Vibrational zero-point energies and thermodynamic functions beyond the harmonic approximation

A Strategy for Modeling Nonstatistical Reactivity Effects: Combining Chemical Activation Estimates with a Vibrational Relaxation Model

The kinetics of many chemical reactions can be readily explained with a statistical approach, for example, using a form of transition state theory and comparing calculated Gibbs energies along the reaction coordinate(s). However, there are cases where this approach fails, notably when the vibrational relaxation of the molecule to its statistical equilibrium occurs on the same time scale as the reaction dynamics, whether it is caused by slow relaxation, a fast reaction, or both. These nonstatistical phenomena are then often explored computationally using (quasi)classical ab initio molecular dynamics by calculating a large number of trajectories while being prone to issues such as zero-point energy leakage. On the other side of the field, we see resource-intensive quantum dynamics simulations, which significantly limit the size of explorable systems. We find that using a Fermi's golden rule type of model for vibrational relaxation, based on anharmonic coupling constants, we can extract the same qualitative information while giving insights into how to enhance (or destroy) the bottlenecks causing the phenomena. We present this model as a middle ground for exploring complex nonstatistical behavior, capable of treating medium-sized organic molecules or biologically relevant fragments. We also cover the challenges involved, in particular quantifying the excess energy in terms of vibrational modes. Relying on readily available electronic structure methods and providing results in a simple master equation form, this model shows promise as a screening tool for opportunities in mode-selective chemistry without external control.

Accurate Vibrational and Ro-Vibrational Contributions to the Properties of Large Molecules by a New Engine Employing Curvilinear Internal Coordinates and Vibrational Perturbation Theory to Second Order

The unbiased comparison between theory and experiment requires approaches more sophisticated than the basic harmonic-oscillator rigid-rotor model, for taking into account vibrational averaging effects and ro-vibrational couplings in molecules of increasing size. Second-order vibrational perturbation theory based on curvilinear internal coordinates (ICs) offers a remarkable compromise between accuracy and computational cost, thanks to the reduction of mode-mode couplings with respect to their counterparts based on Cartesian coordinates. Therefore, we have developed, implemented, and validated a general engine employing ICs, which allows the accurate evaluation of vibrational averages and ro-vibrational couplings for molecules containing up to about 50 atoms beyond the harmonic approximation. After validation of the new tool for relatively small molecules, the effectiveness of ICs has been demonstrated for some flexible and/or quite large molecular bricks of life.

Harmonic and anharmonic vibrational computations for biomolecular building blocks: Benchmarking DFT and basis sets by theoretical and experimental IR spectrum of glycine conformers

Advanced vibrational spectroscopic experiments have reached a level of sophistication that can only be matched by numerical simulations in order to provide an unequivocal analysis, a crucial step to understand the structure-function relationship of biomolecules. While density functional theory (DFT) has become the standard method when targeting medium-size or larger systems, the problem of its reliability and accuracy are well-known and have been abundantly documented. To establish a reliable computational protocol, especially when accuracy is critical, a tailored benchmark is usually required. This is generally done over a short list of known candidates, with the basis set often fixed a priori. In this work, we present a systematic study of the performance of DFT-based hybrid and double-hybrid functionals in the prediction of vibrational energies and infrared intensities at the harmonic level and beyond, considering anharmonic effects through vibrational perturbation theory at the second order. The study is performed for the six-lowest energy glycine conformers, utilizing available "state-of-the-art" accurate theoretical and experimental data as reference. Focusing on the most intense fundamental vibrations in the mid-infrared range of glycine conformers, the role of the basis sets is also investigated considering the balance between computational cost and accuracy. Targeting larger systems, a broad range of hybrid schemes with different computational costs is also tested.

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.

IR spectroscopic characterization of [M,C,2H]+ (M = Ru and Rh) products formed by reacting 4d transition metal cations with oxirane: Spectroscopic evidence for multireference character in RhCH2. Phys Chem Chem Phys 2024;26:11445-11458. [PMID: 38572552 PMCID: PMC11022548 DOI: 10.1039/d4cp00012a]

A combination of infrared multiple-photon dissociation (IRMPD) action spectroscopy and quantum chemical calculations was employed to investigate the [M,C,2H]+ (M = Ru and Rh) species. These ions were formed by reacting laser ablated M+ ions with oxirane (ethylene oxide, c-C2H4O) in a room-temperature ion trap. IRMPD spectra for the Ru species exhibit one major band and two side bands, whereas spectra for the Rh species contain more distinct bands. Comparison with density functional theory (DFT), coupled-cluster (CCSD), and equation-of-motion spin-flip CCSD (EOM-SF-CCSD) calculations allows assignment of the [M,C,2H]+ structures. For the spectrum of [Ru,C,2H]+, a combination of HRuCH+ and RuCH2+ structures reproduces the observed spectrum at all levels of theory. The well-resolved spectrum of [Rh,C,2H]+ could not be assigned unambiguously to any calculated structure using DFT approaches. The EOM-SF-CCSD calculations showed that the ground-state surface has multireference electronic character, and symmetric carbenes in both the 1A1 and 3A2 states are needed to reproduce the observed spectrum.

Prebiotic dimer and trimer peptide formation in gas-phase atmospheric nanoclusters of water

Insight into the origin of prebiotic molecules is key to our understanding of how living systems evolved into the complex network of biological processes on Earth. By modelling diglycine and triglycine peptide formation in the prebiotic atmosphere, we provide a plausible pathway for peptide growth. By examining different transition states (TSs), we conclude that the formation of diglycine and triglycine in atmospheric nanoclusters of water in the prebiotic atmosphere kinetically favors peptide growth by an N-to-C synthesis of glycines through a trans conformation. Addition of water stabilizes the TS structures and lowers the Gibbs free activation energies. At temperatures that model the prebiotic atmosphere, the free energies of activation with a six water nanocluster as part of the TS are predicted to be 16 kcal mol-1 relative to the prereactive complex. Examination of the trans vs. cis six water transition states reveals that a homodromic water network that maximizes the acceptor/donor nature of the six waters is responsible for enhanced kinetic favorability of the trans N-to-C pathway. Compared to the non-hydrated trans TS, the trans six-water TS accelerates the reaction of diglycine and glycine to form triglycine by 13 orders of magnitude at 217 K. Nature uses the trans N-to-C pathway to synthesize proteins in the ribosome, and we note the similarities in hydrogen bond stabilization between the transition state for peptide synthesis in the ribosome and the transition states formed in nanoclusters of water in the same pathway. These results support the hypothesis that small oligomers formed in the prebiotic atmosphere and rained onto earth's surface.

Preparation and Spectroscopic Identification of the Cyclic CO2 Dimer 1,2-Dioxetanedione

We report the preparation and infrared spectroscopic identification of 1,2-dioxetanedione, which is one of the two possible cyclic dimers of carbon dioxide. We prepared this hitherto experimentally incompletely characterized species in a solid nitrogen matrix at 3 K from the reaction of oxalyl dichloride with the urea·hydrogen peroxide complex. Surprisingly, irradiation at 254 nm does not lead to its dissociation into carbon dioxide but rather yields cyclic carbon trioxide. We further assert our spectroscopic assignments by 18O isotopic labeling and high-level N-electron valence state perturbation theory and coupled-cluster computations. The successful isolation of 1,2-dioxetanedione supports its viability as the postulated high-energy intermediate in the well-known and ubiquitously exploited "peroxyoxalate" chemiluminescent system.

Accurate Potential Energy Surfaces Using Atom-Centered Potentials and Minimal High-Level Data

We demonstrate that a Δ-density functional theory (Δ-DFT) approach based on atom-centered potentials (ACPs) represents a computationally inexpensive and accurate method for representing potential energy surfaces (PESs) for the HONO and HFCO molecules and vibrational frequencies derived therefrom. Using as few as 100 CCSD(T)-F12a reference energies, ACPs developed for use with B3LYP/def2-TZVPP are shown to produce PESs for HONO and HFCO with mean absolute errors of 27.7 and 5.8 cm-1, respectively. Application of the multiconfigurational time-dependent Hartree (MCTDH) method with ACP-corrected B3LYP/def2-TZVPP PESs produces vibrational frequencies for cis- and trans-HONO with mean absolute percent errors (MAPEs) of 0.8 and 1.1, compared to 0.8 obtained for the two isomers with CCSD(T)-F12a/cc-pVTZ-F12/MCTDH. For HFCO, the vibrational frequencies obtained using the present (Δ-DFT)/MCTDH approach give a MAPE of 0.1, which is the error obtained with CCSD(T)-F12a/cc-pVTZ-F12/MCTDH. The ACP approach is therefore successful in representing a PES calculated at a high level of theory (CCSD(T)-F12a) and a promising method for the development of a general protocol for the representation of accurate molecular PESs and the calculation of molecular properties from them.

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose-Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh-Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born-Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick's theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn-Luttinger-type nonconvergence.

An approximation to the vibrational coupled-cluster method for CH-stretching of large molecules: application to naphthalene and anthracene

We propose an approximation to the vibrational coupled-cluster method (VCCM) to describe the CH-stretching region of the vibrational spectrum of large molecules. The vibrational modes of a molecule are divided into two sets: the target set and the bath set. The target set includes the CH stretches and the modes that are strongly coupled with the CH stretches and/or involve strong Fermi resonances with a CH stretch fundamental. The rest of the modes are in the bath set. First, the effective harmonic oscillator (EHO) approximation is invoked for the whole system to obtain the zeroth-order frequencies and modified potentials. The effects of interaction between the bath set and the target sets are included in the modified potential from the EHO calculation. The VCCM equations are constructed with the modified potential from the EHO calculations and for the target set only. The transition energies and intensities are calculated using such a truncated VCCM approximation. The proposed method is applied to calculate the IR spectra of naphthalene and anthracene. The results with three different criteria for selecting the modes in the target set are compared with the experimental IR spectra.

Transient 2D IR Spectroscopy and Multiscale Simulations Reveal Vibrational Couplings in the Cyanobacteriochrome Slr1393-g3

Cyanobacteriochromes are bistable photoreceptor proteins with desirable photochemical properties for biotechnological applications, such as optogenetics or fluorescence microscopy. Here, we investigate Slr1393-g3, a cyanobacteriochrome that reversibly photoswitches between a red-absorbing (Pr) and green-absorbing (Pg) form. We applied advanced IR spectroscopic methods to track the sequence of intermediates during the photocycle over many orders of magnitude in time. In the conversion from Pg to Pr, we have revealed a new intermediate with distinct spectroscopic features in the IR, which precedes Pr formation using transient IR spectroscopy. In addition, stationary and transient 2D IR experiments measured the vibrational couplings between different groups of the chromophore and the protein in these intermediate states, as well as their structural disorder. Anharmonic QM/MM calculations predict spectra in good agreement with experimental 2D IR spectra of the initial and final states of the photocycle. They facilitate the assignment of the IR spectra that serve as a basis for the interpretation of the spectroscopic results and suggest structural changes of the intermediates along the photocycle.

Reconstructed Ir‒O‒Mo species with strong Brønsted acidity for acidic water oxidation

Surface reconstruction generates real active species in electrochemical conditions; rational regulating reconstruction in a targeted manner is the key for constructing highly active catalyst. Herein, we use the high-valence Mo modulated orthorhombic Pr₃Ir_1-xMo_xO₇ as model to activate lattice oxygen and cations, achieving directional and accelerated surface reconstruction to produce self-terminated Ir‒O_bri‒Mo (O_bri represents the bridge oxygen) active species that is highly active for acidic water oxidation. The doped Mo not only contributes to accelerated surface reconstruction due to optimized Ir‒O covalency and more prone dissolution of Pr, but also affords the improved durability resulted from Mo-buffered charge compensation, thereby preventing fierce Ir dissolution and excessive lattice oxygen loss. As such, Ir‒O_bri‒Mo species could be directionally generated, in which the strong Brønsted acidity of O_bri induced by remaining Mo assists with the facilitated deprotonation of oxo intermediates, following bridging-oxygen-assisted deprotonation pathway. Consequently, the optimal catalyst exhibits the best activity with an overpotential of 259 mV to reach 10 mA cm_geo^-2, 50 mV lower than undoped counterpart, and shows improved stability for over 200 h. This work provides a strategy of directional surface reconstruction to constructing strong Brønsted acid sites in IrO_x species, demonstrating the perspective of targeted electrocatalyst fabrication under in situ realistic reaction conditions.

Calculating Vibrational Excited State Absorptions with Excited State Constrained Minimized Energy Surfaces

The modeling and interpretation of vibrational spectra are crucial for studying reaction dynamics using vibrational spectroscopy. Most prior theoretical developments focused on describing fundamental vibrational transitions while fewer developments focused on vibrational excited state absorptions. In this study, we present a new method that uses excited state constrained minimized energy surfaces (CMESs) to describe vibrational excited state absorptions. The excited state CMESs are obtained similarly to the previous ground state CMES development in our group but with additional wave function orthogonality constraints. Using a series of model systems, including the harmonic oscillator, Morse potential, double-well potential, quartic potential, and two-dimensional anharmonic potential, we demonstrate that this new procedure provides good estimations of the transition frequencies for vibrational excited state absorptions. These results are significantly better than those obtained from harmonic approximations using conventional potential energy surfaces, demonstrating the promise of excited state CMES-based methods for calculating vibrational excited state absorptions in real systems.

Harmonic Vibrational Frequency Simulation of Pharmaceutical Molecules via a Novel Multi-Molecular Fragment Interception Method

By means of a computational method based on Density Functional Theory (DFT), using commercially available software, a novel method for simulating equilibrium geometry harmonic vibrational frequencies is proposed. Finasteride, Lamivudine, and Repaglinide were selected as model molecules to study the adaptability of the new method. Three molecular models, namely the single-molecular, central-molecular, and multi-molecular fragment models, were constructed and calculated by Generalized Gradient Approximations (GGAs) with the PBE functional via the Material Studio 8.0 program. Theoretical vibrational frequencies were assigned and compared to the corresponding experimental data. The results indicated that the traditional single-molecular calculation and scaled spectra with scale factor exhibited the worst similarity for all three pharmaceutical molecules among the three models. Furthermore, the central-molecular model with a configuration closer to the empirical structure resulted in a reduction of mean absolute error (MAE) and root mean squared error (RMSE) in all three pharmaceutics, including the hydrogen-bonded functional groups. However, the improvement in computational accuracy for different drug molecules using the central-molecular model for vibrational frequency calculation was unstable. Whereas, the new multi-molecular fragment interception method showed the best agreement with experimental results, exhibiting MAE and RMSE values of 8.21 cm^-1 and 18.35 cm^-1 for Finasteride, 15.95 cm^-1 and 26.46 cm^-1 for Lamivudine, and 12.10 cm^-1 and 25.82 cm^-1 for Repaglinide. Additionally, this work provides comprehensive vibrational frequency calculations and assignments for Finasteride, Lamivudine, and Repaglinide, which have never been thoroughly investigated in previous research.

Isotope Effects in the Zundel-Eigen Isomerization of H+(H2O)6

The isomerization pathway between the energetically low-lying Zundel and Eigen isomers of the protonated water hexamer was investigated using high-level ab initio calculations including a treatment of zero-point corrections. On the basis of these calculations, the Zundel-Eigen isomerization was found to proceed through a stable intermediate isomer, which consists of a four-membered ring with two single acceptor water molecules. The inclusion of vibrational zero-point energy is shown to be important for accurately establishing the relative energies of the three relevant isomers involved in the Zundel-Eigen isomerization. Diffusion Monte Carlo calculations including anharmonic vibrational effects show that all three isomers of H⁺(H₂O)₆ and D⁺(D₂O)₆ have well-defined structures. The energetic ordering of the three isomers changes upon deuteration. The implications of these results for the vibrational spectra of H⁺(H₂O)₆ and D⁺(D₂O)₆ are also discussed.

The role of oxygen-vacancy in bifunctional indium oxyhydroxide catalysts for electrochemical coupling of biomass valorization with CO2 conversion

Electrochemical coupling of biomass valorization with carbon dioxide (CO₂) conversion provides a promising approach to generate value-added chemicals on both sides of the electrolyzer. Herein, oxygen-vacancy-rich indium oxyhydroxide (InOOH-O_V) is developed as a bifunctional catalyst for CO₂ reduction to formate and 5-hydroxymethylfurfural electrooxidation to 2,5-furandicarboxylic acid with faradaic efficiencies for both over 90.0% at optimized potentials. Atomic-scale electron microscopy images and density functional theory calculations reveal that the introduction of oxygen vacancy sites causes lattice distortion and charge redistribution. Operando Raman spectra indicate oxygen vacancies could protect the InOOH-O_V from being further reduced during CO₂ conversion and increase the adsorption competitiveness for 5-hydroxymethylfurfural over hydroxide ions in alkaline electrolytes, making InOOH-O_V a main-group p-block metal oxide electrocatalyst with bifunctional activities. Based on the catalytic performance of InOOH-O_V, a pH-asymmetric integrated cell is fabricated by combining the CO₂ reduction and 5-hydroxymethylfurfural oxidation together in a single electrochemical cell to produce 2,5-furandicarboxylic acid and formate with high yields (both around 90.0%), providing a promising approach to generate valuable commodity chemicals simultaneously on both electrodes.

Perturb-Then-Diagonalize Vibrational Engine Exploiting Curvilinear Internal Coordinates

The present paper is devoted to the implementation and validation of a second-order perturbative approach to anharmonic vibrations, followed by variational treatment of strong couplings (GVPT2) based on curvilinear internal coordinates. The main difference with respect to the customary Cartesian-based formulation is that the kinetic energy operator is no longer diagonal, and has to be expanded as well, leading to additional terms which have to be taken into proper account. It is, however, possible to recast all the equations as well-defined generalizations of the corresponding Cartesian-based counterparts, thus achieving a remarkable simplification of the new implementation. Particular attention is paid to the treatment of Fermi resonances with significant number of test cases analyzed fully, validating the new implementation. The results obtained in this work confirm that curvilinear coordinates strongly reduce the strength of inter-mode couplings compared to their Cartesian counterparts. This increases the reliability of low-order perturbative treatments for semi-rigid molecules and paves the way toward the reliable representation of more flexible molecules where small- and large-amplitude motions can be safely decoupled and treated at different levels of theory.

Controllable States and Porosity of Cu-Carbon for CO2 Electroreduction to Hydrocarbons

The electrocatalytic carbon dioxide reduction reaction (CO₂ RR) to value-added chemical products is an effective strategy for both greenhouse effect mitigation and high-density energy storage. However, controllable manipulation of the oxidation state and porous structure of Cu-carbon based catalysts to achieve high selectivity and current density for a particular product remains very challenging. Herein, a strategy derived from Cu-based metal-organic frameworks (MOFs) for the synthesis of controllable oxidation states and porous structure of Cu-carbon (Cu-pC, Cu₂ O-pC, and Cu₂ O/Cu-pC) is demonstrated. By regulating oxygen partial pressure during the annealing process, the valence state of the Cu and mesoporous structures of surrounding carbon are changed, leads to the different selectivity of products. Cu₂ O/CuO-pC with the higher oxidation state exhibits FE_C2H4 of 65.12% and a partial current density of -578 mA cm^-2 , while the Cu₂ O-pC shows the FE_CH4 over 55% and a partial current density exceeding -438 mA cm^-2 . Experimental and theoretical studies indicate that porous carbon-coated Cu₂ O structures favor the CH₄ pathway and inhibit the hydrogen evolution reaction. This work provides an effective strategy for exploring the influence of the various valence states of Cu and mesoporous carbon structures on the selectivity of CH₄ and C₂ H₄ products in CO₂ RR.

Amino Acids Compete with Ammonia in Sulfuric Acid-Based Atmospheric Aerosol Prenucleation: The Case of Glycine and Serine

We present a computational investigation of the sulfuric acid, glycine, serine, ammonia, and water system to understand if this system can form prenucleation clusters, which are precursors to larger aerosols in the atmosphere. We have performed a comprehensive configurational search of all possible clusters in this system, starting with the four different monomers and zero to five waters. Accurate Gibbs free energies of formation have been calculated with the DLPNO-CCSD(T)/complete basis set (CBS) method on ωb97xd/6-31++G** geometries. For the dry dimers of sulfuric acid, the weakest base, serine, is found to form the most stable complex, which is a consequence of the strong di-ionic complex formed between the bisulfate ion and the protonated serine cation. For the dry dimers without sulfuric acid, the glycine-serine complex is more stable than the glycine-ammonia or serine-ammonia complexes, stemming from the detailed structure and not related to base strength. For the larger complexes, sulfuric acid deprotonates and the proton is shifted to glycine, serine, or ammonia. The two amino acids and ammonia are almost interchangeable and there is no easy way to predict which molecule will be protonated without the calculated results. Assuming reasonable starting concentrations and a closed system of sulfuric acid, glycine, serine, ammonia, and five waters, we predict the concentrations of all possible complexes at two temperatures spanning the troposphere. The most negative ΔG° values are a function of the detailed molecular interactions of these clusters. These details are more important than the base strength of ammonia, glycine, and serine.

Toward size-dependent thermodynamics of nanoparticles from quantum chemical calculations of small atomic clusters: a case study of (B2O3)n

We present a method for obtaining canonical partition functions and, accordingly, temperature-dependent thermodynamics of arbitrary-sized (nano) particles from electronic structure calculations of the corresponding small size atomic clusters. The guiding idea here is to extrapolate the basic properties underlying the thermochemistry of clusters (electronic energies, rotational constants, and vibrational frequencies) rather than the thermodynamic functions themselves. The thus obtained scaling dependences for these basic properties expressed in a simple analytical form provide an efficient tool for fast evaluation of the size-selected thermochemical data for particles of any nuclearity. To exemplify the performance of the methodology, neutral stoichiometric boron oxide clusters are considered. To this end, the geometry and various physical properties of the energetically lowest-lying (B₂O₃)_n (n = 1,…,8) structures are found using density functional theory and the authors' multistage hierarchical procedure customized for global optimization of quite large cluster structures. With these data and based on the physically consistent scaling regularities for the principal cluster properties, the size-selected thermodynamic functions of boron oxide particles in the gas phase, such as enthalpy, entropy, and specific heat capacity, are derived. The variation of these characteristics with increasing cluster size is discussed in detail as well. To facilitate handling of the temperature and size dependences we have found here in further chemical kinetic and equilibrium modeling, the tabulated thermodynamic functions of interest are fitted for n = 1,…,1000 to the standard seven-parameter Chemkin polynomials.

How to obtain reaction free energies from free-energy profiles

For chemical reactions that occur via the rearrangement of atoms from a configuration about one minimum (reactant, R) of the potential energy surface (PES) to a configuration about another minimum (product, P), an exact relation between the Helmholtz reaction free energy (Δ FRP) and the free-energy profile (FEP) can be derived. Since the FEP assumes a form similar to that of the PES along the minimum energy path between R and P, there is an unfortunate tendency to regard the FEP as the “free-energy” analog of the minimum energy path and consequently to equate Δ FRP to the difference between the values of the FEP at the minima corresponding to R and P. Analytic treatments of one- and two-dimensional models are presented that show how this mistaken idea leads to errors. In effect, treating the FEP by analogy with the minimum energy path neglects the role of entropy. The FEP is a function of a collective variable (CV), which must be chosen to describe the course of the rearrangement consistently with the exact relation between Δ FRP and the FEP. For large systems of common interest, the PES is often so complex that a straightforward way of choosing a CV is lacking. Consequently, one is forced to make an educated guess. A criterion for judging the quality of the guess is proposed and applied to a two-dimensional model.

Molecular Dynamics with Constrained Nuclear Electronic Orbital Density Functional Theory: Accurate Vibrational Spectra from Efficient Incorporation of Nuclear Quantum Effects

Nuclear quantum effects play a crucial role in many chemical and biological systems involving hydrogen atoms yet are difficult to include in practical molecular simulations. In this paper, we combine our recently developed methods of constrained nuclear-electronic orbital density functional theory (cNEO-DFT) and constrained minimized energy surface molecular dynamics (CMES-MD) to create a new method for accurately and efficiently describing nuclear quantum effects in molecular simulations. By use of this new method, dubbed cNEO-MD, the vibrational spectra of a set of small molecules are calculated and compared with those from conventional ab initio molecular dynamics (AIMD) as well as from experiments. With the same formal scaling, cNEO-MD greatly outperforms AIMD in describing the vibrational modes with significant hydrogen motion characters, demonstrating the promise of cNEO-MD for simulating chemical and biological systems with significant nuclear quantum effects.

Free Energy Profiles of Proton Transfer Reactions: Density Functional Benchmark from Biased Ab Initio Dynamics

By coupling an enhanced sampling algorithm with an orbital-localized variant of Car-Parrinello molecular dynamics, the so-called atomic centered density matrix propagation model, we reconstruct the free energy profiles along reaction pathways using different density functional approximations (DFAs) ranging from locals to hybrids. In particular, we compare the computed free energy barrier height of proton transfer (PT) reactions to those obtained by a more traditional static approach, based on the intrinsic reaction coordinate (IRC), for two case systems, namely malonaldehyde and formic acid dimer. The obtained results show that both the IRC profiles and the potentials of mean force, derived from biased dynamic trajectories, are very sensitive to the density functional approximation applied. More precisely, we observe that, with the notable exception of M06-L, local density functionals always strongly underestimate the reaction barrier heights. More generally, we find that also the shape of the free energy profile is very sensitive to the density functional choice, thus highlighting the effect, often neglected, that the choice of DFA has also in the case of dynamics simulations.

Coupled Anharmonic Thermochemistry from Stratified Monte Carlo Integration

This study presents configuration integral Monte Carlo integration (CIMCI), a new semiclassical method for handling fully coupled anharmonicity in gas-phase thermodynamics that promises to be black boxable, to be applicable to all kinds of anharmonicity, and to scale better at higher dimensionality than other methods for handling gas-phase molecular anharmonicity. The method does so using automatically and recursively stratified, simultaneous Monte Carlo (MC) integration of multiple functions, following a modified version of the standard MISER scheme that converges at a rate of about the square of naïve MC integration. For the small systems analyzed by this study where proper reference data is available (H₂O and H₂O₂), the method's anharmonic entropy corrections match reference data better than those of other black box anharmonic methods, e.g., vibrational perturbation theory (VPT2) and the McClurg hindered rotor model used with automatic detection of rotors; for H₂O₂ and NH₂OH, the method is also in general agreement with one-dimensional hindered rotor treatments at low temperatures. This holds even when sampling with CIMCI is done with primitive force fields, e.g., UFF, while the competing methods are used with proper, comprehensive potentials, e.g., the M06-2X metahybrid density-functional theory (DFT) functional.

Sub-Nanometer Confined Ions and Solvent Molecules Intercalation Capacitance in Microslits of 2D Materials

The ion intercalation behavior in 2D materials is widely applied in energy storage, electrocatalysis, and desalination. However, the detailed effect of ions on the performance, combining the influence of interlayer force and the change of solvent shell, is far less well understood. Here the solvated alkali metal ions with different sizes are intercalated into the lattice of 2D materials with different spacings (Ti₃ C₂ T_x , δ-MnO₂ , and reduced graphene oxide) to construct the intercalation model related with sub-nanometer confined ions and solvent molecules to further understand the intercalation capacitance. Based on electrochemical methods and density functional theory calculation, the ions lose the electrostatic shielding solvent shell or shorten the distance between the layers, resulting in a significant increase in capacitance. It is found that the intercalation capacitance arises from the diffusion of solvated ions and is controlled by quantum and electrochemical capacitance for desolvated ions. This effect of solvation structure on performance can be applied in a variety of electrochemical interface studies and provides a new research view for energy storage mechanisms.

Investigation of the Failure of the MP2 Method to Describe the Out-of-Plane Bending Motions of Carbon-Carbon Double-Bonded Molecules: The Role of Atomic Orbitals

We present a detailed study on the role of atomic orbitals in the unphysical description of the out-of-plane bending (OOPB) vibrations with the MP2 method. The anharmonicities of the OOPB vibrations are found to be unphysically large for several basis sets with the MP2 method. We find that the inclusion of additional valence s and p orbitals to the basis set leads to the lowering of π* orbitals' energies along with the generation of several spurious low-energy virtual molecular orbitals (VMOs). Such erroneous VMOs create a disbalance between the σ and π correlations for the planar structure of the molecules. Since the OOPB vibrations distort the π* orbitals, the disbalance in the σ and π correlations leads to errors in the derivatives of the correlation energy with respect to the displacement along with OOPB modes. The diffuse functions in the basis set enhance the unphysical anharmonicities of the OOPB modes since these functions are of s- and p-type atomic orbitals. The polarization atomic orbitals of higher angular momentum improve the description of the π* orbitals and thereby reduce the disbalance between the σ and π correlations in the MP2 calculations. We find that the unphysical frequencies for the OOPB modes are significantly eliminated with the d and f orbitals on the C atoms in the basis set.

Quantum Mechanical Screening of 2D MBenes for the Electroreduction of CO2 to C1 Hydrocarbon Fuels

In this work, we propose a new family of two-dimensional (2D) transition metal borides (MBenes) to design and explore new high-efficiency catalysts for CO₂ electroreduction according to the Density Functional Theory (DFT) approach. The recently reported MBenes have been synthesized experimentally and have been found to have high electrical conductivities and stability, so they are promising candidates for the development of CO₂ electrocatalytic reduction (RR) catalysts. However, tuning the reaction mechanism such that the production of hydrocarbon species occurs at a low overpotential remains a challenge. Only C1 hydrocarbon products such as CH₄, CH₃OH, HCHO, CO, and HCOOH were identified, indicating that these MBenes have high stability, catalytic activity, and selectivity toward CO₂ reduction and overcome the competing hydrogen evolution reaction (HER). These MBenes possess a metallic feature that can be tuned as a new catalyst for CO₂RR, depending on the ability to control their selectivity and catalytic activity.

General Perturb-Then-Diagonalize Model for the Vibrational Frequencies and Intensities of Molecules Belonging to Abelian and Non-Abelian Symmetry Groups

In this paper, we show that the standard second-order vibrational perturbation theory (VPT2) for Abelian groups can be used also for non-Abelian groups without employing specific equations for two- or threefold degenerate vibrations but rather handling in the proper way all the degeneracy issues and deriving the peculiar spectroscopic signatures of non-Abelian groups (e.g., l -doubling) by a posteriori transformations of the eigenfunctions. Comparison with the results of previous conventional implementations shows a perfect agreement for the vibrational energies of linear and symmetric tops, thus paving the route to the transparent extension of the equations already available for asymmetric tops to the energies of spherical tops and the infrared and Raman intensities of molecules belonging to non-Abelian symmetry groups. The whole procedure has been implemented in our general engine for vibro-rotational computations beyond the rigid rotor/harmonic oscillator model and has been validated on a number of test cases.

Cryogenic Vibrationally Resolved Photoelectron Spectroscopy of OH-(H2O): Confirmation of Multidimensional Franck-Condon Simulation Results for the Transition State of the OH + H2O Reaction

We present a transition state spectroscopic study of the OH + H₂O reaction using the experimental technique of cryogenic negative ion photoelectron spectroscopy (NIPES). The recorded NIPE spectrum at 193 nm exhibits multiple vibrational progressions that include excitations to the shared H atom antisymmetric stretching mode with an interval of 0.32 eV as well as other progressions, mainly involving the H bending and O···O symmetric stretching modes. The vertical detachment energy (VDE) was measured at 3.53 eV, whereas an upper limit for the adiabatic detachment energy (ADE) was estimated at 2.90 eV. These values are in excellent agreement with the theoretically computed values of 3.51 and 2.87 eV, respectively, obtained at the CCSD(T)/aug-cc-pV5Z level of theory. The recorded NIPE spectrum is in very good agreement when compared to the one recently reported from four-dimensional Franck-Condon simulations, in which a similar spectral profile was predicted. Besides observing the ground state, we identified a charge-transfer excited state in the form of [OH^-(H₂O)⁺] with a relative energy of 1.39 eV, well matching the previous prediction of 1.36 eV.

Spectroscopic Signatures and the Cation-π Interaction in Conformational Preferences of the Neurotransmitter Dopamine in Aqueous Solution

The precise determination of the neurotransmitter dopamine's conformational preferences in aqueous solution is crucial for understanding its neurobiological function. The first principle Møller-Plesset perturbation theory (MP2) and dispersion corrected density functional theory (DFT-D3) methods, employing the basis set aug-cc-pVDZ(/pVTZ), are used to reinvestigate the nine lowest-energy (isolated) structures of protonated dopamine (DAH⁺) in both gas and aqueous phases. DAH⁺ trans isomer t₁ is found higher in energy than lowest-energy gauche isomer g⁺¹ (g + 1) by 6.4 and 5.7 kJ mol^-1, at the MP2 and B3LYP-D3 levels of theory, respectively, in the aqueous environment within the polarizable continuum model (PCM). We found that the solvated cation, NH₃⁺, retains its attractive character, which supports the previous report that agonist DAH⁺ can be involved in cation (NH₃⁺)-π interaction in the active states of the D2 dopamine receptor. The dispersion corrected DFT evaluation of anharmonicity allows us to confirm the most experimental frequencies and suggest some new interpretations. The IR and Raman spectra's influential band for both gauche and the trans conformers observed at 1287/1288 cm^-1 were enhanced in aqueous solution. The experimental Raman spectrum for dopamine was compared with the conformer-specific computed Raman spectrum of protonated dopamine (DAH⁺). The intense Raman band at 1451 cm^-1 indicates the necessity of DAH⁺ calculated values in interpreting the Raman spectra. The most intense Raman band at 750 cm^-1 arises due to the trans DAH⁺, t₁, revealed by MP2/aug-cc-pVDZ Raman spectra, indicating trans DAH⁺ dominance in the bulk DAH⁺ of extracellular fluid.

Lactic Acid Spectroscopy: Intra- and Intermolecular Interactions

Lactic acid, a relevant molecule in biology and the environment, is an α-hydroxy acid with a high propensity to form hydrogen bonds, both internally and to other hydrogen-bond-accepting molecules. This work includes the novel recording of infrared spectra of gas-phase lactic acid using Fourier transform infrared spectroscopy, and the vibrational absorption features of lactic acid are assigned with the aid of computationally simulated vibrational spectra with anharmonic corrections. Theoretical chemistry methods are used to relate intramolecular hydrogen-bond strengths to the relative stability of lactic acid conformers. The formation of hydrogen-bonded lactic acid dimers and 1:1 water complexes is investigated by simulated vibrational spectra and calculated thermodynamic parameters for the lactic acid monomer and dimer and its water complex in the gas phase. The results of this study are discussed in the context of environmental chemistry with an emphasis on indoor environments.

Multiresolution continuous wavelet transform for studying coupled solute-solvent vibrations via ab initio molecular dynamics

Vibrational analysis in solution and the theoretical determination of infrared and Raman spectra are of key importance in many fields of chemical interest. Vibrational band dynamics of molecules and their sensitivity to the environment can also be captured by these spectroscopies in their time dependent version. However, it is often difficult to provide an interpretation of the experimental data at the molecular scale, such as molecular mechanisms or the processes hidden behind them. In this work, we present a theoretical-computational protocol based on ab initio molecular dynamics simulations and a combination of normal-like (generalized) mode analysis of solute-solvent clusters with a wavelet transform, for the first time. The case study is the vibrational dynamics of N-methyl-acetamide (NMA) in water solution, a well-known model of hydration of peptides and proteins. Amide modes are typical bands of peptide and protein backbone, and their couplings with the environment are very challenging in terms of the accurate prediction of solvent induced intensity and frequency shifts. The contribution of water molecules surrounding NMA to the composition of generalized and time resolved modes is introduced in our vibrational analysis, showing unequivocally its influence on the amide mode spectra. It is also shown that such mode compositions need the inclusion of the first shell solvent molecules to be accurately described. The wavelet analysis is proven to be strongly recommended to follow the time evolution of the spectra, and to capture vibrational band couplings and frequency shifts over time, preserving at the same time a well-balanced time-frequency resolution. This peculiar feature also allows one to perform a combined structural-vibrational analysis, where the different strengths of hydrogen bond interactions can quantitatively affect the amide bands over time at finite temperature. The proposed method allows for the direct connection between vibrational modes and local structural changes, providing a link from the spectroscopic observable to the structure, in this case the peptide backbone, and its hydration layouts.

Gate-Tuned Interlayer Coupling in van der Waals Ferromagnet Fe_{3}GeTe_{2} Nanoflakes

The weak interlayer coupling in van der Waals (vdW) magnets has confined their application to two dimensional (2D) spintronic devices. Here, we demonstrate that the interlayer coupling in a vdW magnet Fe_{3}GeTe_{2} (FGT) can be largely modulated by a protonic gate. With the increase of the protons intercalated among vdW layers, interlayer magnetic coupling increases. Because of the existence of antiferromagnetic layers in FGT nanoflakes, the increasing interlayer magnetic coupling induces exchange bias in protonated FGT nanoflakes. Most strikingly, a rarely seen zero-field cooled (ZFC) exchange bias with very large values (maximally up to 1.2 kOe) has been observed when higher positive voltages (V_{g}≥4.36  V) are applied to the protonic gate, which clearly demonstrates that a strong interlayer coupling is realized by proton intercalation. Such strong interlayer coupling will enable a wider range of applications for vdW magnets.

The Role of State-of-the-Art Quantum-Chemical Calculations in Astrochemistry: Formation Route and Spectroscopy of Ethanimine as a Paradigmatic Case

The gas-phase formation and spectroscopic characteristics of ethanimine have been re-investigated as a paradigmatic case illustrating the accuracy of state-of-the-art quantum-chemical (QC) methodologies in the field of astrochemistry. According to our computations, the reaction between the amidogen, NH, and ethyl, C2H5, radicals is very fast, close to the gas-kinetics limit. Although the main reaction channel under conditions typical of the interstellar medium leads to methanimine and the methyl radical, the predicted amount of the two E,Z stereoisomers of ethanimine is around 10%. State-of-the-art QC and kinetic models lead to a [E-CH3CHNH]/[Z-CH3CHNH] ratio of ca. 1.4, slightly higher than the previous computations, but still far from the value determined from astronomical observations (ca. 3). An accurate computational characterization of the molecular structure, energetics, and spectroscopic properties of the E and Z isomers of ethanimine combined with millimeter-wave measurements up to 300 GHz, allows for predicting the rotational spectrum of both isomers up to 500 GHz, thus opening the way toward new astronomical observations.

Monitoring the Reactivity of Formamide on Amorphous SiO2 by In-Situ UV-Raman Spectroscopy and DFT Modeling

Formamide has been recognized in the literature as a key species in the formation of the complex molecules of life, such as nucleobases. Furthermore, several studies reported the impact of mineral phases as catalysts for its decomposition/polymerization processes, increasing the conversion and also favoring the formation of specific products. Despite the progresses in the field, in situ studies on these mineral-catalyzed processes are missing. In this work, we present an in situ UV-Raman characterization of the chemical evolution of formamide over amorphous SiO₂ samples, selected as a prototype of silicate minerals. The experiments were carried out after reaction of formamide at 160 °C on amorphous SiO₂ (Aerosil OX50) either pristine or pre-calcined at 450 °C, to remove a large fraction of surface silanol groups. Our measurements, interpreted on the basis of density functional B3LYP-D3 calculations, allow to assign the spectra bands in terms of specific complex organic molecules, namely, diaminomaleonitrile (DAMN), 5-aminoimidazole (AI), and purine, showing the role of the mineral surface on the formation of relevant prebiotic molecules.

Investigation of the Luminescence of [UO2X4]2- (X = Cl, Br) Complexes in the Organic Phase Using Time-Resolved Laser-Induced Fluorescence Spectroscopy and Quantum Chemical Simulations

The luminescence properties of the [UO₂Cl₄]^2- complex in an organic phase, especially the influence of large organic countercations, have been studied by time-resolved laser-induced fluorescence spectroscopy (TRLFS) and ab initio modeling. The experimental spectrum was assigned by vibronic Franck-Condon calculations on quantum chemical methods on the basis of a combination of relativistic density functional approaches. The shape of the luminescence spectrum of the uranyl tetrachloride complex is determined by symmetrical vibrations and geometrical change upon emission. The possible change in the luminescence properties depending on the first and second uranyl coordination spheres was predicted theoretically for the [UO₂Br₄]^2- and [R₄N]₂[UO₂Cl₄] ([R₄N] = [Bu₄N], [A336]) systems. The computations reveal that, for U(VI), the second coordination sphere has little influence on the spectrum shape, making speciation of uranyl complexes with identical first-coordination-sphere ligands tedious to discriminate. The computed structural changes agreed well with experimental trends; theoretical spectra and peak attributions are in good accordance with TRLFS and magnetic circular dichroism (MCD) data, respectively.

Engineering bunched Pt-Ni alloy nanocages for efficient oxygen reduction in practical fuel cells

Development of efficient and robust electrocatalysts is critical for practical fuel cells. We report one-dimensional bunched platinum-nickel (Pt-Ni) alloy nanocages with a Pt-skin structure for the oxygen reduction reaction that display high mass activity (3.52 amperes per milligram platinum) and specific activity (5.16 milliamperes per square centimeter platinum), or nearly 17 and 14 times higher as compared with a commercial platinum on carbon (Pt/C) catalyst. The catalyst exhibits high stability with negligible activity decay after 50,000 cycles. Both the experimental results and theoretical calculations reveal the existence of fewer strongly bonded platinum-oxygen (Pt-O) sites induced by the strain and ligand effects. Moreover, the fuel cell assembled by this catalyst delivers a current density of 1.5 amperes per square centimeter at 0.6 volts and can operate steadily for at least 180 hours.

Vibrations of the guanine-cytosine pair in chloroform: an anharmonic computational study

We compute at the anharmonic level the vibrational spectra of the Watson-Crick dimer formed by guanosine (G) and cytidine (C) in chloroform, together with those of G, C and the most populated GG dimer. The spectra for deuterated and partially deuterated GC are also computed. We use DFT calculations, with B3LYP and CAM-B3LYP as reference functionals. Solvent effects from chloroform are included via the Polarizable Continuum Model (PCM), and by performing tests on models including up two chloroform molecules. Both B3LYP and CAM-B3LYP calculations reproduce the shape of the experimental spectra well in the fingerprint region (1500-1700 cm-1) and in the N-H stretching region (2800-3600 cm-1), with B3LYP providing better quantitative agreement with experiments. According to our calculations, the N-H amido streching mode of G falls at ∼2900 cm-1, while the N-H amino of G and C falls at ∼3100 cm-1 when hydrogen-bonded, or ∼3500 cm-1 when free. Overtone and combination bands strongly contribute to the absorption band at ∼3300 cm-1. Inclusion of bulk solvent effects significantly increases the accuracy of the computed spectra, while solute-solvent interactions have a smaller, though still noticeable, effect. Some key aspects of the anharmonic treatment of strongly vibrationally coupled supermolecular systems and the related methodological issues are also discussed.