Analytic Nuclear Gradients for Complete Active Space Linearized Pair-Density Functional Theory

Accurately modeling photochemical reactions is difficult due to the presence of conical intersections and locally avoided crossings, as well as the inherently multiconfigurational character of excited states. As such, one needs a multistate method that incorporates state interaction in order to accurately model the potential energy surface at all nuclear coordinates. The recently developed linearized pair-density functional theory (L-PDFT) is a multistate extension of multiconfiguration PDFT, and it has been shown to be a cost-effective post-MCSCF method (as compared to more traditional and expensive multireference many-body perturbation methods or multireference configuration interaction methods) that can accurately model potential energy surfaces in regions of strong nuclear-electronic coupling in addition to accurately predicting Franck-Condon vertical excitations. In this paper, we report the derivation of analytic gradients for L-PDFT and their implementation in the PySCF-forge software, and we illustrate the utility of these gradients for predicting ground- and excited-state equilibrium geometries and adiabatic excitation energies for formaldehyde, s-trans-butadiene, phenol, and cytosine.

Photoion Mass-Selected Threshold Photoelectron Spectroscopy to Detect Reactive Intermediates in Catalysis: From Instrumentation and Examples to Peculiarities and a Database

Photoion mass-selected threshold photoelectron spectroscopy (ms-TPES) is a synchrotron-based, universal, sensitive, and multiplexed detection tool applied in the areas of catalysis, combustion, and gas-phase reactions. Isomer-selective vibrational fingerprints in the ms-TPES of stable and reactive intermediates allow for unequivocal assignment of spectral carriers. Case studies are presented on heterogeneous catalysis, revealing the role of ketenes in the methanol-to-olefins process, the catalytic pyrolysis mechanism of lignin model compounds, and the radical chemistry upon C-H activation in oxyhalogenation. These studies demonstrate the potential of ms-TPES as an analytical technique for elucidating complex reaction mechanisms. We examine the robustness of ms-TPES assignments and address sampling effects, especially the temperature dependence of ms-TPES due to rovibrational broadening. Data acquisition approaches and the Stark shift from the extraction field are also considered to arrive at general recommendations. Finally, the PhotoElectron PhotoIon Spectral Compendium (https://pepisco.psi.ch), a spectral database hosted at Paul Scherrer Institute to support assignment, is introduced.

How to Predict Excited State Geometry by Using Empirical Parameters Obtained from Franck-Condon Analysis of Optical Spectrum

Excited state geometries of molecules can be calculated with highly reliable wavefunction schemes. Most of such schemes, however, are applicable to small molecules and can hardly be viewed as error-free for excited state geometries. In this study, a theoretical approach is presented in which the excited state geometries of molecules can be predicted by using vibrationally resolved experimental absorption spectrum in combination with the theoretical modelling of vibrational pattern based on Franck-Condon approximation. Huang-Rhys factors have been empirically determined and used as input for revealing the structural changes occurring between the ground and the excited state geometries upon photoexcitation. Naphthalene molecule has been chosen as a test case to show the robustness of the proposed theoretical approach. Predicted 1B_2u excited state geometry of the naphthalene has similar but slightly different bond length alternation pattern when compared with the geometries calculated with CIS, B3LYP, and CC2 methods. Excited state geometries of perylene and pyrene molecules are also determined with the presented theoretical approach. This powerful method can be applied to other molecules and specifically to relatively large molecules rather easily as long as vibrationally resolved experimental spectra are available to use.

Generalized Analytic Approach for Determination of Multidimensional Franck-Condon Factors: Simulated Photoelectron Spectra of Polynuclear Aromatic Hydrocarbons

An enhanced generalized analytic approach for determination of multidimensional Franck-Condon Factors (FCFs) enables efficient computational prediction of photoelectron spectra for large-dimensional systems. Incorporation of the automated assignment of Cartesian coordinate handedness and coordinate superposition between the ground and excited electronic states satisfies the Eckart conditions and allows evaluation of the Duschinsky effect. The model shows excellent agreement with experiments for the determination of FCFs and photoelectron spectra of a series of increasing dimensions polynuclear hydrocarbons (PAHs), including naphthalene, anthracene, phenanthrene, and pyrene. In addition, a high-resolution prediction of the PES for the 84-dimensional PAH corannulene provides motivation for an additional experimental study. For FCFs, coordinate transformation between the initial and final states rather than the dimension of the systems more greatly influences the complexity of the spectral band shapes.

Pentadiynylidene and Its Methyl-Substituted Derivates: Threshold Photoelectron Spectroscopy of R1-C5-R2 Triplet Carbon Chains

Mass-selective threshold photoelectron spectroscopy in the gas phase was employed to characterize the dialkynyl triplet carbenes pentadiynylidene (HC₅H), methylpentadiynylidene (MeC₅H), and dimethylpentadiynylidene (MeC₅Me). Diazo compounds were employed as precursors to generate the carbenes by flash pyrolysis. The R₁-C₅-R₂ carbon chains were photoionized by vacuum ultraviolet (VUV) synchrotron radiation in photoelectron photoion coincidence (PEPICO) experiments. High-level ab initio computations were carried out to support the interpretation of the experiments. For the unsubstituted pentadiynylidene (R₁ = R₂ = H) the recorded spectrum yields an adiabatic ionization energy (IE_ad) of 8.36 ± 0.03 eV. In addition, a second carbene isomer, 3-(didehydrovinylidene)cyclopropene, with a singlet electronic ground state, was identified in the spectrum based on the IE_ad of 8.60 ± 0.03 eV and Franck-Condon simulations. We found that multireference computations are required to reliably calculate the IE_ad for this molecule. CASPT2 computations predicted an IE_ad = 8.55 eV, while coupled-cluster computations significantly overestimate the IE. The cyclic isomer is most likely formed from another isomer of the precursor present in the sample. Stepwise methyl-substitution of the carbene leads to a reduction of the IE to 7.77 ± 0.04 eV for methylpentadiynylidene and 7.27 ± 0.06 eV for dimethylpentadiynylidene. The photoionization and dissociative photoionization of the precursors is investigated as well.

Rotationally resolved electronic spectroscopy of the rotamers of 1,3-dimethoxybenzene

Conformational assignments in molecular beam experiments are often based on relative energies, although there are many other relevant parameters, such as conformer-dependent oscillator strengths, Franck-Condon factors, quantum yields and vibronic couplings. In the present contribution, we investigate the conformational landscape of 1,3-dimethoxybenzene using a combination of rotationally resolved electronic spectroscopy and high level ab initio calculations. The electronic origin of one of the three possible planar rotamers (rotamer (0,180) with both substituents pointing at each other) has not been found. Based on the calculated potential energy surface of 1,3-dimethoxybenzene in the electronic ground and lowest excited state, we show that this can be explained by a distorted non-planar geometry of rotamer (0,180) in the S₁ state.

Electronic spectra of 2- and 3-tolunitrile in the gas phase. II. Geometry changes from Franck-Condon fits of fluorescence emission spectra

We determined the changes of the geometries of 2- and 3-tolunitrile upon excitation to the lowest excited singlet states from Franck-Condon fits of the vibronic intensities in several fluorescence emission spectra and of the rotational constant changes upon excitation. These structural changes can be connected to the altered electron distribution in the molecules and are compared to the results of ab initio calculations. We show how the torsional barriers of the methyl groups in both components are used as probe of the molecular changes upon electronic excitation.

Far-infrared spectra of the tryptamine A conformer by IR-UV ion gain spectroscopy

Single-far-infrared photon excited tryptamine has structured resonance enhanced multi-photon ionization UV spectra, revealing the mode composition of the S₁-state. Upon multiple-far-infrared photon absorption, the UV spectrum broadens allowing ion gain spectroscopy to be performed.

Decomposition of diazomeldrum's acid: a threshold photoelectron spectroscopy study

Derivatives of meldrum's acid are known precursors for a number of reactive intermediates. Therefore, we investigate diazomeldrum's acid (DMA) and its pyrolysis products by photoionization using vacuum ultraviolet (VUV) synchrotron radiation. The threshold photoelectron spectrum of DMA yields an ionization energy (IE) of 9.68 eV. Several channels for dissociative photoionization are observed. The first one is associated with loss of CH3, leading to a daughter ion with m/z = 155. Its appearance energy AE0K was determined to be 10.65 eV by fitting the experimental data using statistical theory. A second parallel channel leads to m/z = 69, corresponding to N2CHCO, with an AE0K of 10.72 eV. Several other channels open up at higher energy, among them the formation of acetone cation, a channel expected to be the result of a Wolff-rearrangement (WR) in the cation. When diazomeldrum's acid is heated in a pyrolysis reactor, three thermal decomposition pathways are observed. The major one is well-known and yields acetone, N2 and CO as consequence of the WR. However, two further channels were identified: The formation of 2-diazoethenone, NNCCO, together with acetone and CO2 as the second channel and E-formylketene (OCCHCHCO), propyne, N2 and O2 as a third one. 2-Diazoethenone and E-formylketene were identified based on their threshold photoelectron spectra and accurate ionization energies could be determined. Ionization energies for several isomers of both molecules were also computed. One of the key findings of this study is that acetone is observed upon decomposition of DMA in the neutral as well as in the ion and both point to a Wolff rearrangement to occur. However, the ion is subject to other decomposition channels favored at lower internal energies.

Photoionization and pyrolysis of a 1,4-azaborinine: retro-hydroboration in the cation and identification of novel organoboron ring systems

The photoionization and dissociative photoionization of 1,4-di-tert-butyl-1,4-azaborinine by means of synchrotron radiation and threshold photoelectron photoion coincidence spectroscopy is reported. The ionization energy of the compound was determined to be 7.89 eV. Several low-lying electronically excited states in the cation were identified. The various pathways for dissociative photoionization were modeled by statistical theory, and appearance energies AE0K were obtained. The loss of isobutene in a retro-hydroboration reaction is the dominant pathway, which proceeds with a reverse barrier. Pyrolysis of the parent compound in a chemical reactor leads to the generation of several yet unobserved boron compounds. The ionization energies of the C4 H6 BN isomers 1,2- and 1,4-dihydro-1,4-azaborinine and the C3 H6 BN isomer 1,2-dihydro-1,3-azaborole were determined from threshold photoelectron spectra.

Full-dimensional potentials and state couplings and multidimensional tunneling calculations for the photodissociation of phenol

Full-dimensional potentials and state couplings were developed for the photodissociation of phenol. We also present multidimensional tunneling calculations at the transition state on the shoulder of the first conical intersection.

Photoionisation of the tropyl radical

We present a study on the photoionisation of the cycloheptatrienyl (tropyl) radical, C₇H₇, using tunable vacuum ultraviolet synchrotron radiation. Tropyl is generated by flash pyrolysis from bitropyl. Ions and electrons are detected in coincidence, permitting us to record mass-selected photoelectron spectra. The threshold photoelectron spectrum of tropyl, corresponding to the X^{+ 1}A₁’ ← X²E₂” transition, reveals an ionisation energy of 6.23 ± 0.02 eV, in good agreement with Rydberg extrapolations, but slightly lower than the value derived from earlier photoelectron spectra. Several vibrations can be resolved and are reassigned to the C–C stretch mode ν₁₆⁺ and to a combination of ν₁₆⁺ with the ring breathing mode ν₂⁺. Above 10.55 eV dissociative photoionisation of tropyl is observed, leading to the formation of C₅H₅⁺ and C₂H₂.

Determination of the Geometry Change of the Phenol Dimer upon Electronic Excitation

The change of the phenol dimer (PH2) structure upon electronic excitation is determined by a Franck-Condon analysis of the intensities in the fluorescence emission spectra obtained via excitation of seven different vibronic bands. A total of 547 emission band intensities are fitted, together with the changes of rotational constants upon electronic excitation of fi ve isotopomers. These rotational constants are taken from previously published [Schmitt et al. ChemPhysChem 2006, 7, 1241-1249] high-resolution LIF measurements. The geometry change upon electronic excitation of the pipi* state of the donor moiety can be described by a strong shortening of the hydrogen bond, a shortening of the CO bond in the donor moiety, an overall symmetric expansion of the donor phenol ring, and a nearly unchanged acceptor moiety. The resulting geometry changes are interpreted on the basis of ab initio calculations.

Improved Determination of Structural Changes of 2-Pyridone-(H2O)1 upon Electronic Excitation

The change of the 2-pyridone-water cluster (2PYH(2)O) structure upon electronic excitation is determined by a Franck-Condon analysis of the intensities in the fluorescence emission spectra obtained via excitation of three different vibronic bands as well as a structural fit based on the rotational constants of eight isotopomers that have been reported by Held and Pratt (J. Am. Chem. Soc., 1993, 115, 9708]. A total of 93 emission band intensities were fit, together with the changes of rotational constants of 8 isotopomers. The geometry change upon electronic excitation to the pipi* state can be described by a strong and unsymmetrical elongation of the hydrogen bonds, a contraction of the OH bond involved in the cyclic cluster arrangement, and an unsymmetrical ring deformation. The resulting geometry changes are interpreted on the basis of ab initio calculations.

Automated parameter optimization in modeling absorption spectra and resonance Raman excitation profiles

An automated method is described for optimizing the molecular parameters in simultaneous modeling of optical absorption spectra and resonance Raman excitation profiles. The method utilizes a previously developed Fortran routine that calculates absorption spectra and Raman excitation profiles for polyatomic molecules in solution from a model for the potential energy surfaces and spectral broadening mechanisms. It is combined here with an optimization routine from the commercial MATLAB package that iteratively adjusts the parameters of the molecular model to minimize the least-squared error between calculated and experimental spectra. Optimizations that typically require days to weeks of human time when performed interactively can be accomplished automatically in less than an hour of computer time. The method can handle large molecules (we show results for as many as 23 Raman-active modes) and mixtures of spectral broadening mechanisms (lifetime, Brownian oscillator, and inhomogeneous), and is robust toward noise or missing data points.

Investigation of the UV/Visible Absorption Spectra of Merocyanine Dyes Using Time-Dependent Density Functional Theory

The visible spectral properties of a set of merocyanine dyes have been determined experimentally and compared to theoretical estimates calculated using time-dependent density functional theory. Three families of merocyanines have been investigated. The merocyanines of the first class contain the 4-thiazolidinone, 2-thioxo group in resonance with different donor groups. In the second family, they present a common pyrrolo[2,3-c]pyrazole-6-(2H)-acetic acid, the 4-[4-(dialkylamino)phenyl]-3,5-dihydro-3,5-dioxo-2-phenyl group with different substituents on the two phenyl rings, while in the third family, they are constituted of an isoxazolone group linked via a conjugated polyenic segment to an aminophenyl group. Two hybrid exchange-correlation functionals have been used, whereas solvent effects have been included using the integral equation formalism of the polarizable continuum model. Moreover, for one compound, the vibrational structure of the electronic transitions has been determined by calculating the Franck-Condon factors within the Born-Oppenheimer approximation. The calculations show that the dominant transitions present a pi-pi(*) character. This approach reproduces nicely the variations of excitation energies with the nature of the merocyanine so that least-squares fits can be used to correct for the major systematic errors of the computational scheme and to reach an accuracy of 0.09 eV or better. Part of these systematic errors is shown to originate from the description of the solvent effects, whereas vibronic effects can account for most of the remaining differences.

Excited-State Ab Initio Calculations and Multidimensional Franck−Condon Simulations on Guanine

The guanine enol and keto N7H and N9H tautomers have been optimized at the CASSCF/cc-pVDZ levels of theory. Except for the enol N7H tautomer, CASSCF predicts distorted nonplanar S1 state geometries. Among the vibronic simulations carried out with the optimized structures only the enol N7H tautomer qualitatively mirrors the appearance of the experimental R2PI spectrum. Refined symmetry-adapted cluster configuration interaction (SACCI) geometries of the enol N7H tautomer produce simulations in good agreement with experiment and support the assignment of the first vibronic band and associated vibronic features of the R2PI spectrum to this tautomer. The sharp spectral features and the fact that Franck-Condon simulations based on the harmonic approximation allow for a faithful reproduction of the spectral signature associated with the enol N7H tautomer indicate that within the simulated energy window the S1 potential energy surface of this isomer is fairly harmonic and free from conical intersections involved in the S1 state lifetime-shortening relaxation processes of other DNA bases and possibly the remaining tautomers of guanine.

High resolution photofragment translational spectroscopy studies of the near ultraviolet photolysis of phenol

The fragmentation dynamics of gas phase phenol molecules following excitation at many wavelengths in the range 279.145 > or = lambdaphot > or = 206.00 nm have been investigated by H Rydberg atom photofragment translational spectroscopy. Many of the total kinetic energy release (TKER) spectra so derived show structure, the analysis of which confirms the importance of O-H bond fission and reveals that the resulting phenoxyl cofragments are formed in a very limited subset of their available vibrational state density. Spectra recorded at lambdaphot > or = 248 nm show a feature centered at TKER approximately 6500 cm(-1). These H atom fragments, which show no recoil anisotropy, are rationalized in terms of initial S1<--S0 (pi*<--pi) excitation, and subsequent dissociation via two successive radiationless transitions: internal conversion to ground (S0) state levels carrying sufficient O-H stretch vibrational energy to allow efficient transfer towards, and passage around, the conical intersection (CI) between the S0 and S2(1pisigma*) potential energy surfaces (PESs) at larger R(O-H), en route to ground state phenoxyl products. The observed phenoxyl product vibrations indicate that parent modes nu16a and nu11 can both promote nonadiabatic coupling in the vicinity of the S0S2 CI. Spectra recorded at lambdaphot < or = 248 nm reveal a faster, anisotropic distribution of recoiling H atoms, centered at TKER approximately 12,000 cm(-1). These we attribute to H+phenoxyl products formed by direct coupling between the optically excited S1(1pi pi*) and repulsive S2(1pi sigma*) PESs. Parent mode nu16b is identified as the dominant coupling mode at the S1/S2 CI, and the resulting phenoxyl radical cofragments display a long progression in nu18b, the C-O in-plane wagging mode. Analysis of all structured TKER spectra yields D0(H-OC6H5) = 30,015 +/- 40 cm(-1). The present findings serve to emphasize two points of wider relevance in contemporary organic photochemistry: (i) The importance of 1) pi sigma* states in the fragmentation of gas phase heteroaromatic hydride molecules, even in cases where the 1pi sigma* state is optically dark. (ii) The probability of observing strikingly mode-specific product formation, even in "indirect" predissociations, if the fragmentation is driven by ultrafast nonadiabatic couplings via CIs between excited (and ground) state PESs.