Analytical gradients for molecular-orbital-based machine learning.

Molecular-orbital-based machine learning (MOB-ML) enables the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. Here, we present the derivation, implementation, and numerical demonstration of MOB-ML analytical nuclear gradients, which are formulated in a general Lagrangian framework to enforce orthogonality, localization, and Brillouin constraints on the molecular orbitals. The MOB-ML gradient framework is general with respect to the regression technique (e.g., Gaussian process regression or neural networks) and the MOB feature design. We show that MOB-ML gradients are highly accurate compared to other ML methods on the ISO17 dataset while only being trained on energies for hundreds of molecules compared to energies and gradients for hundreds of thousands of molecules for the other ML methods. The MOB-ML gradients are also shown to yield accurate optimized structures at a computational cost for the gradient evaluation that is comparable to a density-corrected density functional theory calculation.

OrbNet Denali: A machine learning potential for biological and organic chemistry with semi-empirical cost and DFT accuracy.

We present OrbNet Denali, a machine learning model for an electronic structure that is designed as a drop-in replacement for ground-state density functional theory (DFT) energy calculations. The model is a message-passing graph neural network that uses symmetry-adapted atomic orbital features from a low-cost quantum calculation to predict the energy of a molecule. OrbNet Denali is trained on a vast dataset of 2.3 × 106 DFT calculations on molecules and geometries. This dataset covers the most common elements in biochemistry and organic chemistry (H, Li, B, C, N, O, F, Na, Mg, Si, P, S, Cl, K, Ca, Br, and I) and charged molecules. OrbNet Denali is demonstrated on several well-established benchmark datasets, and we find that it provides accuracy that is on par with modern DFT methods while offering a speedup of up to three orders of magnitude. For the GMTKN55 benchmark set, OrbNet Denali achieves WTMAD-1 and WTMAD-2 scores of 7.19 and 9.84, on par with modern DFT functionals. For several GMTKN55 subsets, which contain chemical problems that are not present in the training set, OrbNet Denali produces a mean absolute error comparable to those of DFT methods. For the Hutchison conformer benchmark set, OrbNet Denali has a median correlation coefficient of R2 = 0.90 compared to the reference DLPNO-CCSD(T) calculation and R2 = 0.97 compared to the method used to generate the training data (ωB97X-D3/def2-TZVP), exceeding the performance of any other method with a similar cost. Similarly, the model reaches chemical accuracy for non-covalent interactions in the S66x10 dataset. For torsional profiles, OrbNet Denali reproduces the torsion profiles of ωB97X-D3/def2-TZVP with an average mean absolute error of 0.12 kcal/mol for the potential energy surfaces of the diverse fragments in the TorsionNet500 dataset.

Approximate singly excited states from a two-component Hartree-Fock reference.

For many molecules, relaxing the spin symmetry constraint on the wave function results in the lowest energy mean-field solution. The two-component Hartree-Fock (2cHF) method relaxes all spin symmetry constraints, and the wave function is no longer an eigenfunction of the total spin, spin projection, or time-reversal symmetry operators. For ground state energies, 2cHF is a superior mean-field method for describing spin-frustrated molecules. For excited states, the utility of 2cHF is uncertain. Here, we implement the 2cHF extensions of two single-reference excited state methods, the two-component configuration interaction singles and time-dependent Hartree-Fock. We compare the results to the analogous methods based off of the unrestricted Hartree-Fock approximation, as well as the full configuration interaction for three small molecules with distinct 2cHF solutions, and discuss the nature of the 2cHF excited state solutions.

Time-dependent non-equilibrium dielectric response in QM/continuum approaches.

The Polarizable Continuum Models (PCMs) are some of the most inexpensive yet successful methods for including the effects of solvation in quantum-mechanical calculations of molecular systems. However, when applied to the electronic excitation process, these methods are restricted to dichotomously assuming either that the solvent has completely equilibrated with the excited solute charge density (infinite-time limit), or that it retains the configuration that was in equilibrium with the solute prior to excitation (zero-time limit). This renders the traditional PCMs inappropriate for resolving time-dependent solvent effects on non-equilibrium solute electron dynamics like those implicated in the instants following photoexcitation of a solvated molecular species. To extend the existing methods to this non-equilibrium regime, we herein derive and apply a new formalism for a general time-dependent continuum embedding method designed to be propagated alongside the solute's electronic degrees of freedom in the time domain. Given the frequency-dependent dielectric constant of the solvent, an equation of motion for the dielectric polarization is derived within the PCM framework and numerically integrated simultaneously with the time-dependent Hartree fock/density functional theory equations. Results for small molecular systems show the anticipated dipole quenching and electronic state dephasing/relaxation resulting from out-of-phase charge fluctuations in the dielectric and embedded quantum system.

Stability of the complex generalized Hartree-Fock equations.

For molecules with complex and competing magnetic interactions, it is often the case that the lowest energy Hartree-Fock solution may only be obtained by removing the spin and time-reversal symmetry constraints of the exact non-relativistic Hamiltonian. To do so results in the complex generalized Hartree-Fock (GHF) method. However, with the loss of variational constraints comes the greater possibility of converging to higher energy minima. Here, we report the implementation of stability test of the complex GHF equations, along with an orbital update scheme should an instability be found. We apply the methodology to finding the local minima of several spin-frustrated hydrogen rings, as well as the non-collinear molecular magnet Cr3, illustrating the utility of the broken symmetry GHF method and some of its lesser-known nuances.

Ab initio two-component Ehrenfest dynamics.

We present an ab initio two-component Ehrenfest-based mixed quantum/classical molecular dynamics method to describe the effect of nuclear motion on the electron spin dynamics (and vice versa) in molecular systems. The two-component time-dependent non-collinear density functional theory is used for the propagation of spin-polarized electrons while the nuclei are treated classically. We use a three-time-step algorithm for the numerical integration of the coupled equations of motion, namely, the velocity Verlet for nuclear motion, the nuclear-position-dependent midpoint Fock update, and the modified midpoint and unitary transformation method for electronic propagation. As a test case, the method is applied to the dissociation of H2 and O2. In contrast to conventional Ehrenfest dynamics, this two-component approach provides a first principles description of the dynamics of non-collinear (e.g., spin-frustrated) magnetic materials, as well as the proper description of spin-state crossover, spin-rotation, and spin-flip dynamics by relaxing the constraint on spin configuration. This method also holds potential for applications to spin transport in molecular or even nanoscale magnetic devices.

Quantum coherent plasmon in silver nanowires: a real-time TDDFT study.

A plasmon-like phenomenon, arising from coinciding resonant excitations of different electronic characteristics in 1D silver nanowires, has been proposed based on theoretical linear absorption spectra. Such a molecular plasmon holds the potential for anisotropic nanoplasmonic applications. However, its dynamical nature remains unexplored. In this work, quantum dynamics of longitudinal and transverse excitations in 1D silver nanowires are carried out within the real-time time-dependent density functional theory framework. The anisotropic electron dynamics confirm that the transverse transitions of different electronic characteristics are collective in nature and oscillate in-phase with respect to each other. Analysis of the time evolutions of participating one-electron wave functions suggests that the transverse transitions form a coherent wave packet that gives rise to a strong plasmon resonance at the molecular level.

Ab initio non-relativistic spin dynamics.

Many magnetic materials do not conform to the (anti-)ferromagnetic paradigm where all electronic spins are aligned to a global magnetization axis. Unfortunately, most electronic structure methods cannot describe such materials with noncollinear electron spin on account of formally requiring spin alignment. To overcome this limitation, it is necessary to generalize electronic structure methods and allow each electron spin to rotate freely. Here, we report the development of an ab initio time-dependent non-relativistic two-component spinor (TDN2C), which is a generalization of the time-dependent Hartree-Fock equations. Propagating the TDN2C equations in the time domain allows for the first-principles description of spin dynamics. A numerical tool based on the Hirshfeld partitioning scheme is developed to analyze the time-dependent spin magnetization. In this work, we also introduce the coupling between electron spin and a homogenous magnetic field into the TDN2C framework to simulate the response of the electronic spin degrees of freedom to an external magnetic field. This is illustrated for several model systems, including the spin-frustrated Li3 molecule. Exact agreement is found between numerical and analytic results for Larmor precession of hydrogen and lithium atoms. The TDN2C method paves the way for the ab initio description of molecular spin transport and spintronics in the time domain.

An efficient method for calculating dynamical hyperpolarizabilities using real-time time-dependent density functional theory.

In this paper we present a time-domain time-dependent density functional theory (TDDFT) approach to calculate frequency-dependent polarizability and hyperpolarizabilities. In this approach, the electronic degrees of freedom are propagated within the density matrix based TDDFT framework using the efficient modified midpoint and unitary transformation algorithm. We use monochromatic waves as external perturbations and apply the finite field method to extract various orders of the time-dependent dipole moment. By fitting each order of time-dependent dipole to sinusoidal waves with harmonic frequencies, one can obtain the corresponding (hyper)polarizability tensors. This approach avoids explicit Fourier transform and therefore does not require long simulation time. The method is illustrated with application to the optically active organic molecule para-nitroaniline, of which the frequency-dependent polarizability α(-ω; ω), second-harmonic generation ß(-2ω; ω, ω), optical rectification ß(0; -ω, ω), third-harmonic generation γ(-3ω; ω, ω, ω), and degenerate four-wave mixing γ(-ω; ω, ω, -ω) are calculated.

Polymer triplet energy levels need not limit photocurrent collection in organic solar cells.

We study charge recombination via triplet excited states in donor/acceptor organic solar cells and find that, contrary to intuition, high internal quantum efficiency (IQE) can be obtained in polymer/fullerene blend devices even when the polymer triplet state is significantly lower in energy than the intermolecular charge transfer (CT) state. Our model donor system comprises the copolymer PIDT-PhanQ: poly(indacenodithiophene-co-phenanthro[9,10-b]quinoxaline), which when blended with phenyl-C(71)-butyric acid methyl ester (PC(71)BM) is capable of achieving power conversion efficiencies of 6.0% and IQE ≈ 90%, despite the fact that the polymer triplet state lies 300 meV below the interfacial CT state. However, as we push the open circuit voltage (V(OC)) higher by tailoring the fullerene reduction potential, we observe signatures of a new recombination loss process near V(OC) = 1.0 V that we do not observe for PCBM-based devices. Using photoinduced absorption and photoluminescence spectroscopy, we show that a new recombination path opens via the fullerene triplet manifold as the energy of the lowest CT state approaches the energy of the fullerene triplet. This pathway appears active even in cases where direct recombination via the polymer triplet remains thermodynamically accessible. These results suggest that kinetics, as opposed to thermodynamics, can dominate recombination via triplet excitons in these blends and that optimization of charge separation and kinetic suppression of charge recombination may be fruitful paths for the next generation of panchromatic organic solar cell materials with high V(OC) and J(SC).

Modeling ultrafast solvated electronic dynamics using time-dependent density functional theory and polarizable continuum model.

A first-principles solvated electronic dynamics method is introduced. Solvent electronic degrees of freedom are coupled to the time-dependent electronic density of a solute molecule by means of the implicit reaction field method, and the entire electronic system is propagated in time. This real-time time-dependent approach, incorporating the polarizable continuum solvation model, is shown to be very effective in describing the dynamical solvation effect in the charge transfer process and yields a consistent absorption spectrum in comparison to the conventional linear response results in solution.

Mechanisms of bridge-mediated electron transfer: a TDDFT electronic dynamics study.

We present a time-dependent density functional theory approach for probing the dynamics of electron transfer on a donor-bridge-acceptor polyene dye scaffold. Two kinds of mechanisms, namely, the superexchange mechanism and the sequential mechanism, may be involved in the electron transfer process. In this work, we have focused on the crossover between these two charge transfer mechanisms on a series of donor-bridge-acceptor polyene dye systems with varying lengths of conjugated bridges. A number of methods and quantities are used to assist in the analysis, including the phase relationship of charge evolution and frequency domain spectra of the time-dependent dipole. Our simulations show that the superexchange mechanism plays a dominant role in the electron transfer from donor to acceptor when the bridge length is small, and the sequential mechanism becomes more important as the polyene bridge is lengthened. Full Ehrenfest dynamics with nuclear motion show that molecular vibrations play a very small role in such ultrafast charge transfer processes.

On the gauge invariance of nonperturbative electronic dynamics using the time-dependent Hartree-Fock and time-dependent Kohn-Sham.

Nonperturbative electronic dynamics using the time-dependent Hartree-Fock (TDHF) and time-dependent Kohn-Sham (TDKS) theories with the adiabatic approximation is a powerful tool in obtaining insights into the interaction between a many-electron system and an external electromagnetic field. In practical applications of TDHF/TDKS using a truncated basis set, the electronic dynamics and molecular properties become gauge-dependent. Numerical simulations are carried out in the length gauge and velocity gauge to verify the extent of gauge-dependence using incomplete basis sets. Electronic dynamics of two many-electron systems, a helium atom and a carbon monoxide molecule in high-intensity linearly polarized radiation fields are performed using the TDHF and TDKS with two selected adiabatic exchange-correlation (xc) functionals. The time evolution of the expectation values of the dipole moment and harmonic spectra are calculated in the two gauges, and the basis set dependence on the gauge-invariance of these properties is investigated.

Small Nuclear Quantum Effects in Scattering of H and D from Graphene.

We study nuclear quantum effects in H/D sticking to graphene, comparing scattering experiments at near-zero coverage with classical, quantized, and transition-state calculations. The experiment shows H/D sticking probabilities that are indistinguishable from one another and markedly smaller than those expected from a consideration of zero-point energy shifts of the chemisorption transition state. Inclusion of dynamical effects and vibrational anharmonicity via ring-polymer molecular dynamics (RPMD) yields results that are in good agreement with the experimental results. RPMD also reveals that nuclear quantum effects, while modest, arise primarily from carbon and not from H/D motion, confirming the importance of a C atom rehybridization mechanism associated with H/D sticking on graphene.

Computational study of bridge-assisted intervalence electron transfer.

Intervalence electron transfer reactions were studied computationally by means of density functional theory and constrained density functional theory (CDFT). Two ferrocene moieties, connected via various bridge structures, were used as model mixed-valence compounds in the computational investigation. Features of the frontier orbitals were analyzed to offer a qualitative account of the intervalence characteristics of the model complexes. The effective electronic coupling between the donor and acceptor sites was calculated using the CDFT method, which provided a quantitative measure of the intervalence electronic communication. The relationship between the bridge linkage and the effectiveness of intervalence transfer was discussed on the basis of the theoretical results and compared to experimental data available in the literature.

Embedded Mean-Field Theory for Solution-Phase Transition-Metal Polyolefin Catalysis.

Decreasing the wall-clock time of quantum mechanics/molecular mechanics (QM/MM) calculations without sacrificing accuracy is a crucial prerequisite for widespread simulation of solution-phase dynamical processes. In this work, we demonstrate the use of embedded mean-field theory (EMFT) as the QM engine in QM/MM molecular dynamics (MD) simulations to examine polyolefin catalysts in solution. We show that employing EMFT in this mode preserves the accuracy of hybrid-functional DFT in the QM region, while providing up to 20-fold reductions in the cost per SCF cycle, thereby increasing the accessible simulation time-scales. We find that EMFT reproduces DFT-computed binding energies and optimized bond lengths to within chemical accuracy, as well as consistently ranking conformer stability. Furthermore, solution-phase EMFT/MM simulations provide insight into the interaction strength of strongly coordinating and bulky counterions.

First-principles calculation of pKa values for organic acids in nonaqueous solution.

Electronic structure theory, mainly the density functional theory (DFT), is applied to calculate the pK(a) values for a variety of organic acids in several nonaqueous solvents: namely DMSO, MeCN, and THF. Following the supermolecule approach the solute molecule, together with a few solvent molecules in close proximity, is treated explicitly by the electronic structure theory, and the remaining solvent environment is approximated by using a standard dielectric continuum model. It is found that in most cases including only one explicit solvent molecule gives satisfactory results for pK(a) estimations. Next, the equilibrium position free energy difference is calculated between a reference acid-base pair whose pK(a) is known experimentally and the acid-base pair whose pK(a) is to be determined theoretically. This bypasses the step of treating the solvated proton that most of the current theories have difficulty with and, to a large extent, induces favorable error cancelations in the final theoretical results. Accurate theoretical predictions of pK(a) values are thus obtained at a moderate level of theory (MP2 single point on B3LYP/6-31+G(d) optimized geometry) for a series of organic acids spanning a wide range of acidities in DMSO, MeCN, and THF. Furthermore, the correlation between the pK(a) values of these acids in different solutions is investigated theoretically, and excellent agreement is found with the experimental results.

Ligand dependence of binding to three-coordinate Fe(II) complexes.

A series of three- and four-coordinate iron(II) complexes with nitrogen, chlorine, oxygen, and sulfur ligands is presented. The electronic variation is explored by measuring the association constant of the neutral ligands and the reduction potential of the iron(II) complexes. Varying the neutral ligand gives large changes in K(eq), which decrease in the order CN(t)Bu > pyridine >2-picoline > DMF > MeCN > THF > PPh(3). These differences can be attributed to a mixture of steric effects and electronic effects (both sigma-donation and pi-backbonding). The binding constants and the reduction potentials are surprisingly insensitive to changes in an anionic spectator ligand. This suggests that three-coordinate iron(II) complexes may have similar binding trends as proposed three-coordinate iron(II) intermediates in the FeMoco of nitrogenase, even though the anionic spectator ligands in the synthetic complexes differ from the sulfides in the FeMoco.

Imaging covalent bond formation by H atom scattering from graphene.

Viewing the atomic-scale motion and energy dissipation pathways involved in forming a covalent bond is a longstanding challenge for chemistry. We performed scattering experiments of H atoms from graphene and observed a bimodal translational energy loss distribution. Using accurate first-principles dynamics simulations, we show that the quasi-elastic channel involves scattering through the physisorption well where collision sites are near the centers of the six-membered C-rings. The second channel results from transient C-H bond formation, where H atoms lose 1 to 2 electron volts of energy within a 10-femtosecond interaction time. This remarkably rapid form of intramolecular vibrational relaxation results from the C atom's rehybridization during bond formation and is responsible for an unexpectedly high sticking probability of H on graphene.

Thermodynamics of hydrogen atom transfer to a high-valent iron imido complex.

Thermodynamic investigations relevant to hydrogen atom transfer by the high-valent iron imido complex [LMesFe[triple bond]NAd]OTf have been undertaken. The complex is found to be weakly oxidizing by cyclic voltammetry (E1/2 = -0.98 V vs Cp2Fe+/Cp2Fe in MeCN). A combination of experimental and computational studies has been used to determine the acidity of LMesFe-N(H)Ad+ (pKa = 37 in MeCN), allowing the N-H BDFE (88(5) kcal/mol) to be calculated from a thermodynamic cycle. Consistent with this value, [LMesFe[triple bond]NAd]OTf reacts with 9,10-dihydroanthracene (C-H BDE = 78(1) kcal/mol) to form anthracene.