Photophysical Outcomes of Water-Solvated Heterocycles: Single-Conformation Ultraviolet and Infrared Spectroscopy of Microsolvated 2-Phenylpyrrole.

The molecular chromophores within brown carbon (BrC) aerosols absorb solar radiation at visible and near-ultraviolet wavelengths. This contributes to the overall warming of the troposphere and the photochemical aging of aerosols. In this investigation, we combine a suite of experimental and theoretical methods to reveal the conformation-specific ultraviolet and infrared spectroscopy of 2-phenylpyrrole (2PhPy)─an extended π-conjugated pyrrole derivative and a model BrC chromophore─along with its water microsolvated molecular complexes (2PhPy:nH2O, n = 1-3). Using resonant two-photon ionization and double-resonance holeburning techniques alongside MP3 (ground state) and ADC(3) (excited state) torsional potential energy surfaces and discrete variable representation simulations, we characterized the ultraviolet spectra of 2PhPy and 2PhPy:1H2O. This analysis revealed evidence for Herzberg-Teller vibronic coupling along the CH wagging and NH stretching coordinates of the aromatic rings. Conformation-specific infrared spectroscopy revealed extended hydrogen-bonding networks of the 2PhPy:nH2O complexes. Upon stepwise addition of H2O solvation, the nearest H2O acceptor forms a strong, noncovalent interaction with the pyrrole NH donor, while the second and third H2O partners interface with the phenyl and pyrrole aromatic rings through growing van der Waals π/H atom stabilization. A local-mode Hamiltonian approach was employed for comparison with the experimental spectra, thus identifying the vibrational spectral signatures to specific 2PhPy:nH2O oscillators.

Theoretical Study of the Photochemical Mechanisms of the Electronic Quenching of NO(A2Σ+) with CH4, CH3OH, and CO2.

The electronic quenching of NO(A2Σ+) with molecular partners occurs through complex non-adiabatic dynamics that occurs on multiple coupled potential energy surfaces. Moreover, the propensity for NO(A2Σ+) electronic quenching depends heavily on the strength and nature of the intermolecular interactions between NO(A2Σ+) and the molecular partner. In this paper, we explore the electronic quenching mechanisms of three systems: NO(A2Σ+) + CH4, NO(A2Σ+) + CH3OH, and NO(A2Σ+) + CO2. Using EOM-EA-CCSD calculations, we rationalize the very low electronic quenching cross-section of NO(A2Σ+) + CH4 as well as the outcomes observed in previous NO + CH4 photodissociation studies. Our analysis of NO(A2Σ+) + CH3OH suggests that it will undergo facile electronic quenching mediated by reducing the intermolecular distance and significantly stretching the O-H bond of CH3OH. For NO(A2Σ+) + CO2, intermolecular attractions lead to a series of low-energy ON-OCO conformations in which the CO2 is significantly bent. For both the NO(A2Σ+) + CH3OH and NO(A2Σ+) + CO2 systems, we see evidence of the harpoon mechanism and low-energy conical intersections between NO(A2Σ+) + M and NO(X2Π) + M. Overall, this work provides the first detailed theoretical study on the NO(A2Σ+) + M potential energy surface of each of these systems and will inform future velocity map imaging experiments.

Reactive quenching of NO (A2Σ+) with H2O leads to HONO: a theoretical analysis of the reactive and nonreactive electronic quenching mechanisms.

The electronic quenching of NO (A2Σ+) with molecular partners exemplifies the rich non-adiabatic dynamics that occurs on multiple, coupled potential energy surfaces (PESs). The mechanistic details of the electronic quenching depend sensitively on the nature and strength of the intermolecular interactions between NO (A2Σ+) and the molecular partner. In this paper, we reveal the electronic quenching mechanisms of NO (A2Σ+) with H2O, a non-adiabatic process with an extremely large cross section of 121 Å2 near room temperature. In doing so, we demonstrate that the NO (A2Σ+) + H2O PES funnels a wide range of initial intermolecular orientations to the same minimum-energy geometry. Furthermore, we reveal low-energy pathways to conical intersections between NO (A2Σ+) + H2O and NO (X2Π) + H2O that primarily involve decreasing the intermolecular distance and elongating a single O-H bond of H2O. Based on these geometric distortions, we predict that nonreactive electronic quenching will be associated with significant vibrational excitation in a local O-H stretch mode in H2O. Reactive quenching will produce a H-atom and HONO, an important intermediate in atmospheric and combustion chemistry and a precursor to the hydroxyl radical. Overall, our work provides the first detailed theoretical study of the mechanism of the electronic quenching of NO (A2Σ+) with a polyatomic molecular partner, as well as makes concrete predictions to inform future velocity map imaging experiments.

Computationally Probing the Mechanism of the Blue-Light-Driven O-H Functionalization of Alcohols by Aryldiazoacetates: Photobasicity or Carbene Chemistry.

Photochemistry provides green alternatives to traditional reaction conditions and opens up routes toward products that are otherwise difficult to make. Recent work by Koenigs and co-workers demonstrated the blue-light-driven O-H functionalization of alcohols by aryldiazoacetates. Based on spectroscopic and computational analyses, Koenigs and co-workers demonstrated that the alcohols form a hydrogen-bonding complex with aryldiazoacetates prior to the light absorption, with the strength of hydrogen bonding correlated with the product yield. Because methyl phenyldiazoacetate (MPDA) was observed to preferentially react with alcohols over cyclopropanation with styrene, the reaction was speculated to occur via excited-state proton transfer, with MPDA acting as a photobase. In this paper, we use time-dependent density functional theory to show that the electronic excited state of aryldiazoacetates is inconsistent with photobasicity. Instead, we argue that the reaction proceeds via a carbene intermediate generated through the photolysis of the aryldiazoacetate. Using density functional theory, we demonstrate that the reaction between the singlet state of the carbene intermediate and the alcohol is thermodynamically favorable and very fast. Moreover, we provide a rationalization for the experimentally observed preference for O-H functionalization with alcohols over cyclopropanation with alkenes. Overall, this work provides a refined mechanistic understanding of an interesting photochemical transformation.

Stereodynamic Control of Collision-Induced Nonadiabatic Dynamics of NO (A2Σ+) with H2, N2, and CO: Intermolecular Interactions Drive Collision Outcomes.

Intermolecular interactions, stereodynamics, and coupled potential energy surfaces (PESs) all play a significant role in determining the outcomes of molecular collisions. A detailed knowledge of such processes is often essential for a proper interpretation of spectroscopic observations. For example, nitric oxide (NO), an important radical in combustion and atmospheric chemistry, is commonly quantified using laser-induced fluorescence on the A2Σ+ ← X2Π transition band. However, the electronic quenching of NO (A2Σ+) with other molecular species provides alternative nonradiative pathways that compete with fluorescence. While the cross sections and rate constants of NO (A2Σ+) electronic quenching have been experimentally measured for a number of important molecular collision partners, the underlying photochemical mechanisms responsible for the electronic quenching are not well understood. In this paper, we describe the development of high-quality PESs that provide new physical insights into the intermolecular interactions and conical intersections that facilitate the branching between the electronic quenching and scattering of NO (A2Σ+) with H2, N2, and CO. The PESs are calculated at the EOM-EA-CCSD/d-aug-cc-pVTZ//EOM-EA-CCSD/aug-cc-pVDZ level of theory, an approach that ensures a balanced treatment of the valence and Rydberg electronic states and an accurate description of the open-shell character of NO. Our PESs show that H2 is incapable of electronically quenching NO (A2Σ+) at low collision energies; instead, the two molecules will likely undergo scattering. The PESs of NO (A2Σ+) with N2 and CO are highly anisotropic and demonstrate evidence of electron transfer from NO (A2Σ+) into the lowest unoccupied molecular orbital of the collision partner, that is, the harpoon mechanism. In the case of ON + CO, the PES becomes strongly attractive at longer intermolecular distances and funnels population to a conical intersection between NO (A2Σ+) + CO and NO (X2Π) + CO. In contrast, for ON + N2, the conical intersection is preceded by an ∼0.40 eV barrier. Overall, our work shines new light into the impact of coupled PESs on the nonadiabatic dynamics of open-shell systems.

Computational Investigation of the Formation of Substituted Isoindole N-Oxides through the Photo-oxidative Cyclization of 2'-Alkynylacetophenone Oximes.

Our recently published joint experiment-theory study of the photo-oxidative intramolecular cyclization of 2'-alkynylacetophenone oximes, performed in collaboration with the de Lijser group, presented the first reported formation of isoindole N-oxides. That study focused on determining a mechanistic explanation for the unexpected chemistry observed when three 2'-alkynylacetophenone oximes were photo-oxidized with 9,10-dicyanoanthracene (DCA), specifically the derivatives with a phenyl, isopropyl, or n-butyl substituent at the alkynyl group. Here, we use density functional theory to develop a broader understanding of the scope of this chemistry. In particular, we demonstrate that substituents on the alkynyl group and on the central benzene ring can significantly modulate the thermodynamic driving force for oxime radical cation generation when DCA is used as the photosensitizer. In contrast, substituents are shown to have a small impact on the chemical reactivity of the radical cation intermediates. In particular, 5-exo radical cation cyclization, which ultimately results in an isoindole N-oxide product, is always kinetically and sometimes also thermodynamically preferred over 6-endo radical cation cyclization, which would produce an isoquinoline N-oxide product. Overall, this study provides mechanistic insights into the diversity of isoindole N-oxides that can be produced through the photo-oxidative cyclization of 2'-alkynylacetophenone oximes.

Chiroptical characterization tools for asymmetric small molecules - experimental and computational approaches for electronic circular dichroism (ECD) and anisotropy spectroscopy.

Synchrotron radiation electronic circular dichroism (SRECD) and anisotropy spectroscopy for both enantiomers of a group of small non-planar chiral molecules are reported here. The experimental SRECD spectra are compared to computational ECD spectra generated using time-dependent density functional theory and a thermal averaging over relevant molecular configurations. The combination of these experimental and computational characterization methodologies for such molecules enables the prediction and understanding of the spectral behavior of other small molecules, in addition to chiroptically characterizing members of the mandelic acid family substructure. Enantiomeric purity of samples can be evaluated in comparison with these spectra and the extent of photolytic enantioinduction can also be predicted using these experimental/calculated SRECD and anisotropy spectra.

Structure-Photochemical Function Relationships in the Photobasicity of Aromatic Heterocycles Containing Multiple Ring Nitrogen Atoms.

Photobases are compounds that become more basic when promoted to an excited electronic state. Previous experimental and computational studies have demonstrated that several quinoline and quinoline-derived compounds are strong photobases (pKa* > 14). Moreover, the strength of photobasicity was shown to depend strongly on the identity and position of the substituent group(s), with the strongest photobases having multiple electron-donating substituents on a fused benzene ring as opposed to the ring containing the photobasic nitrogen atom. These electron-donating substituents build up electron density on one side of the molecule that shifts onto the nitrogen-containing ring in the electronic transition. This shift in electron density produces an increase in negative charge on the ring nitrogen atom responsible for the photobasicity. In this paper, we expand on our previous investigation to study the effect of an additional ring nitrogen atom on photobasicity in aromatic heterocycles. In particular, we consider how the thermodynamic driving force for excited-state protonation can be tuned by changing the relative placement of the ring nitrogen atoms and varying the position and number of electron-donating substituents. In the set of 112 molecules screened, we identified 42 strong photobases with generally comparable pKa* but lower vertical excitation energies than the quinoline derivatives with only a single ring nitrogen atom. We additionally explored photobasicity in substituted azaindole and carboline derivatives, identifying 76 strongly photobasic compounds with pKa* as large as 22.6 out of the 155 compounds that we considered. Overall, this work provides new insights into the design principles necessary to develop next-generation photocatalysts that employ photobasicity.

Mechanistic Investigation of the Formation of Isoindole N-Oxides in the Electron Transfer-Mediated Oxidative Cyclization of 2'-Alkynylacetophenone Oximes.

This paper describes a joint experiment-theory investigation of the formation and cyclization of 2'-alkynylacetophenone oxime radical cations using photoinduced electron transfer (PET) with DCA as the photosensitizer. Using a combination of experimental 1H and 13C nuclear magnetic resonance (NMR) spectra, high-resolution mass spectrometry, and calculated NMR chemical shifts, we identified the products to be isoindole N-oxides. The reaction was found to be stereoselective; only one of the two possible stereoisomers is formed under these conditions. A detailed computational investigation of the cyclization reaction mechanism suggests facile C-N bond formation in the radical cation leading to a 5-exo intermediate. Back-electron transfer from the DCA radical anion followed by barrierless intramolecular proton transfer leads to the final product. We argue that the final proton transfer step in the mechanism is responsible for the stereoselectivity observed in experiment. As a whole, this work provides new insights into the formation of complex heterocycles through oxime and oxime ether radical cation intermediates produced via PET. Moreover, it represents the first reported formation of isoindole N-oxides.

Dynamical signatures from competing, nonadiabatic fragmentation pathways of S-nitrosothiophenol.

S-Nitrosothiols (RSNOs) are derived from the combination of sulfur and nitric oxide (NO) radicals in the Earth's atmosphere and fragment to products following photolysis. Extensive theoretical studies have focused on the thermodynamic and, to a lesser extent, photochemical properties of RSNOs. However, experimental studies of these compounds have been limited due to the inherent instability of RSNOs at room temperature. Using velocity map imaging (VMI), we explore the photodissociation dynamics of jet-cooled S-nitrosothiophenol (PhSNO) from 355 nm photolysis. We report the translational and internal energy distributions of the NO and thiophenoxy (PhS) co-fragments, which are determined by spatial detection of the ionized NO photofragments using 1+1 resonance-enhanced multiphoton ionization (REMPI). The velocity distributions indicate competing PhSNO nonadiabatic dissociation pathways, in which PhS is formed in the ground and first excited electronic states when probing high- and low-energy NO (X2Π1/2, v'', J'') rovibrational states, respectively. The results of multireference electronic structure calculations suggest that direct dissociation on the bright S2 state results in PhS formed in its excited electronic state, whereas intersystem crossing into the triplet manifold leads to population of PhS in its electronic ground state. The dynamical signatures from the dissociation processes are imprinted on the fragments' quantum states and relative translation, which we explore in rigorous detail using state-resolved imaging and high-level theoretical calculations.

Structure-Photochemical Function Relationships in Nitrogen-Containing Heterocyclic Aromatic Photobases Derived from Quinoline.

Photobases are compounds that become strong bases after electronic excitation. Recent experimental studies have highlighted the photobasicity of the 5-R quinoline compounds, demonstrating a strong substituent dependence to the pKa*. In this paper, we describe our systematic study of how the thermodynamic driving force for photobasicity is tuned through substituents in four families of nitrogen-containing heterocyclic aromatics. We show that substituent position and identity both significantly impact the pKa*. We demonstrate that the substituent effects are additive and identify many disubstituted compounds with substantially greater photobasicity than the most photobasic 5-R quinoline compound identified previously. We show that the addition of a second fused benzene ring to quinoline, along with two electron-donating substituents, lowers the S0 → SPBS vertical excitation energy into the visible region while still maintaining a pKa* > 14. Overall, the structure-function relationships developed in this study provide new insights to guide the development of new photocatalysts that employ photobasicity.

Computational Investigation of Substituent Effects on the Formation and Intramolecular Cyclization of 2'-Arylbenzaldehyde and 2'-Arylacetophenone Oxime Ether Radical Cations.

This work describes our computational study of substituent effects on the formation and cyclization of 2'-arylbenzaldehyde and 2'-arylacetophenone oxime ether radical cations. Recent experimental work by de Lijser and co-workers has demonstrated that these reactive intermediates, which are generated through photoinduced electron transfer (PET) with a photosensitizer, undergo intramolecular cyclization to yield substituted phenanthridines. The experimental study further showed correlations between the yield of cyclized products and the Hammett σPara+ parameter of the substituent on the aryl group, with both strongly electron-withdrawing and electron-donating substituents shown to significantly reduce the product yield. By analyzing the ΔGPET associated with radical cation formation as well as the thermodynamics and kinetics of radical cation cyclization, we provide an explanation for these observations. We then computationally extend this mechanistic analysis to 2'-arylbenzaldehyde oxime ethers with substituents also present on the central benzene ring and show that such substituents generally have a larger impact on the PET-induced cyclization than those on the aryl group. Overall, this work extends our understanding of the overall scope of this photooxidative route toward substituted phenanthridines as well as makes clear predictions as to how the formation of oxime ether radical cations can be tuned by substituents.

Nonstatistical Dissociation Dynamics of Nitroaromatic Chromophores.

Organic carbon in the atmosphere is emitted from biogenic and anthropogenic sources and plays a key role in atmospheric chemistry, air quality, and climate. Recent studies have identified several of the major nitroaromatic chromophores embedded in organic "brown carbon" (BrC) aerosols. Indeed, nitroaromatic chromophores are responsible for the enhanced solar absorption of BrC aerosols, extending into the near UV (300-400 nm) and visible regions. Furthermore, BrC chromophores serve as temporary reservoirs of important oxidizing intermediates including hydroxyl (OH) and nitric oxide (NO) radicals that are released upon electronic excitation. The present work represents the first study of the 355 nm photolysis of known BrC chromophores ortho-nitrophenol and 2-nitroresorcinol, as well as the prototypical nitroaromatic, nitrobenzene. Experiments are carried out in a pulsed supersonic jet expansion with velocity map imaging of NO X2Π (ν″ = 0, J″) fragments to report on the photodissociation dynamics. The total kinetic energy release (TKER) distributions and the NO X2Π (ν″ = 0, J″) product state distributions deviate significantly from Prior simulations, indicating that energy is partitioned nonstatistically following dissociation. Experiments are conducted in tandem with complementary calculations using multireference Møller-Plesset second-order perturbation theory (MRMPT2) for stationary points obtained by using multiconfiguration self-consistent field (MCSCF) with an aug-cc-pVDZ basis on the ground and lowest energy triplet electronic states. Furthermore, insights into the partitioning of energy upon photodissociation are achieved by using relaxed scans at the MCSCF/aug-cc-pVDZ level of theory. As a whole, the results suggest that upon excitation to S1, all three nitroaromatics share a common overall mechanism for NO production involving isomerization of the nitro group, nonradiative relaxation to S0, and dissociation to form rotationally hot NO.

Simple and Efficient Theoretical Approach To Compute 2D Optical Spectra.

A highly efficient scheme is proposed and benchmarked to compute 2D optical spectra. This scheme is ideally designed for electronic spectroscopy; however, the method can be applied in a straightforward way to vibrational spectroscopy as well. Our scheme performs dynamics only for the t2 duration, eliminating explicit t1 and t3 coherent dynamics and thus can achieve dramatic improvements in efficiency. To gain this efficiency, we assume the system is in the inhomogeneous regime and that there is no significant nonadiabatic transfer of population during the t1 and t3 coherence times. Preliminary results are presented for the Frenkel Hamiltonian. We obtain excellent agreement with numerically exact results (which are possible for this simplistic model Hamiltonian), capturing all relevant trends at least qualitatively (and sometimes quantitatively).

Appraisal of Surface Hopping as a Tool for Modeling Condensed Phase Linear Absorption Spectra.

Whereas surface hopping is usually used to study populations and mean-field dynamics to study coherences, in two recent papers, we described a procedure for calculating dipole-dipole correlation functions (and therefore absorption spectra) directly from ensembles of surface hopping trajectories. We previously applied this method to a handful of one-dimensional model problems intended to mimic the gas phase. In this article, we now benchmark this new procedure on a set of multidimensional model problems intended to mimic the condensed phase and compare our results against other standard semiclassical methods. By comparison, we demonstrate that methods that include only dynamical information from one PES (the standard Kubo approaches) exhibit large discrepancies with the results of exact quantum dynamics. Furthermore, for model problems with nonadiabatic excited state dynamics but no quantized vibrational structure in the spectra, our surface hopping approach performs comparably to using Ehrenfest dynamics to calculate the electronic coherences. That being said, however, when quantized vibrational structures are present in the spectra but the electronic states are uncoupled, performing the dynamics on the mean PES still outperforms our present method. These benchmark results should influence future studies that use ensembles of independent semiclassical trajectories to model linear as well as multidimensional spectra in the condensed phase.

Calculating time-resolved differential absorbance spectra for ultrafast pump-probe experiments with surface hopping trajectories.

We report a surface hopping approach for modeling the full time- and frequency-resolved differential absorbance spectra (beyond the inhomogenous limit) obtained in ultrafast pump-probe experiments. In our approach, we combine dynamical information obtained from ensembles of classical trajectories propagated on the ground and on the excited potential energy surfaces to directly calculate optical response functions and hence spectral lineshapes. We demonstrate that our method is exact for the model problem of two shifted harmonic potentials with identical harmonic frequencies in the absence of electronic relaxation. We then consider a model three state system with electronic relaxation and show that our method is able to capture the effects of nonadiabatic excited state dynamics on the time-dependent differential absorbance spectra. Furthermore, by comparing our spectra against those spectra calculated with either an (1) inhomogenous expression, (2) ground-state Kubo theory, or (3) excited-state Kubo theory, we show that including dynamical information from both the ground and excited potential energy surfaces significantly improves the reliability of the semiclassical approximations. As such, our surface hopping method should find immediate use in modeling the time-dependent differential abosrbance spectra of ultrafast pump-probe experiments.

Infrared-driven unimolecular reaction of CH3CHOO Criegee intermediates to OH radical products.

Ozonolysis of alkenes, an important nonphotolytic source of hydroxyl (OH) radicals in the troposphere, proceeds through energized Criegee intermediates that undergo unimolecular decay to produce OH radicals. Here, we used infrared (IR) activation of cold CH3CHOO Criegee intermediates to drive hydrogen transfer from the methyl group to the terminal oxygen, followed by dissociation to OH radicals. State-selective excitation of CH3CHOO in the CH stretch overtone region combined with sensitive OH detection revealed the IR spectrum of CH3CHOO, effective barrier height for the critical hydrogen transfer step, and rapid decay dynamics to OH products. Complementary theory provides insights on the IR overtone spectrum, as well as vibrational excitations, structural changes, and energy required to move from the minimum-energy configuration of CH3CHOO to the transition state for the hydrogen transfer reaction.

How to calculate linear absorption spectra with lifetime broadening using fewest switches surface hopping trajectories: a simple generalization of ground-state Kubo theory.

In this paper, we develop a surface hopping approach for calculating linear absorption spectra using ensembles of classical trajectories propagated on both the ground and excited potential energy surfaces. We demonstrate that our method allows the dipole-dipole correlation function to be determined exactly for the model problem of two shifted, uncoupled harmonic potentials with the same harmonic frequency. For systems where nonadiabatic dynamics and electronic relaxation are present, preliminary results show that our method produces spectra in better agreement with the results of exact quantum dynamics calculations than spectra obtained using the standard ground-state Kubo formalism. As such, our proposed surface hopping approach should find immediate use for modeling condensed phase spectra, especially for expensive calculations using ab initio potential energy surfaces.

Simultaneous evaluation of multiple rotationally excited states of H3(+), H3O(+), and CH5(+) using diffusion Monte Carlo.

An extension to diffusion Monte Carlo (DMC) is proposed for simultaneous evaluation of multiple rotationally excited states of fluxional molecules. The method employs an expansion of the rotational dependence of the wave function in terms of the eigenstates of the symmetric top Hamiltonian. Within this DMC approach, each walker has a separate rotational state vector for each rotational state of interest. The values of the coefficients in the expansion of the rotational state vector associated with each walker, as well as the locations of the walkers, evolve in imaginary time under the action of a propagator based on the imaginary-time time-dependent Schrödinger equation. The approach is first applied to H3(+), H2D(+), and H3O(+) for which the calculated energies can be compared to benchmark values. For low to moderate values of J the DMC results are found to be accurate to within the evaluated statistical uncertainty. The rotational dependence of the vibrational part of the wave function is also investigated, and significant rotation­vibration interaction is observed. Based on the successful application of this approach to H3(+), H2D(+), and H3O(+), the method was applied to calculations of the rotational energies and wave functions for CH5(+) with v = 0 and J ≤ 10. Based on these calculations, the rotational energy progression is shown to be consistent with that for a nearly spherical top molecule, and little evidence of rotation­vibration interaction is found in the vibrational wave function.

Diffusion Monte Carlo in internal coordinates.

An internal coordinate extension of diffusion Monte Carlo (DMC) is described as a first step toward a generalized reduced-dimensional DMC approach. The method places no constraints on the choice of internal coordinates other than the requirement that they all be independent. Using H(3)(+) and its isotopologues as model systems, the methodology is shown to be capable of successfully describing the ground state properties of molecules that undergo large amplitude, zero-point vibrational motions. Combining the approach developed here with the fixed-node approximation allows vibrationally excited states to be treated. Analysis of the ground state probability distribution is shown to provide important insights into the set of internal coordinates that are less strongly coupled and therefore more suitable for use as the nodal coordinates for the fixed-node DMC calculations. In particular, the curvilinear normal mode coordinates are found to provide reasonable nodal surfaces for the fundamentals of H(2)D(+) and D(2)H(+) despite both molecules being highly fluxional.