Kernel Methods for Predicting Yields of Chemical Reactions.

The use of machine learning methods for the prediction of reaction yield is an emerging area. We demonstrate the applicability of support vector regression (SVR) for predicting reaction yields, using combinatorial data. Molecular descriptors used in regression tasks related to chemical reactivity have often been based on time-consuming, computationally demanding quantum chemical calculations, usually density functional theory. Structure-based descriptors (molecular fingerprints and molecular graphs) are quicker and easier to calculate and are applicable to any molecule. In this study, SVR models built on structure-based descriptors were compared to models built on quantum chemical descriptors. The models were evaluated along the dimension of each reaction component in a set of Buchwald-Hartwig amination reactions. The structure-based SVR models outperformed the quantum chemical SVR models, along the dimension of each reaction component. The applicability of the models was assessed with respect to similarity to training. Prospective predictions of unseen Buchwald-Hartwig reactions are presented for synthetic assessment, to validate the generalizability of the models, with particular interest along the aryl halide dimension.

Vibrational Spectroscopic Map, Vibrational Spectroscopy, and Intermolecular Interaction.

Vibrational spectroscopy is an essential tool in chemical analyses, biological assays, and studies of functional materials. Over the past decade, various coherent nonlinear vibrational spectroscopic techniques have been developed and enabled researchers to study time-correlations of the fluctuating frequencies that are directly related to solute-solvent dynamics, dynamical changes in molecular conformations and local electrostatic environments, chemical and biochemical reactions, protein structural dynamics and functions, characteristic processes of functional materials, and so on. In order to gain incisive and quantitative information on the local electrostatic environment, molecular conformation, protein structure and interprotein contacts, ligand binding kinetics, and electric and optical properties of functional materials, a variety of vibrational probes have been developed and site-specifically incorporated into molecular, biological, and material systems for time-resolved vibrational spectroscopic investigation. However, still, an all-encompassing theory that describes the vibrational solvatochromism, electrochromism, and dynamic fluctuation of vibrational frequencies has not been completely established mainly due to the intrinsic complexity of intermolecular interactions in condensed phases. In particular, the amount of data obtained from the linear and nonlinear vibrational spectroscopic experiments has been rapidly increasing, but the lack of a quantitative method to interpret these measurements has been one major obstacle in broadening the applications of these methods. Among various theoretical models, one of the most successful approaches is a semiempirical model generally referred to as the vibrational spectroscopic map that is based on a rigorous theory of intermolecular interactions. Recently, genetic algorithm, neural network, and machine learning approaches have been applied to the development of vibrational solvatochromism theory. In this review, we provide comprehensive descriptions of the theoretical foundation and various examples showing its extraordinary successes in the interpretations of experimental observations. In addition, a brief introduction to a newly created repository Web site (http://frequencymap.org) for vibrational spectroscopic maps is presented. We anticipate that a combination of the vibrational frequency map approach and state-of-the-art multidimensional vibrational spectroscopy will be one of the most fruitful ways to study the structure and dynamics of chemical, biological, and functional molecular systems in the future.

Static Electron Correlation in Anharmonic Molecular Vibrations: A Hybrid TAO-DFT Study.

Hybrid thermally-assisted-occupation density functional theory is used to examine the effects of static electron correlation on the prediction of a benchmark set of experimentally observed molecular vibrational frequencies. The B3LYP and B97-1 thermally-assisted-occupation measure of static electron correlation is important for describing the vibrations of many of the molecules that make up several popular test sets of experimental data. Shifts are seen for known multireference systems and for many molecules containing atoms from the second row of the periodic table of elements. Several molecules only show significant shifts in select vibrational modes, and significant improvements are seen for the prediction of hydrogen stretching frequencies throughout the test set.

Influence of molecular design on radical spin multiplicity: characterisation of BODIPY dyad and triad radical anions.

A strategy to create organic molecules with high degrees of radical spin multiplicity is reported in which molecular design is correlated with the behaviour of radical anions in a series of BODIPY dyads. Upon reduction of each BODIPY moiety radical anions are formed which are shown to have different spin multiplicities by electron paramagnetic resonance (EPR) spectroscopy and distinct profiles in their cyclic voltammograms and UV-visible spectra. The relationship between structure and multiplicity is demonstrated showing that the balance between singlet, biradical or triplet states in the dyads depends on relative orientation and connectivity of the BODIPY groups. The strategy is applied to the synthesis of a BODIPY triad which adopts an unusual quartet state upon reduction to its radical trianion.

Möbius and Hückel Cyclacenes with Dewar and Ladenburg Defects.

Cyclacene nanobelts have not been synthesized in over 60 years and remain one of the last unsynthesized building blocks of carbon nanotubes. Recent work has predicted that Hückel-cyclacenes containing Dewar benzenoid ring isomers are the most stable isomeric forms for several of the smaller sizes of cyclacene belts. Here, we give a more complete picture of the isomers that are possible within these nanobelt systems by simulating embedded Ladenburg (prismane) benzenoid rings in Hückel-[n]cyclacenes (n = 5-14) and embedded Dewar benzenoid rings in twisted Möbius-[n]cyclacenes (n = 9-14). The Möbius-[9]cyclacene isomer containing one Dewar benzenoid defect and the Hückel-[5]cyclacene isomer containing two maximally spaced Ladenburg benzenoid defects are found to be more stable than their conventional Kekulé benzenoid ring counterparts. The isomers that contain Dewar and Ladenburg benzenoid rings have larger electronic singlet-triplet energy gaps and lower polyradical character when compared with the conventional isomers.

Monitoring the Formation and Reactivity of Organometallic Alkane and Fluoroalkane Complexes with Silanes and Xe Using Time-Resolved X-ray Absorption Fine Structure Spectroscopy.

Complexes with weakly coordinating ligands are often formed in chemical reactions and can play key roles in determining the reactivity, particularly in catalytic reactions. Using time-resolved X-ray absorption fine structure (XAFS) spectroscopy in combination with time-resolved IR (TRIR) spectroscopy and tungsten hexacarbonyl, W(CO)6, we are able to structurally characterize the formation of an organometallic alkane complex, determine the W-C distances, and monitor the reactivity with silane to form an organometallic silane complex. Experiments in perfluorosolvents doped with xenon afford initially the corresponding solvated complex, which is sufficiently reactive in the presence of Xe that we can then observe the coordination of Xe to the metal center, providing a unique insight into the metal-xenon bonding. These results offer a step toward elucidating the structure, bonding, and chemical reactivity of transient species by X-ray absorption spectroscopy, which has sensitivity to small structural changes. The XAFS results indicate that the bond lengths of metal-alkane (W-H-C) bond in W(CO)5(heptane) as 3.07 (±0.06) Å, which is longer than the calculated W-C (2.86 Å) for binding of the primary C-H, but shorter than the calculated W-C (3.12 Å) for the secondary C-H. A statistical average of the calculated W-C alkane bond lengths is 3.02 Å, and comparison of this value indicates that the value derived from the XAFS measurements is averaged over coordination of all C-H bonds consistent with alkane chain walking. Photolysis of W(CO)6 in the presence of HSiBu3 allows the conversion of W(CO)5(heptane) to W(CO)5(HSiBu3) with an estimated W-Si distance of 3.20 (±0.03) Å. Time-resolved TRIR and XAFS experiments following photolysis of W(CO)6 in perfluoromethylcyclohexane (PFMCH) allows the characterization of W(CO)5(PFMCH) with a W-F distance of 2.65 (±0.06) Å, and doping PFMCH with Xe allows the characterization of W(CO)5Xe with a W-Xe bond length of 3.10 (±0.02) Å.

The effect of coordination of alkanes, Xe and CO2 (η1-OCO) on changes in spin state and reactivity in organometallic chemistry: a combined experimental and theoretical study of the photochemistry of CpMn(CO)3.

A combined experimental and theoretical study is presented of several ligand addition reactions of the triplet fragment 3CpMn(CO)2 formed upon photolysis of CpMn(CO)3. Experimental data are provided for reactions in n-heptane and perfluoromethylcyclohexane (PFMCH), as well as in PFMCH doped with C2H6, Xe and CO2. In PFMCH we find that the conversion of 3CpMn(CO)2 to 1CpMn(CO)2(PFMCH) is much slower (τ = 18 (±3) ns) than the corresponding reactions in conventional alkanes (τ = 111 (±10) ps). We measure the effect of the coordination ability by doping PFMCH with alkane, Xe and CO2; these doped ligands form the corresponding singlet adducts with significantly variable formation rates. The reactivity as measured by the addition timescale follows the order 1CpMn(CO)2(C5H10) (τ = 270 (±10) ps) > 1CpMn(CO)2Xe (τ = 3.9 (±0.4) ns) ∼ 1CpMn(CO)2(CO2) (τ = 4.7 (±0.5) ns) > 1CpMn(CO)2(C7F14) (τ = 18 (±3) ns). Electronic structure theory calculations of the singlet and triplet potential energy surfaces and of their intersections, together with non-adiabatic statistical rate theory, reproduce the observed rates semi-quantitatively. It is shown that triplet adducts of the ligand and 3CpMn(CO)2 play a role in the kinetics, and account for the variable timescales observed experimentally.

Dimers of acetic acid in helium nanodroplets.

The structural arrangement of small carboxylic acid molecules in the liquid phase remains a controversial topic. Some studies indicate a dominance of the cyclic dimer that prevails in the gas phase, whilst other studies favor short fragments of the infinite catemer chains that are found in the crystalline phase. Furthermore, difficulties in preparing and probing size-selected catemer segments have resulted in a lack of benchmark data upon which theoretical models of the condensed phases can be built. To address these issues, we have combined infrared spectroscopy and quantum chemical calculations to explore regions of the intermolecular potential energy surface associated with the formation of metastable dimer isomers. The OH stretching region of the spectrum shows that aggregation of acetic acid molecules inside liquid helium nanodroplets yields two distinct metastable dimers, whilst negligible signal is observed from the cyclic dimer that typically overwhelms this spectral region. We deduce that the most abundant isomer in superfluid helium has one strong O-HO[double bond, length as m-dash]C and one weak C-HO[double bond, length as m-dash]C hydrogen bond. Since this bonding motif is common to the dimeric repeating unit of the catemer, it is of fundamental importance for understanding intermolecular interactions in the condensed phases of small carboxylic acids.

Benchmarking DFT-D Dispersion Corrections for Anharmonic Vibrational Frequencies and Harmonic Scaling Factors.

Improvements in the form of the DFT-D empirical dispersion corrections to hybrid density functional theory are shown to have made corrections sufficiently accurate to improve the calculation of both anharmonic frequencies and scaled harmonic vibrational frequencies across a wide range of commonly tested molecules. The Becke-Johnson damping function is noted as being particularly versatile across the molecules tested, and the B3LYP-D3M(BJ) and B3LYP-D3(CSO) methods are found to be the most widely applicable. Dispersion corrections are shown to be important for accurately describing carbon-hydrogen bond stretching vibrations, and standard triple-dipole based three-body terms are found to cause large errors in these anharmonic frequencies. Preliminary results also indicate that there is a cancellation of error at this level of theory when using smaller finite difference step sizes to calculate anharmonic derivatives of the nuclear potential energy surface.

Excited-State Vibrational Frequencies: Restricted Virtual Space Time-Dependent Density Functional Theory.

Calculating accurate vibrational frequencies for molecules with electronically excited states has an important function in many areas of photochemistry. However, calculations are often limited to smaller molecules due to the rapid growth in the degrees of freedom that must be taken into account to accurately describe larger systems. The applicability of the restricted virtual space (RVS) approximation has been studied within adiabatic linear response time-dependent density functional theory when calculating excited-state nuclear vibrational frequencies. Using the S1 and T1 electronic states of CO, CN-, HOF, H2CS, and C2H4 as representative examples, it is found that vibrational frequency calculations are particularly sensitive to this approximation, with no more than 10-20% of orbitals recommended for safe removal without a priori knowledge when using the 6-311+G(d,p) and aug-cc-pVTZ basis sets. Higher-frequency vibrations such as those with a high degree of CH bond stretching character are found to be less sensitive to the RVS than the lower-frequency vibrations, and several of the triplet states are also found to be less sensitive to this approximation than their equivalent singlet states. Occupied core orbitals and high-energy virtual orbitals with core character can also be removed without introducing significant error.

A scaled CIS(D) based method for the calculation of valence and core electron ionization energies.

The calculation of electron ionization energies is a key component for the simulation of photoelectron spectroscopy. CIS(D) is a perturbative doubles correction for the single excitation configuration interaction (CIS) method which provides a new approach for computing excitation energies. It is shown that by introducing a virtual orbital subspace that consists of a single "ghost" orbital, valence electron ionization energies can be computed using a scaled CIS(D) approach with an accuracy comparable with considerably more computationally intensive methods, such as ionization-potential equation of motion coupled cluster theory, and simulated spectra show a significant improvement relative to spectra based upon Koopmans' theorem. When the model is applied to the ionization energies for core orbitals, there is an increase in the error, particularly for the heavier nuclei considered (silicon to chlorine), although the relative energy of the ionization energies are predicted accurately. In addition to its inherent computational efficiency relative to other wavefunction based approaches, a significant advantage of this approach is that the ionization energies for all electrons can be obtained in a single calculation, in contrast to Δself-consistent field based methods.

Photoaquation Mechanism of Hexacyanoferrate(II) Ions: Ultrafast 2D UV and Transient Visible and IR Spectroscopies.

Ferrous iron(II) hexacyanide in aqueous solutions is known to undergo photoionization and photoaquation reactions depending on the excitation wavelength. To investigate this wavelength dependence, we implemented ultrafast two-dimensional UV transient absorption spectroscopy, covering a range from 280 to 370 nm in both excitation and probing, along with UV pump/visible probe or time-resolved infrared (TRIR) transient absorption spectroscopy and density functional theory (DFT) calculations. As far as photoaquation is concerned, we find that excitation of the molecule leads to ultrafast intramolecular relaxation to the lowest triplet state of the [Fe(CN)6]4- complex, followed by its dissociation into CN- and [Fe(CN)5]3- fragments and partial geminate recombination, all within <0.5 ps. The subsequent time evolution is associated with the [Fe(CN)5]3- fragment going from a triplet square pyramidal geometry, to the lowest triplet trigonal bipyramidal state in 3-4 ps. This is the precursor to aquation, which occurs in ∼20 ps in H2O and D2O solutions, forming the [Fe(CN)5(H2O/D2O)]3- species, although some aquation also occurs during the 3-4 ps time scale. The aquated complex is observed to be stable up to the microsecond time scale. For excitation below 310 nm, the dominant channel is photooxidation with a minor aquation channel. The photoaquation reaction shows no excitation wavelength dependence up to 310 nm, that is, it reflects a Kasha Rule behavior. In contrast, the photooxidation yield increases with decreasing excitation wavelength. The various intermediates that appear in the TRIR experiments are identified with the help of DFT calculations. These results provide a clear example of the energy dependence of various reactive pathways and of the role of spin-states in the reactivity of metal complexes.

Infrared Spectroscopy of NaCl(CH3OH)n Complexes in Helium Nanodroplets.

Infrared (IR) spectra of complexes between NaCl and methanol have been recorded for the first time. These complexes were formed in liquid helium nanodroplets by consecutive pick-up of NaCl and CH3OH molecules. For the smallest NaCl(CH3OH)n, complexes where n = 1-3, the IR data suggest that the lowest-energy isomer is the primary product in each case. The predominant contribution to the binding comes from ionic hydrogen bonds between the OH in each methanol molecule and the chloride ion in the NaCl, as established by the large red shift of the OH stretching bands compared with the isolated CH3OH molecule. For n ≥ 4, there is a dramatic shift from discrete vibrational bands to very broad absorption envelopes, suggesting a profound change in the structural landscape and, in particular, access to multiple low-energy isomers.

Intermediate vibrational coordinate localization with harmonic coupling constraints.

Optimized normal coordinates can significantly improve the speed and accuracy of vibrational frequency calculations. However, over-localization can occur when using unconstrained spatial localization techniques. The unintuitive mixtures of stretching and bending coordinates that result can make interpreting spectra more difficult and also cause artificial increases in mode-coupling during anharmonic calculations. Combining spatial localization with a constraint on the coupling between modes can be used to generate coordinates with properties in-between the normal and fully localized schemes. These modes preserve the diagonal nature of the mass-weighted Hessian matrix to within a specified tolerance and are found to prevent contamination between the stretching and bending vibrations of the molecules studied without a priori classification of the different types of vibration present. Relaxing the constraint can also be used to identify which normal modes form specific groups of localized modes. The new coordinates are found to center on more spatially delocalized functional groups than their fully localized counterparts and can be used to tune the degree of vibrational correlation energy during anharmonic calculations.

Examining the impact of harmonic correlation on vibrational frequencies calculated in localized coordinates.

Carefully choosing a set of optimized coordinates for performing vibrational frequency calculations can significantly reduce the anharmonic correlation energy from the self-consistent field treatment of molecular vibrations. However, moving away from normal coordinates also introduces an additional source of correlation energy arising from mode-coupling at the harmonic level. The impact of this new component of the vibrational energy is examined for a range of molecules, and a method is proposed for correcting the resulting self-consistent field frequencies by adding the full coupling energy from connected pairs of harmonic and pseudoharmonic modes, termed vibrational self-consistent field (harmonic correlation). This approach is found to lift the vibrational degeneracies arising from coordinate optimization and provides better agreement with experimental and benchmark frequencies than uncorrected vibrational self-consistent field theory without relying on traditional correlated methods.

Calculating singlet excited states: Comparison with fast time-resolved infrared spectroscopy of coumarins.

In contrast to the ground state, the calculation of the infrared (IR) spectroscopy of molecular singlet excited states represents a substantial challenge. Here, we use the structural IR fingerprint of the singlet excited states of a range of coumarin dyes to assess the accuracy of density functional theory based methods for the calculation of excited state IR spectroscopy. It is shown that excited state Kohn-Sham density functional theory provides a high level of accuracy and represents an alternative approach to time-dependent density functional theory for simulating the IR spectroscopy of singlet excited states.

Photochemical dihydrogen production using an analogue of the active site of [NiFe] hydrogenase.

Photoproduction of dihydrogen (H2) by a low molecular weight analogue of the active site of [NiFe] hydrogenase has been investigated by reduction of the [NiFe2] cluster, 1, by a photosensitier PS (PS = [ReCl(CO)3(bpy)] or [Ru(bpy)3][PF6]2). Reductive quenching of the (3)MLCT excited state of the photosensitizer by NEt3 or N(CH2CH2OH)3 (TEOA) generates PS(•-), and subsequent intermolecular electron transfer to 1 produces the reduced anionic form of 1. Time-resolved infrared spectroscopy (TRIR) has been used to probe the intermediates throughout the reduction of 1 and subsequent photocatalytic H2 production from [HTEOA][BF4], which was monitored by gas chromatography. Two structural isomers of the reduced form of 1 (1a(•-) and 1b(•-)) were detected by Fourier transform infrared spectroscopy (FTIR) in both CH3CN and DMF (dimethylformamide), while only 1a(•-) was detected in CH2Cl2. Structures for these intermediates are proposed from the results of density functional theory calculations and FTIR spectroscopy. 1a(•-) is assigned to a similar structure to 1 with six terminal carbonyl ligands, while calculations suggest that in 1b(•-) two of the carbonyl groups bridge the Fe centers, consistent with the peak observed at 1714 cm(-1) in the FTIR spectrum for 1b(•-) in CH3CN, assigned to a ν(CO) stretching vibration. Formation of 1a(•-) and 1b(•-) and production of H2 was studied in CH3CN, DMF, and CH2Cl2. Although the more catalytically active species (1a(•-) or 1b(•-)) could not be determined, photocatalysis was observed only in CH3CN and DMF.

Calculating excited state properties using Kohn-Sham density functional theory.

The accuracy of excited states calculated with Kohn-Sham density functional theory using the maximum overlap method has been assessed for the calculation of adiabatic excitation energies, excited state structures, and excited state harmonic and anharmonic vibrational frequencies for open-shell singlet excited states. The computed Kohn-Sham adiabatic excitation energies are improved significantly by post self-consistent field spin-purification, but remain too low compared with experiment with a larger error than time-dependent density functional theory. Excited state structures and vibrational frequencies are also improved by spin-purification. The structures show a comparable accuracy to time-dependent density functional theory, while the harmonic vibrational frequencies are found to be more accurate for the majority of vibrational modes. The computed harmonic vibrational frequencies are also further improved by perturbative anharmonic corrections, suggesting a good description of the potential energy surface. Overall, excited state Kohn-Sham density functional theory is shown to provide an efficient method for the calculation of excited state structures and vibrational frequencies in open-shell singlet systems and provides a promising technique that can be applied to study large systems.

Investigating the calculation of anharmonic vibrational frequencies using force fields derived from density functional theory.

The calculation of anharmonic vibrational frequencies for a set of small molecules has been examined to explore the merit of applying such computationally expensive approaches for large molecules with density functional theory. The performance of different hybrid and gradient-corrected exchange-correlation functionals has been assessed for the calculation of anharmonic vibrational frequencies using second-order vibrational perturbation theory with two- and four-mode couplings and compared to the recently developed transition optimized shifted Hermite method. A range of exchange-correlation functionals (B3LYP, BLYP, EDF1, EDF2, B97-1, B97-2, HCTH-93, HCTH-120, HCTH-147, and HCTH-407) have been evaluated with reference to a large experimental data set comprising 88 species and 655 modes as well as a smaller set of shifts in frequency because of anharmonicity derived from experimental data. The anharmonic frequencies calculated using hybrid functionals provide the best agreement with experiment, and are not significantly improved by frequency scaling factors, indicating an absence of significant systematic error. For the molecules studied, the B97-1 and B97-2 functionals give the closest overall agreement with experiment, although the improvement over the best case for pure harmonic frequencies is modest. Predictions of the experimental anharmonic shifts are closest for the B3LYP and EDF2 functionals, with B97-1 performing well because of a good description of the harmonic force field. Investigations using modified hybrid functionals with increased fractions of Hartree-Fock exchange indicate that approximately 20% Hartree-Fock exchange is optimal.