The Role of Electrical Anharmonicity in the Association Band in the Water Spectrum

The origin of the intensity of the feature in the spectrum of liquid water near 2100 cm^–1 is investigated through calculations of the spectra of water clusters based on low-order expansions of the potential and dipole surfaces in internal and normal mode coordinates. The intensity near 2100 cm^–1 is attributed to combination bands involving the HOH bend and intermolecular vibrations that break the hydrogen bonding network. Further, the leading contribution to the intensity reflects large second derivatives of the dipole moment with respect to the internal coordinates that are excited, or electrical anharmonicity. This picture changes if the derivatives of the potential and dipole surfaces are taken with respect to normal modes. In the normal mode representation, the second derivatives of the dipole moment are often vanishingly small, while the mixed third and fourth derivatives of the potential become quite large. On the basis of this result, mechanical anharmonicity appears to be responsible for the intensity in the 2100 cm^–1 region. This strong dependence of the interpretation of the origins of the intensity in the 2100 cm^–1 region of the water spectrum is investigated and discussed

Investigation of the Structure and Spectroscopy of H₅⁺ Using Diffusion Monte Carlo

The results of diffusion Monte Carlo (DMC) calculations of the ground and selected excited states of H₅⁺ and its deuterated analogues are presented. Comparisons are made between the results obtained from two recently reported potential surfaces. Both of these surfaces are based on CCSD­(T) electronic energies, but the fits display substantial differences in the energies of low-lying stationary points. Little sensitivity to these features is found in the DMC results, which yield zero-point energies based on the two surfaces that differ by between 20 and 30 cm^–1 for all twelve isotopologues of H₅⁺. Likewise, projections of the ground state probability amplitudes, evaluated for the two surfaces, are virtually identical. By using the ground state probability amplitudes, vibrationally averaged rotational constants and dipole moments were calculated. On the basis of these calculations, all isotopologues are shown to be near-prolate symmetric tops. Further, in cases where the ion had a nonzero dipole moment, the magnitude of the vibrationally averaged dipole moment was found to range from 0.33 to 1.15 D, which is comparable to the dipole moments of H₂D⁺ and HD₂⁺. Excited states with up to three quanta in the shared proton stretch and one quantum in the in-phase stretch of the outer H₂ groups were also investigated. Trends in the energies and the properties of these states are discussed

Probing the Relationship Between Large-Amplitude Motions in H₅⁺ and Proton Exchange Between H₃⁺ and H₂

Understanding the spectroscopy and dynamics of H₅⁺ is central in gaining insights into the H₃⁺ + H₂ → H₅⁺ → H₂ + H₃⁺ proton transfer reaction. This molecular ion exhibits large-amplitude vibrations, which allow for the transfer of a proton between H₃⁺ and H₂ even in its ground vibrational state. With vibrational excitation, the number of open channels for permutations of protons increase. In this work, the minimized energy path variant of diffusion Monte Carlo is used to investigate how the energetically accessible proton permutations evolve as H₅⁺ is dissociated into H₃⁺ + H₂. Two mechanisms for proton permutation are investigated. The first is the proton hop, which correlates to large-amplitude vibrations of the central proton in H₅⁺. The second is the exchange of a pair of hydrogen atoms between H₃⁺ and H₂. This mechanism requires several proton hops along with a 120° rotation of H₃⁺ within the H₅⁺ molecular ion. This analysis shows that while there is a narrow region of configuration space over which both isomerization processes are energetically accessible, full permutation of the five protons in H₅⁺ more likely occurs through a stepwise mechanism. Such full permutation of the protons becomes accessible when the shared proton stretch is excited to the <i>v</i>_pt = 2 or 3 excited state. The effects of deuteration and rotational excitation of the H₂ and H₃⁺ products are also investigated. Deuteration inhibits permutation of protons, while rotational excitation has only a small impact on these processes

Isotopic Effects on the Dynamics of the CH₃⁺ + H₂ → CH₅⁺ → CH₃⁺ + H₂ Reaction

Diffusion Monte Carlo is used to investigate the anharmonic zero-point energy corrected energies for the CH₃⁺ + H₂→ CH₅⁺ → CH₃⁺ + H₂ process as a function of the center of mass separation of the two fragments. In addition to the title reaction, all possible deuterated and several tritiated (CH₄T⁺ and CH₃T₂⁺) analogues of this reaction are investigated. As anticipated, the replacement of one or more of the hydrogen atoms with deuterium or tritium atoms lowers the zero-point energy of the system. Further, in the partially deuterated or tritiated isotopologues, the lowest energy configuration generally has the heavy atoms in the CH₃⁺ fragment. Analysis of the wave functions allows us to study how zero-point energy influences the approach geometries sampled during low-energy collisions between CH₃⁺ and H₂, and to gain insights into how the dynamics is affected by the substitution of heavier isotopes for one or more of the hydrogen atoms. Differences between quantum and classical descriptions of the title reaction are also discussed

Minimum Energy Path Diffusion Monte Carlo Approach for Investigating Anharmonic Quantum Effects: Applications to the CH₃⁺ + H₂ Reaction

A method for evaluating anharmonic corrections to energies along a minimum energy path is developed and described. The approach is based upon the Diffusion Monte Carlo theory as initially developed by Anderson. Diffusion Monte Carlo has been shown to be effective for evaluating the ground-state properties of highly anharmonic systems. By using Jacobi coordinates, the evaluation of anharmonic corrections to the energies along a minimum energy path are straightforward to implement using Diffusion Monte Carlo. In this work, the CH₃⁺ + H₂ → CH₅⁺ reaction and its singly deuterated analogues are investigated. In addition to exploring how the energetics of this reaction change upon partial deuteration, projections of the probability amplitude onto various internal coordinates are evaluated and used to provide a quantum mechanical description of how deuteration affects the orientation of the two fragments as they combine to form the CH₄D⁺ molecular ion

Virtual Issue Highlighting Articles That Describe New Methodologies Soon To Be Considered for Publication in <i>JPC</i>

Virtual Issue Highlighting Articles That Describe New Methodologies Soon To Be Considered for Publication in <i>JPC</i

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 H₃⁺ 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 H₂D⁺ and D₂H⁺ despite both molecules being highly fluxional

Rotation/Torsion Coupling in H₅⁺, D₅⁺, H₄D⁺, and HD₄⁺ Using Diffusion Monte Carlo

Two methods for studying the rotation/torsion coupling in H₅⁺ are described. The first involves a fixed-node treatment in which the nodal surfaces are obtained from a reduced dimensional calculation in which only the rotations of the outer H₂ groups are considered. In the second, the torsion and rotation dependence of the wave function is described in state space, and the other internal coordinates are described in configuration space. Such treatments are necessary for molecules, like H₅⁺, where there is a very low-energy barrier to internal rotation. The results of the two approaches are found to be in good agreement with previously reported energies for <i>J</i> = 0. The diffusion Monte Carlo treatment allows us to extend the calculations to low <i>J</i>, and results are reported for the three lowest energy torsion excited states with <i>J</i> ≤ 3. For the level of rotational and vibrational excitation investigated, only modest changes in the vibrational wave functions are found. The effects of deuteration are also investigated, focusing on D₅⁺ and the symmetric variants of H₄D⁺ and HD₄⁺

Dynamics of Small, Ultraviolet-Excited ICN^– Cluster Anions

The ultraviolet (UV) photodissociation of mass-selected ICN^–Ar_<i>n</i> and ICN^–(CO₂)_<i>n</i> clusters (<i>n</i> = 0–5) is studied using a secondary reflectron mass spectrometer. Relative photodissociation cross sections of bare ICN^– show the dominance of the I^– photoproduct from 270 to 355 nm, the entire wavelength range studied. UV excitation populates both the ²Σ⁺ state that produces I* + CN^– and the ²Π states that produce I^– + CN*. While the excited ²Π states directly produce I^–, excitation to the ²Σ⁺ state also produces some I^– product via nonadiabatic transitions to the ²Π_1/2 state, which produces I^– + CN. Partial solvation of the anion by Ar atoms or CO₂ molecules alters the UV-branching percentages between the various dissociation channels: I* + CN^– and I^– + CN or I^– + CN*. In addition, solvation by two or more Ar atoms or three or more CO₂ molecules results in recombination, reforming ICN^–. Examination of the potential surfaces and transition moments in combination with the results of quantum dynamics calculations performed on the relevant excited states assist in the analysis of the experimental results

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 <i>J</i> 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 rotation–vibration 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 <i>v</i> = 0 and <i>J</i> ≤ 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 rotation–vibration interaction is found in the vibrational wave function