gaussian-type bases. All these bases feature the diagonal approximation for the electron-electron interactions so that the Hamiltonian is completely defined by two Nb × Nb matrices, where Nb ≈ 104 is small enough to permit fast calculations at the Hartree-Fock level. In constructing these bases, we have gained new mathematical insight into the construction of one-dimensional diagonal bases. In particular, we have proved an important theorem relating four key basis set properties: completeness, orthogonality, zero-moment conditions, and diagonalization of the coordinate operator matrix. We test our basis sets on small systems with a focus on high accuracy, obtaining, for example, an accuracy of 2 × 10-5 Ha for the total Hartree-Fock energy of the neon atom in the complete basis set limit.

Gas-Phase Alkali-Metal Cation Affinities of Stabilized Enolates

The chemistry of alkali-metal enolates is dominated by ion pairing. To improve our understanding of the intrinsic interactions between the alkali-metal cations and the enolate anions, we have applied Cooks' kinetic method to determine relative M+ (M=Li, Na, K) affinities of the stabilized enolates derived from acetylacetone, ethyl acetoacetate, diethyl malonate, ethyl cyanoacetate, 2-cyanoacetamide, and methyl malonate monoamide in the gas phase. Quantum chemical calculations support the experimental results and moreover afford insight into the structures of the alkali-metal enolate complexes. The affinities decrease with increasing size of the alkali-metal cations, reflecting weaker electrostatic interactions and lower charge densities of the free M+ ions. For the different enolates, a comparison of their coordinating abilities is complicated by the fact that some of the free anions undergo conformational changes resulting in stabilizing intramolecular interactions. If these complicating effects are disregarded, the M+ affinities correlate with the electron density of the chelating functionalities, that is, the carbonyl and/or the nitrile groups of the enolates. A comparison with the known association constants of the corresponding alkali-metal enolates in solution points to the importance of solvation effects for these systems.

Benchmarking Basis Sets for Density Functional Theory Thermochemistry Calculations: Why Unpolarized Basis Sets and the Polarized 6-311G Family Should Be Avoided

Basis sets are a crucial but often largely overlooked choice in setting up quantum chemistry calculations. The choice of the basis set can be critical in determining the accuracy and calculation time of your quantum chemistry calculations. Clear recommendations based on thorough benchmarking are essential but not readily available currently. This study investigates the relative quality of basis sets for general properties by benchmarking basis set performance for a diverse set of 139 reactions (from the diet-150-GMTKN55 data set). In our analysis, we find the distributions of errors are often significantly non-Gaussian, meaning that the joint consideration of median errors, mean absolute errors, and outlier statistics is helpful to provide a holistic understanding of basis set performance. Our direct comparison of performance between most modern basis sets provides quantitative evidence for basis set recommendations that broadly align with the established understanding of basis set experts and is evident in the design of modern basis sets. For example, while zeta is a good measure of quality, it is not the only determining factor for an accurate calculation with unpolarized double- and triple-ζ basis sets (like 6-31G and 6-311G) having very poor performance. Appropriate use of polarization functions (e.g., 6-31G*) is essential to obtain the accuracy offered by double- or triple-ζ basis sets. In our study, the best performances for double- and triple-ζ basis sets are 6-31++G** and pcseg-2, respectively. However, the performances of singly polarized double-ζ and doubly polarized triple-ζ basis sets are quite similar with one key exception: the polarized 6-311G basis set family has poor parametrization, which means its performance is more like a double-ζ than a triple-ζ basis set. All versions of the 6-311G basis set family should be avoided entirely for valence chemistry calculations moving forward.

Triphenylphosphine─Closed-Shell Metal Cation Interactions

The interactions between group 1 and 11 monocations and group 2 dications with triphenylphosphine were studied by using a combination of correlated molecular orbital theory and density functional theory. Two binding modes were found: the front side (phosphorus lone pair) and back side (phenyl rings). Group 1 and 2 cations prefer binding to the π system rather than to the lone pair of the phosphorus atom, and their ligand binding energies (LBEs) correlate with the atomic ionic radii as well as the hardness of the atomic ion. Group 11 monocations prefer binding to the lone pair of the phosphorus atom, and their LBEs are correlated with the hardness of the cation but exhibit a different trend than for the groups 1 and 2 cations. The LBEs of the cations with C2H4, C6H6, and C6H5PH2 are also reported to aid in the analysis of the cation-π interactions and the influence of the PH2 substituent on the energy of this interaction. The LBEs for binding to C2H4 and C6H6 are the most complete and reliable set of values for these species.

Magnetic optical rotation from real-time simulations in finite magnetic fields

We present a numerical approach to magnetic optical rotation based on real-time time-dependent electronic-structure theory. Not relying on perturbation expansions in the magnetic field strength, the formulation allows us to test the range of validity of the linear relation between the rotation angle per unit path length and the magnetic field strength that was established empirically by Verdet 160 years ago. Results obtained from time-dependent coupled-cluster and time-dependent current density-functional theory are presented for the closed-shell molecules H2, HF, and CO in magnetic fields up to 55 kT at standard temperature and pressure conditions. We find that Verdet's linearity remains valid up to roughly 10-20 kT, above which significant deviations from linearity are observed. Among the three current density-functional approximations tested in this work, the current-dependent Tao-Perdew-Staroverov-Scuseria hybrid functional performs the best in comparison with time-dependent coupled-cluster singles and doubles results for the magnetic optical rotation.

Cooperativity and Frustration Effects (or Lack Thereof) in Polarizable and Non-polarizable Force Fields

Understanding cooperativity and frustration is crucial for studying biological processes such as molecular recognition and protein aggregation. Force fields have been extensively utilized to explore cooperativity in the formation of protein secondary structures and self-assembled systems. Multiple studies have demonstrated that polarizable force fields provide more accurate descriptions of this phenomenon compared to fixed-charge pairwise nonpolarizable force fields, thanks to the incorporation of polarization effects. In this study, we assess the performance of the AMOEBA polarizable force field and the AMBER and OPLS nonpolarizable pairwise force fields in capturing positive and negative cooperativity recently explored in neutral and charged molecular clusters using density functional theory. Our findings show that polarizable and nonpolarizable force fields qualitatively reproduce the relative cooperativity observed in electron structure calculations. However, AMBER and OPLS fail to describe absolute cooperativity. In contrast, AMOEBA accounts for the absolute cooperativity by considering interactions beyond pairwise interactions. According to the energy decomposition analysis, it is observed that the electrostatic interactions calculated with the AMBER and OPLS force fields seem to play an important and counterintuitive role in reproducing the adiabatic interaction energies calculated with density functional theory. However, it is important to note that these force fields, due to their nature, do not explicitly incorporate many-body effects, which limits their ability to accurately describe cooperativity. On the other hand, frustration in polarizable and nonpolarizable force fields is caused by changes in bond stretching and angle bending terms of the building blocks when they are forming a complex.

Corrected density functional theory and the random phase approximation: Improved accuracy at little extra cost

We recently introduced an efficient methodology to perform density-corrected Hartree-Fock density functional theory [DC(HF)-DFT] calculations and an extension to it we called "corrected" HF DFT [C(HF)-DFT] [Graf and Thom, J. Chem. Theory Comput. 19 5427-5438 (2023)]. In this work, we take a further step and combine C(HF)-DFT, augmented with a straightforward orbital energy correction, with the random phase approximation (RPA). We refer to the resulting methodology as corrected HF RPA [C(HF)-RPA]. We evaluate the proposed methodology across various RPA methods: direct RPA (dRPA), RPA with an approximate exchange kernel, and RPA with second-order screened exchange. C(HF)-dRPA demonstrates very promising performance; for RPA with exchange methods, on the other hand, we often find over-corrections.

Direct Determination of Optimal Real-Space Orbitals for Correlated Electronic Structure of Molecules

We demonstrate how to determine numerically nearly exact orthonormal orbitals that are optimal for the evaluation of the energy of arbitrary (correlated) states of atoms and molecules by minimization of the energy Lagrangian. Orbitals are expressed in real space using a multiresolution spectral element basis that is refined adaptively to achieve the user-specified target precision while avoiding the ill-conditioning issues that plague AO basis set expansions traditionally used for correlated models of molecular electronic structure. For light atoms, the orbital solver, in conjunction with a variational electronic structure model [selected Configuration Interaction (CI)] provides energies of comparable precision to a state-of-the-art atomic CI solver. The computed electronic energies of atoms and molecules are significantly more accurate than the counterparts obtained with the orbital sets of the same rank expanded in Gaussian AO bases, and can be determined even when linear dependence issues preclude the use of the AO bases. It is feasible to optimize more than 100 fully correlated numerical orbitals on a single computer node, and significant room exists for additional improvement. These findings suggest that real-space orbital representations might be the preferred alternative to AO representations for high-end models of correlated electronic states of molecules and materials.

Comparison of Density-Functional Theory Dispersion Corrections for the DES15K Database

While density-functional theory (DFT) remains one of the most widely used tools in computational chemistry, most functionals fail to properly account for the effects of London dispersion. Hence, there are many popular post-self-consistent methods to add a dispersion correction to the DFT energy. Until now, the most popular methods have never been compared on equal footing due to not being implemented in the same electronic structure packages. In this work, we performed a large-scale benchmarking study, directly comparing the accuracy of the exchange-hole dipole moment (XDM), D3BJ, D4, TS, MBD, and MBD-NL dispersion models when applied to the recent DES15K database of nearly 15,000 molecular complexes at both expanded and compressed geometries. Our study showed similarly good performance for all dispersion methods (except TS) when applied to neutral complexes. However, they all performed worse for ionic complexes, particularly those involving dications of alkaline earth metals, due to systematic overbinding by the base PBE0 density functional. Investigation of the largest outliers also revealed that only the MBD and MBD-NL methods demonstrate surprising errors for complexes involving alkali metal cations at compressed geometries where they tended to significantly overbind. As we would expect minimal dispersion binding for such complexes, we further investigated the origins of these errors for the potential energy curve of a model cation-π complex. Overall, there is little choice between the XDM, D3BJ, D4, MBD, and MBD-NL dispersion methods for most systems. However, the MBD-based methods are not recommended for complexes involving organic species and alkali or alkaline earth metal cations, for example when modeling Li+ intercalation into graphite.

Semiempirical Methods for Molecular Systems in Strong Magnetic Fields

A general scheme is presented to extend semiempirical methods to include the effects of arbitrary strength magnetic fields, while maintaining computational efficiency. The approach utilizes three main modifications; a London atomic orbital (LAO) basis set is introduced, field-dependent kinetic energy corrections are added to the model Hamiltonian, and spin-Zeeman interaction energy terms are included. The approach is applied to the widely available density-functional tight-binding method GFN1-xTB. Considering the basis set requirements for the kinetic energy corrections in a magnetic field leads to two variants: a single-basis approach GFN1-xTB-M0 and a dual-basis approach GFN1-xTB-M1. The LAO basis in the latter includes the appropriate nodal structure for an accurate representation of the kinetic energy corrections. The variants are assessed by benchmarking magnetizabilities and nuclear magnetic resonance shielding constants calculated using weak magnetic fields. Remarkably, the GFN1-xTB-M1 approach also exhibits excellent performance for strong fields, |B | ≤ 0.2B0 (B0 = 2.3505 × 105 T), recovering exotic features such as the para- to dia-magnetic transition in the BH molecule and the preferred electronic configuration, molecular conformation, and orientation of benzene. At stronger field strengths, |B | > 0.2B0, a degradation in the quality of the results is observed. The utility of GFN1-xTB-M1 is demonstrated by performing conformer searches in a range of field strengths for the cyclooctatetraene molecule, with GFN1-xTB-M1 capturing the transition from tub to planar conformations at high field, consistent with much more computationally demanding current-density functional theory calculations. Magnetically induced currents are also shown to be well described for the benzene and infinitene molecules, the latter demonstrating the flexibility and computational efficiency of the approach. The GFN1-xTB-M1 approach is a useful tool for the study of structure, conformation, and dynamics of large systems in magnetic fields at the semiempirical level as well as for preoptimization of molecular structure in ab initio calculations, enabling more efficient exploration of complex potential energy surfaces and reactivity in the presence of external fields.

Photoelectron Velocity Map Imaging Spectroscopy of the Beryllium Trimer and Tetramer

Computational studies of small beryllium clusters (BeN) predict dramatic, nonmonotonic changes in the bonding mechanisms and per-atom cohesion energies with increasing N. To date, experimental tests of these quantum chemistry models are lacking for all but the Be2 molecule. In the present study, we report spectroscopic data for Be3 and Be4 obtained via anion photodetachment spectroscopy. The trimer is predicted to have D3h symmetric equilibrium structures for both the neutral molecule and the anion. Photodetachment spectra reveal transitions that originate from the X2A2″ ground state and the 12A1' electronically excited state. The state symmetries were assigned on the basis of anisotropic photoelectron angular distributions. The neutral and anionic forms of Be4 are predicted to be tetrahedral. Franck-Condon diagonal photodetachment was observed with a photoelectron angular distribution consistent with the expected Be4-X2A1 → Be4X1A1 transition. The electron affinities of Be3 and Be4 were determined to be 11363 ± 60 and 13052 ± 50 cm-1, respectively.

Neutral gas pressure dependence of ion-ion mutual neutralization rate constants using Landau-Zener theory coupled with trajectory simulations

In this computational study, we describe a self-consistent trajectory simulation approach to capture the effect of neutral gas pressure on ion-ion mutual neutralization (MN) reactions. The electron transfer probability estimated using Landau-Zener (LZ) transition state theory is incorporated into classical trajectory simulations to elicit predictions of MN cross sections in vacuum and rate constants at finite neutral gas pressures. Electronic structure calculations with multireference configuration interaction and large correlation consistent basis sets are used to derive inputs to the LZ theory. The key advance of our trajectory simulation approach is the inclusion of the effect of ion-neutral interactions on MN using a Langevin representation of the effect of background gas on ion transport. For H+ - H- and Li+ - H(D)-, our approach quantitatively agrees with measured speed-dependent cross sections for up to ∼105 m/s. For the ion pair Ne+ - Cl-, our predictions of the MN rate constant at ∼1 Torr are a factor of ∼2 to 3 higher than the experimentally measured value. Similarly, for Xe+ - F- in the pressure range of ∼20 000-80 000 Pa, our predictions of the MN rate constant are ∼20% lower but are in excellent qualitative agreement with experimental data. The paradigm of using trajectory simulations to self-consistently capture the effect of gas pressure on MN reactions advanced here provides avenues for the inclusion of additional nonclassical effects in future work.

Correlation Consistent Basis Sets for Explicitly Correlated Theory: The Transition Metals

We present correlation consistent basis sets for explicitly correlated (F12) calculations, denoted VnZ(-PP)-F12-wis (n = D,T), for the d-block elements. The cc-pVDZ-F12-wis basis set is contracted to [8s7p5d2f] for the 3d-block, while its ECP counterpart for the 4d and 5d-blocks, cc-pVDZ-PP-F12-wis, is contracted to [6s6p5d2f]. The corresponding contracted sizes for cc-pVTZ(-PP)-F12-wis are [9s8p6d3f2g] for the 3d-block elements and [7s7p6d3f2g] for the 4d and 5d-block elements. Our VnZ(-PP)-F12-wis basis sets are evaluated on challenging test sets for metal-organic barrier heights (MOBH35) and group-11 metal clusters (CUAGAU-2). In F12 calculations, they are found to be about as close to the complete basis set limit as the combination of standard cc-pVnZ-F12 on main-group elements with the standard aug-cc-pV(n+1)Z(-PP) basis sets on the transition metal(s). While our basis sets are somewhat more compact than aug-cc-pV(n+1)Z(-PP), the CPU time benefit is negligible for catalytic complexes that contain only one or two transition metals among dozens of main-group elements; however, it is somewhat more significant for metal clusters.