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Abstract This Roadmap article provides a succinct, comprehensive overview of the state of electronic structure (ES) methods and software for molecular and materials simulations. Seventeen distinct sections collect insights by 51 leading scientists in the field. Each contribution addresses the status of a particular area, as well as current challenges and anticipated future advances, with a particular eye towards software related aspects and providing key references for further reading. Foundational sections cover density functional theory and its implementation in real-world simulation frameworks, Green’s function based many-body perturbation theory, wave-function based and stochastic ES approaches, relativistic effects and semiempirical ES theory approaches. Subsequent sections cover nuclear quantum effects, real-time propagation of the ES, challenges for computational spectroscopy simulations, and exploration of complex potential energy surfaces. The final sections summarize practical aspects, including computational workflows for complex simulation tasks, the impact of current and future high-performance computing architectures, software engineering practices, education and training to maintain and broaden the community, as well as the status of and needs for ES based modeling from the vantage point of industry environments. Overall, the field of ES software and method development continues to unlock immense opportunities for future scientific discovery, based on the growing ability of computations to reveal complex phenomena, processes and properties that are determined by the make-up of matter at the atomic scale, with high precision. 

Abstract Three binuclear species [LCo^III₂(μ‐Pz)₂](ClO₄)₃(1), [LNi^II₂(CH₃OH)₂Cl₂]ClO₄(2), and [LZn^II₂Cl₂]PF₆(3) supported by the deprotonated form of the ligand 2,6‐bis[bis(2‐pyridylmethyl) amino‐methyl]‐4‐methylphenol were synthesized, structurally characterized as solids and in solution, and had their electrochemical and spectroscopic behavior established. Species1–3had their water reduction ability studied aiming to interrogate the possible cooperative catalytic activity between two neighboring metal centers. Species1and2reduced H₂O to H₂effectively at an applied potential of −1.6 V_Ag/AgCl, yielding turnover numbers of 2,820 and 2,290, respectively, after 30 minutes. Species3lacked activity and was used as a negative control to eliminate the possibility of ligand‐based catalysis. Pre‐ and post‐catalytic data gave evidence of the molecular nature of the process within the timeframe of the experiments. Species1showed structural, rather than electronic cooperativity, while species2displayed no obvious cooperativity. DFT methods complemented the experimental results determining plausible mechanisms. 

We report on a new water-soluble cobalt(II) complex capable of water splitting bifunctionality, i.e., water reduction and water oxidation. The species [CoII(LQpy)H2O]ClO4 (1), where LQpy is the deprotonated form of the new tripodal ligand N1,N1-bis(pyridin-2-ylmethyl)-N2-(quinolin-8-yl)benzene-1,2-diamine, HLQpy, was developed aiming to replace an oxidation prone methylene group by a sturdy and redox stable quinoline. The molecular and electronic structures of 1 were evaluated by multiple spectroscopic, spectrometric, electrochemical and computational methods, and detailed pre- and post-catalytic studies were conducted to ascertain the molecular nature of the conversions. Complex 1 performs water reduction at a low onset overpotential (eta) of 0.65 V at pH 7, reaching TON3h 2900 (TOF 970 h-1) and TON18h 12 100 (TOF 672 h-1) with up to 98% faradaic efficiency (FE). Species 1 also promotes water oxidation at eta = 0.34 V under pH 8, achieving TON3h 193 (TOF 64 h-1) at 84% FE. Experimental and DFT results enabled us to propose reaction intermediates and mechanisms. 

Quantum mechanics is central to our understanding of chemistry both qualitatively and quantitatively. Modern electronic structure calculations can yield energies and structures of small to medium size molecules to chemical accuracy, thereby providing a computational model for chemistry. A potential energy surface describes the energy of a molecule as a function of its geometric parameters. The features of potential energy surfaces provide the connections between quantum mechanics and the traditional chemical concepts such as structure, bonding and reactivity. This brief perspective presents an overview of tools for exploring potential energy surfaces such as optimizing equilibrium geometries, finding transition states, following reaction paths and simulating molecular dynamics. 

For simulations of strong field ionization using time-dependent configuration with a complex absorbing potential (TDCI-CAP), standard molecular basis set must be augmented by several sets of diffuse functions to support the wavefunction as it is distorted by the strong field and interacts with the absorbing potential. Various sets of diffuse functions used in previous studies have been extended and evaluated for their ability to model the angular dependence of strong field ionization. These sets include diffuse s, p, d and f gaussian functions with selected even-tempered exponents of the form 0.0001×2n placed on each atom. For single-centered test cases, the largest contribution to the ionization rate is from functions with a maximum in the radial distribution close to the onset of the complex absorbing potential, while functions with smaller exponents also contributed to the rate. For molecules, diffuse functions on adjacent centers overlap strongly, leading to linear dependencies. The transformation to remove these linear dependencies mixes functions of different angular momenta making it difficult to assess the importance of individual s, p, d and f functions in simulating the rate for molecules. As an alternative, a hierarchy of diffuse basis sets was constructed starting with a small set and adding one or two functions at a time. These basis sets were evaluated for their ability to reproduce the rate and the shape of the angular dependence of strong field ionization. When combined with the aug-cc-pVTZ molecular basis set and an absorbing potential starting at 3.5 times the van der Waals radius for each atom, the most diffuse s, p, d and f functions need to have exponents of 0.0032, 0.0032, 0.0064 and 0.0064, respectively, or smaller. Strong field ionization from electronegative atoms such as oxygen required additional f functions with tight exponents of 0.0512 and 0.1024. Diffuse basis sets that perform well for the angular dependence of the ionization rate with a static field are equally effective for strong field ionization with a linearly polarized 7 cycle 800 nm pulse. 

The lack of catalytic stereoselective approaches for producing 1,2-cis S-furanosides emphasizes the critical need for further research in this area. Herein, we present a stereoselective S-furanosylation method, utilizing a 4,7-dipiperidine-substituted phenanthroline catalyst. This developed protocol fills a gap in the field, enabling the coupling of cysteine residues and thiols with furanosyl bromide electrophiles. The process allows for stereoselective access to 1,2-cis S-furanosides. Through computational and experimental investigations, thiol is found to be less reactive than alcohol but exhibits greater stereoselectivity. The 1,2-cis stereoselectivity of O-products depends on the nature of the electrophile, while S-products are obtained with excellent 1,2-cis stereoselectivity, irrespective of the furanose structure. The displaced bromide ion from the glycosyl electrophile influences the reaction’s reactivity and stereoselectivity. Alcohol-OH forms a stronger hydrogen bond with bromide ion than thiol-SH, contributing to the difference in their reactivity. The energy difference between forming S-furanoside and O-furanoside transition states is 3.7 kcal/mol, supporting the increased reactivity of alcohol over thiol. The difference in transition state energies between the major and minor S-product is greater than that for the major and minor O-product. This is consistent with experimental data showing how thiol is more stereoselective than alcohol. The catalyst and reaction conditions utilized for the generation of 1,2-cis O-furanosides in our prior studies are found to be unsuitable for the synthesis of 1,2-cis S-furanosides. In the present study, a highly reactive phenanthroline catalyst and specific reaction conditions have been developed to achieve stereoselective S-linked product formation. 

Modeling charge migration resulting from the coherent superposition of cation ground and excited states requires information about the potential energy surfaces of the relevant cation states. Since these states are often of the same electronic symmetry as the ground state of the cation, conventional single reference methods such as coupled cluster cannot be used for the excited states. The EOMCCSD-IP (equation of motion coupled cluster with single and double excitations and ionization) is a convenient and reliable “black-box” method that can be used for the ground and excited states of cations, yielding results of CCSD (coupled cluster with singles and double excitation) quality. Charge migration in haloacetylene cations arises from the superposition of the X and A states of HCCX+ (X = F, Cl, Br and I). The geometries, ionization potentials and vibrational frequencies have been calculated by CCSD/cc-pVTZ for neutral HCCX and the X state of HCCX+ and by EOM CCSD-IP/cc-pVTZ for the X and A states of HCCX+. The results agree very well with each other and with experiment. The very good agreement between CCSD and EOMCCSD-IP for the X states demonstrates that EOMCCSD-IP is a suitable method for calculating the structure and properties of ground and excited states for the HCCX cations. 

Carbohydrate molecules with an alpha-glycosylated carboxylic acid motif provide access to biologically relevant chemical space but are difficult to synthesize with high selectivity. To address this challenge, we report a mild and operationally simple protocol to synthesize a wide range of functionally and structurally diverse alpha-glycosylated carboxylic acids in good yields with high diastereoselectivity. While there is no apparent correlation between reaction conversion and the pKa of carboxylic acids, there is a notable trend in selectivity. Carboxylic acids with a pKa ranging from 4 to 5 exhibit high selectivity, whereas those with a pKa of 2.5 or lower do not display the same level of selectivity. Our strategy utilizes readily available 2,9-dibutyl-1,10-phenanthroline as an effective nucleophilic catalyst to displace a bromide leaving group from an activated sugar electrophile in a nucleophilic substitution reaction, forming phenanthrolinium intermediates. The attack of the carboxylic acid takes place from the alpha-face of the more reactive intermediate, resulting in the formation of alpha-glycosylated carboxylic acid. Previous calculations suggested that the hydroxyl group participates in the hydrogen bond interaction with the basic C2-oxygen of a sugar moiety and serves as a nucleophile to attack the C1-anomeric center. In contrast, our computational studies reveal that the carbonyl oxygen of the carboxylic acid serves as a nucleophile, with the carboxylic acid-OH forming a hydrogen bond with the basic C2-oxygen of the sugar moiety. This strong hydrogen bond (1.65 Å) interaction increases the nucleophilicity of the carbonyl oxygen of carboxylic acid and plays a critical role in the selectivity-determining step. In contrast, when alcohol acts as a nucleophile, this scenario is not possible since the -OH group of the alcohol interacts with the C2-oxygen and attacks the C1-anomeric carbon of the sugar moiety. This is also reflected in alcohol-OH's weak hydrogen bond (1.95 Å) interaction with the C2-oxygen. The O(C2)-HO (carboxylic acid) angle was measured to be 171° while the O(C2)-HO (alcohol) angle at 122° deviates from linearity, resulting in weak hydrogen bonding. 

Strong field ionization of molecules by intense laser pulses can be simulated by time-dependent configuration interaction (TD-CI) with a complex absorbing potential (CAP). Standard molecular basis sets need to be augmented with several sets of diffuse functions for effective interaction with the CAP. This dramatically increases the number of configurations and the cost of the TD-CI simulations as the size of the molecules increases. The cost can be reduced by making use of spin symmetry and by employing an orbital energy cut-off to limit the number of virtual orbitals used to construct the excited configurations. Greater reductions in the number of virtual orbitals can be obtained by examining their interaction with the absorbing potential during simulations and their contributions to the strong field ionization rate. This can be determined from the matrix elements of the absorbing potential and the TD-CI coefficients from test simulations. Compared to a simple 3 hartree cut-off in the orbital energies, these approaches reduce the number of virtual orbitals by 20% - 35% for neutral molecules and 5%-10% for cations. As a result, the cost of simulations is reduced by 35% - 60% for neutral molecules and 5% - 10% for cations. The number of virtual orbitals needed can also be estimated by second-order perturbation theory without the need for test simulations. The number of virtual orbitals can be reduced further by adapting orbitals to the laser field using natural orbitals derived from test simulations. This is particularly effective for cations, yielding reductions of more than 20%. 

We provide an approach to sample rare events during classical ab initio molecular dynamics and quantum wavepacket dynamics. For classical AIMD, a set of fictitious degrees of freedom are introduced that may harmonically interact with the electronic and nuclear degrees of freedom to steer the dynamics in a conservative fashion toward energetically forbidden regions. A similar approach when introduced for quantum wavepacket dynamics has the effect of biasing the trajectory of the wavepacket centroid toward the regions of the potential surface that are difficult to sample. The approach is demonstrated for a phenol-amine system, which is a prototypical problem for condensed phase-proton transfer, and for model potentials undergoing wavepacket dynamics. In all cases, the approach yields trajectories that conserve energy while sampling rare events.