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A virtual reality (VR) session was introduced to an Advanced Inorganic Chemistry class, a class open to junior and senior undergraduate students at University of California, Los Angeles. The VR session helped the students to learn complicated aspects of metal coordination chemistry and molecular orbitals via a three-dimension, immersed experience.
Nonadiabatic dynamical processes such as proton-coupled electron transfer and excited state intramolecular proton transfer have been the subject of much research. One of the promising theoretical methods to describe these processes is the nuclear–electronic orbital (NEO) approach. This approach inherently accounts for nuclear quantum effects within quantum chemistry calculations, and it has recently been extended to directly simulate nonadiabatic processes with the development of real-time NEO methods. These processes can also be significantly dependent on the surrounding chemical environment, however, and capturing the effects of the environment is often necessary for analyzing experimentally relevant systems. This work couples the NEO density functional theory and real-time time-dependent density functional theory approaches with solvation through the polarizable continuum model. Here, the effects of this coupling are investigated for ground state properties, solvent-dependent vibrational frequencies, and direct excited state intramolecular proton transfer dynamics.
The effective fragment molecular orbital (EFMO) method has been developed to predict the total energy of a very large molecular system accurately (with respect to the underlying quantum mechanical method) and efficiently by taking advantage of the locality of strong chemical interactions and employing a two-level hierarchical parallelism. The accuracy of the EFMO method is partly attributed to the accurate and robust intermolecular interaction prediction between distant fragments, in particular, the many-body polarization and dispersion effects, which require the generation of static and dynamic polarizability tensors by solving the coupled perturbed Hartree–Fock (CPHF) and time-dependent HF (TDHF) equations, respectively. Solving the CPHF and TDHF equations is the main EFMO computational bottleneck due to the inefficient (serial) and I/O-intensive implementation of the CPHF and TDHF solvers. In this work, the efficiency and scalability of the EFMO method are significantly improved with a new CPU memory-based implementation for solving the CPHF and TDHF equations that are parallelized by either message passing interface (MPI) or hybrid MPI/OpenMP. Here, the accuracy of the EFMO method is demonstrated for both covalently bonded systems and noncovalently bound molecular clusters by systematically examining the effects of basis sets and a key distance-related cutoff parameter, R cut . R cut determines whether a fragment pair (dimer) is treated by the chosen ab initio method or calculated using the effective fragment potential (EFP) method (separated dimers). Decreasing the value of Rcut increases the number of separated (EFP) dimers, thereby decreasing the computational effort. It is demonstrated that excellent accuracy (<1 kcal/mol error per fragment) can be achieved when using a sufficiently large basis set with diffuse functions coupled with a small R cut value. With the new parallel implementation, the total EFMO wall time is substantially reduced, especially with a high number of MPI ranks. Given a sufficient workload, nearly ideal strong scaling is achieved for the CPHF and TDHF parts of the calculation. For the first time, EFMO calculations with the inclusion of long-range polarization and dispersion interactions on a hydrated mesoporous silica nanoparticle with explicit water solvent molecules (more than 15k atoms) are achieved on a massively parallel supercomputer using nearly 1000 physical nodes. In addition, EFMO calculations on the carbinolamine formation step of an amine-catalyzed aldol reaction at the nanoscale with explicit solvent effects are presented.
We introduce an exact-two-component complete active space self-consistent-field (X2C-CASSCF) method formulated under the restricted-magnetic-balance condition. This framework allows for the nonperturbative treatment of static magnetic fields using gauge-including atomic orbitals (GIAOs). The GIAO-X2C-CASSCF methodology effectively captures all microstates within the same 2J + 1-degenerate manifold and their splitting in a static magnetic field, which are not accessible through single-reference-based methods. We also present mathematical recursive expressions for evaluating one-electron relativistic integrals by using GIAOs in the presence of a finite magnetic field. Benchmark studies include oxygen and nitrogen K-edge X-ray magnetic circular dichroism spectroscopy (XMCD) for closed-shell organic compounds, as well as L-edge XMCD spectroscopy for the high-spin open-shell transition metal ion Mn 2+ and the tetrahedral Mn(II)O 4 6– complex.
Hydrogen transfer is a critical component of many chemical and biological processes. The ratio of rate constants for hydrogen and deuterium transfer defines the H/D kinetic isotope effect (KIE), which is a powerful tool for elucidating hydrogen transfer mechanisms. Interpretation of experimental H/D KIEs relies on accurate and affordable computational methods. However, due to their light mass, hydrogen and deuterium can undergo tunneling, which is challenging to describe in multidimensional molecular systems. Herein, we introduce the nuclear–electronic orbital general rate theory (NEO-GRT), which enables the efficient prediction of H/D KIEs based on full-dimensional molecular quantum chemistry calculations. The NEO-GRT approach describes the hydrogen transfer rate constant with a general expression that spans the vibrationally adiabatic and nonadiabatic hydrogen tunneling regimes. The input quantities are computed using NEO density functional theory, which treats the transferring hydrogen or deuterium nucleus quantum mechanically on the same level as the electrons. We investigate two intramolecular proton transfer reactions in organic molecules at temperatures down to 50 K to evaluate the performance of NEO-GRT by comparison to transition state theory and ring-polymer instanton theory. The KIEs computed with NEO-GRT agree with those calculated using ring-polymer instanton theory for the full-dimensional molecular systems at the same level of electronic structure theory. This agreement indicates that NEO-GRT captures the deep hydrogen tunneling effects, in contrast to transition state theory, which neglects such effects. Given its relatively low computational cost, NEO-GRT is a promising approach for predicting H/D KIEs in large organic and organometallic systems.
Accurate modeling of important nuclear quantum effects, such as nuclear delocalization, zero-point energy, and tunneling, as well as non-Born-Oppenheimer effects, requires treatment of both nuclei and electrons quantum mechanically. The nuclear–electronic orbital (NEO) method provides an elegant framework to treat specified nuclei, typically protons, on the same level as the electrons. In conventional electronic structure theory, finding a converged ground state can be a computationally demanding task; converging NEO wavefunctions, due to their coupled electronic and nuclear nature, is even more demanding. Herein, we present an efficient simultaneous optimization method that uses the direct inversion in the iterative subspace method to simultaneously converge wavefunctions for both the electrons and quantum nuclei. In conclusion, benchmark studies show that the simultaneous optimization method can significantly reduce the computational cost compared to the conventional stepwise method for optimizing NEO wavefunctions for multicomponent systems.
In this work, the results of calculations of the properties of the anion UN – including electron detachment are described, which further expand our knowledge of this diatomic molecule. High-level electronic structure calculations were conducted for the UN and UN – diatomic molecules and compared to photoelectron spectroscopy measurements. The low-lying Ω states were obtained using multireference CASPT2 including spin-orbit effects up to ~20,000 cm –1 . At the Feller–Peterson–Dixon (FPD) level, the adiabatic electron affinity (AEA) of UN is estimated to be 1.402 eV and the vertical detachment energy (VDE) is 1.423 eV. The assignment of the UN excited states shows good agreement with the experimental results with a VDE of 1.424 eV. An Ω = 4 ground state was obtained for UN – which is mainly associated with the 3 H ΛS state. Thermochemical calculations estimate a bond dissociation energy (BDE) for UN – (U – + N) of 665.9 kJ/mol, ~15% larger than that of UN and UN + . The NBO analysis reveals U–N triple bonds for the UN, UN – , and UN + species.
Accurate simulations of many chemical processes require the inclusion of both nuclear quantum effects and a solvent environment. The nuclear–electronic orbital (NEO) approach, which treats electrons and select nuclei quantum mechanically on the same level, combined with a polarizable continuum model (PCM) for the solvent environment, addresses this challenge in a computationally practical manner. In this work, the NEO-PCM approach is extended beyond the IEF-PCM (integral equation formalism PCM) and C-PCM (conductor PCM) approaches to the SS(V)PE (surface and simulation of volume polarization for electrostatics) and ddCOSMO (domain decomposed conductor-like screening model) approaches. IEF-PCM, SS(V)PE, C-PCM, and ddCOSMO all exhibit similar solvation energies as well as comparable nuclear polarization within the NEO framework. The calculations show that the nuclear density does not leak out of the molecular cavity because it is much more localized than the electronic density. Finally, the polarization of quantized protons is analyzed in both continuum solvent and explicit solvent environments described by the polarizable MB-pol model, illustrating the impact of specific hydrogen-bonding interactions captured only by explicit solvation. Furthermore, these calculations highlight the relationship among solvation formalism, nuclear polarization, and energetics.
The extent of electronic wave function delocalization for the charge carrier (electron or hole) in double helical DNA plays an important role in determining the DNA charge transfer mechanism and kinetics. The size of the charge carrier’s wave function delocalization is regulated by the solvation induced localization and the quantum delocalization among the π stacked base pairs at any instant of time. Using a newly developed localized orbital scaling correction (LOSC) density functional theory method, we accurately characterized the quantum delocalization of the hole wave function in double helical B-DNA. This approach can be used to diagnose the extent of delocalization in fluctuating DNA structures. Our studies indicate that the hole state tends to delocalize among 4 guanine–cytosine (GC) base pairs and among 3 adenine–thymine (AT) base pairs when these adjacent bases fluctuate into degeneracy. The relatively small delocalization in AT base pairs is caused by the weaker π–π interaction. This extent of delocalization has significant implications for assessing the role of coherent, incoherent, or flickering coherent carrier transport in DNA.
Dexter energy transfer (DET), also known as spin forbidden energy transfer (e.g., 3 D 1 A → 1 D 3 A), is undergoing renewed interest because of its utility in energy science, photocatalysis, and biomedical imaging. The DET reactions enable exciton fission and fusion and have been recently used to facilitate nanoscale imaging of protein assemblies on cell surfaces. While DET and Förster energy transfer rates are often well described using Fermi’s golden rule, the donor–acceptor couplings for DET may be bridge-state-mediated and depend on the electronic structure of and interactions among the donor, bridge, and acceptor. We provide a simple approach to approximate DET couplings using a product of molecular orbital overlap factors. This approach may be used to guide the design of DET systems with targeted energy-transfer kinetics.
The quantum mechanical treatment of both electrons and nuclei is crucial in nona- diabatic dynamical processes such as proton-coupled electron transfer. The nuclear electronic orbital (NEO) method provides an elegant framework for including nuclear quantum effects beyond the Born-Oppenheimer approximation. To enable the study of nonequilibrium properties, we derive and implement a real-time NEO (RT-NEO) approach based on time-dependent Hatree-Fock or density functional theory, in which both the electronic and nuclear degrees of freedom are propagated in a time-dependent variational framework. Nuclear and electronic spectral features can be resolved from the time-dependent dipole moment computed using the RT-NEO method. The test cases demonstrate the dynamical interplay between the quantum nuclei and the electrons through vibronic coupling. Moreover, vibrational excitation in the RT-NEO approach is demonstrated by applying a resonant driving eld, and electronic excitation is demonstrated by simulating excited state intramolecular proton transfer. This work shows that the RT-NEO approach is a promising tool to study nonadiabatic quantum dynamical processes within a time-dependent variational description for the coupled electronic and nuclear degrees of freedom.
The accurate description of excited vibronic states is important for modeling a wide range of photoinduced processes. The nuclear-electronic orbital (NEO) approach, which treats specified protons on the same level as the electrons, can describe excited electronic-protonic states. Herein the multicomponent equation-of-motion coupled cluster with singles and doubles (NEO-EOM-CCSD) method and its time-domain counterpart, TD-NEO-EOM-CCSD, are developed and implemented. The application of these methods to the HCN molecule highlights their capabilities. These methods predict qualitatively reasonable energies and intensities for a combination band corresponding to simultaneous excitation of two vibrational modes, as well as an overtone. These methods also describe states with double excitation character, such as excited electronic-protonic states corresponding to the simultaneous excitation of an electron and a proton. The ability of the NEO-EOM-CCSD method and its time-dependent counterpart to describe combination bands, overtones, and double excitations will enable a wide range of photochemical applications.
The recent development of the Ehrenfest dynamics approach in the nuclear-electronic orbital (NEO) framework provides a promising way to simulate coupled nuclear-electronic dynamics. Our previous study showed that the NEO-Ehrenfest approach with a semi- classical traveling proton basis method yields accurate predictions of molecular vibrational frequencies. In this work, we provide a more thorough analysis of the semiclassical traveling proton basis method to elucidate its validity and convergence behavior. We also conduct NEO-Ehrenfest dynamics simulations to study an excited state intramolecular proton transfer process. These simulations reveal that nuclear quantum effects influence the predictions of proton transfer reaction rates and kinetic isotope effects due to the intrinsic delocalized nature of the quantum nuclear wave function. This work illustrates the importance of nuclear quantum effects in coupled nuclear-electronic dynamical processes and shows that the NEO-Ehrenfest approach can be a powerful tool to provide insights and predictions for these processes.
To explicitly account for nuclear quantum effects and solvent environments in simulations of chemical processes, the nuclear-electronic orbital approach is coupled with a polarizable continuum model (PCM). This NEO–PCM approach is used to explore the influence of solvation on nuclear polarization through applications to a water dimer and a set of protonated water tetramers. Nuclear polarization in these species is analyzed in terms of changes in proton density and oxygen–hydrogen bond length. Solvation is shown to enhance nuclear polarization with increasing dielectric constant. For the water dimer, the internal, hydrogen-bonded proton is shown to polarize more than the external, free proton. Moreover, proton quantization leads to greater solvent polarization through their mutual polarization. Furthermore, these calculations highlight the complex interplay among electronic, nuclear, and solvent polarization in chemical systems.
Simulating the nuclear–electronic quantum dynamics of large-scale molecular systems in the condensed phase is key for studying biologically and chemically important processes such as proton transfer and proton-coupled electron transfer reactions. Herein, the real-time nuclear–electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) approach is combined with a hybrid quantum mechanical/molecular mechanical (QM/MM) strategy to enable the accurate description of coupled nuclear–electronic quantum dynamics in the presence of heterogeneous environments such as solvent or proteins. The densities of the electrons and quantum protons are propagated in real time, while the other nuclei are propagated classically on the instantaneous electron–proton vibronic surface. This approach is applied to phenol bound to lysozyme, intramolecular proton transfer in malonaldehyde, and nonequilibrium excited-state intramolecular proton transfer in o-hydroxybenzaldehyde. Furthermore, these examples illustrate that the RT-NEO-TDDFT framework, coupled with an atomistic representation of the environment, allows the simulation of condensed-phase systems that exhibit significant nuclear quantum effects.
Most nonrelativistic electron correlation methods can be adapted to account for relativistic effects, as long as the relativistic molecular spinor integrals are available, from either a four-, two-, or one-component mean-field calculation. Furthermore, relativistic multireference correlation methods remain a relatively unexplored area, with mixed evidence regarding the improvements brought by perturbative treatments. We report, for the first time, the implementation of state-averaged four-component relativistic multireference perturbation theories to second and third order based on the driven similarity renormalization group (DSRG). With our methods, named 4c-SA-DSRG-MRPT2 and 3, we find that the dynamical correlation included on top of 4c-CASSCF references can significantly improve the spin-orbit splittings in p-block elements and potential energy surfaces when compared to 4c-CASSCF and 4c-CASPT2 results. We further show that 4c-DSRG-MRPT2 and 3 are applicable to these systems over a wide range of the flow parameter, with systematic improvement from second to third order in terms of both improved error statistics and reduced sensitivity with respect to the flow parameter.
Localized surface plasmons generated on metallic nanostructures can be used to accelerate molecular transformations; however, the efficiency is limited by the challenge to control the energy/charge transfer at the interfaces. Here, we combine density functional theory (DFT) calculations and experiments to reveal the mechanism of nitrophenol reduction on Au nanoparticles under visible-light irradiation and propose a strategy to further enhance the reaction rates. DFT calculations show a reduced activation barrier under electronic excitation on Au(111), thus explaining the measured higher rates under visible-light irradiation. Furthermore, we propose a heterostructure with Au nanoparticles covered by a thin film of hexagonal boron nitride; the latter is used to decouple the molecular orbitals from the metal to enable charge localization in the molecule. DFT calculations show that, by this electronic decoupling, the activation barrier can be lowered by a factor of five. Furthermore, this work thus provides a valuable strategy for optimizing catalytic efficiency.
While preparing a follow-up manuscript, we found an error in one of the orbital reduction factors used in our crystal field models, given in Scheme 2. The third equation in that scheme was published as ka2t2 = 1 - 12 N2 2 a'p ; however, the correct formula is k a2t2 = 1 - 12 N'a'p2. (Table Presented).