Margaret Mandziuk

van der Waals vibrational states of atom–large molecule complexes by a 3D discrete variable representation method: Naphthalene⋅Ar

We present an accurate and efficient method for calculating highly excited 3D van der Waals (vdW) vibrational states of structurally nonrigid M⋅R complexes between an atom R and a large, arbitrarily shaped molecule M. Our method combines the atom–molecule Hamiltonian of Brocks and van Koeven, in which Cartesian components of the vector connecting R and the center of mass of M are used as internal coordinates, with the 3D discrete variable representation (DVR) of all three intermolecular large amplitude degrees of freedom. Our 3D DVR method is aimed at highly anisotropic M⋅R complexes, in which the size of the molecule is typically larger than the average atom–molecule distance. The symmetry of the complex (if any) is exploited by constructing symmetry adapted 3D DVRs which transform under the irreducible representations of the symmetry group, and bring the Hamiltonian matrix to a block diagonal form. The 3D DVR is particularly well suited for description of excited and strongly coupled, delocalized vdW states, and internal motions on very anharmonic intermolecular potentials with multiple minima. We use this method to calculate vdW vibrational energy levels and wave functions of a floppy complex naphthalene⋅Ar. The lower‐lying vdW states are assigned by inspection of the wave function plots.

RESONANCE IN THE DYNAMICS OF CHEMICAL SYSTEMS SIMULATED BY THE IMPLICIT MIDPOINT SCHEME

Abstract The numerical behavior of the symplectic, implicit midpoint method with a wide range of integration timesteps is examined through an application to a diatomic molecule governed by a Morse potential. Our oscillator with a 12.6 fs period exhibits notable, integrator induced, timestep- ( Δt ) dependent resonances and we predict approximate values of Δt where they will occur. The particular case of a third-order resonance ( Δt ≈ 7 fs here) leads to instability, and higher-order resonances ( n = 4, 5) to large energetic fluctuations and/or corrupted phase diagrams. Significantly, for Δt > 10 fs the energy errors remain bound.

Resonances in the photodissociation of HCl in the Ar–HCl van der Waals complex: How prominent are they?

We investigate the cage effect in the ultraviolet (UV) photodissociation of the Ar...HCl van der Waals complex, especially the possibility of resonance structures caused by trapping of the hydrogen atom between its heavy partners as recently highlighted by Garcia‐Vela and Gerber [J. Chem. Phys. 98, 427 (1993)]. The dynamics is described by solving the time‐dependent Schrodinger equation employing the standard Jacobi coordinates which are routinely used for triatomic systems. Due to the large size of the required grid, exact three‐dimensional (3D) wave packet calculations are extremely time consuming and could be followed up to 20 fs only. This time is sufficient for calculating the absorption spectrum, but too short for determining the final kinetic energy distributions of the fragment atoms. Therefore, the photodissociation dynamics is mainly treated in a vibrationally sudden approximation, in which the dynamical calculations are performed for a range of fixed ArCl bond distances, and the results averaged over this bond length. 3D classical trajectory calculations show that the energy transfer out of the dissociative HCl mode is very weak (∼5% of the total energy), supporting the application of the sudden approximation. In this approximation, both the absorption spectrum and the kinetic energy distribution associated with the dissociating HCl motion exhibit very weak diffuse structures (resonances) which, following the work of Garcia‐Vela and Gerber, can be assigned to the transient vibrational motion of hydrogen between Ar and Cl. However, in our calculations these structures are much less pronounced than in the work of Garcia‐Vela and Gerber. The very small amplitudes of the resonance features indicate that trapping in the dissociation of HCl in Ar...HCl is marginal, and much less important than suggested by the previous studies of Garcia‐Vela et al. Furthermore, in contrast to the work reported by Garcia‐Vela et al., we do not find any evidence for the narrow, irregular features superimposed on the resonance structures.We investigate the cage effect in the ultraviolet (UV) photodissociation of the Ar...HCl van der Waals complex, especially the possibility of resonance structures caused by trapping of the hydrogen atom between its heavy partners as recently highlighted by Garcia‐Vela and Gerber [J. Chem. Phys. 98, 427 (1993)]. The dynamics is described by solving the time‐dependent Schrodinger equation employing the standard Jacobi coordinates which are routinely used for triatomic systems. Due to the large size of the required grid, exact three‐dimensional (3D) wave packet calculations are extremely time consuming and could be followed up to 20 fs only. This time is sufficient for calculating the absorption spectrum, but too short for determining the final kinetic energy distributions of the fragment atoms. Therefore, the photodissociation dynamics is mainly treated in a vibrationally sudden approximation, in which the dynamical calculations are performed for a range of fixed ArCl bond distances, and the results average...

Intermolecular vibrations of the 2,3‐dimethylnaphthalene⋅Ar van der Waals complex: Experiment and quantum three‐dimensional calculations

A combined experimental and theoretical study of the intermolecular vibrations of 2,3‐dimethylnaphthalene⋅Ar (2,3‐DMN⋅Ar), for the first excited electronic state (S1), is reported. Methyl groups at C2 and C3 positions of naphthalene lower the symmetry of the complex, so that transitions involving excitation of the intermolecular long‐axis in‐plane x mode become allowed in electronic spectra, in addition to the out‐of‐plane z mode. Two‐color resonant two‐photon ionization (2C‐R2PI) spectrum of the van der Waals (vdW)‐mode region (000+70 cm−1) of 2,3‐DMN⋅Ar exhibits six bands to the high‐frequency side of the electronic origin 000, which arise from excitation of low‐frequency intermolecular vibrations of the complex in the S1 state. Accurate quantum three‐dimensional (3D) calculations of vdW vibrational (J=0) levels of S1 2,3‐DMN⋅Ar have been performed, using a recently developed quantum method based on the 3D discrete variable representation. Since no approximation is made in the treatment of coupled, very...

Intermolecular vibrations of o‐xylene⋅Ar in the S0 and S1 states: Experiment and quantum three dimensional calculations

A combined experimental and theoretical study of the intermolecular vibrations of the o‐xylene⋅Ar van der Waals complex is reported for both the S0 and S1 electronic states. Two‐color resonant two‐photon ionization and fluorescence emission spectra of the vdW mode region of supersonic jet‐cooled o‐xylene⋅Ar exhibit five bands within 70 cm−1 of the electronic origin, which arise from low‐frequency large‐amplitude intermolecular vibrations. Accurate quantum 3D calculations of vdW vibrational levels were performed, based on the 3D discrete variable representation. Apart from the restriction to the J=0 state the calculated eigenstates are exact for the intermolecular potential energy surface (PES) employed. The PES is represented as a sum of Lennard‐Jones (LJ) pair potentials, and the direct comparison between theory and experiment enabled calibration of the LJ parameters. Very good agreement was achieved for both the S0 and S1 states of o‐xylene⋅Ar. The quantum 3D calculations provide a quantitative descript...

A separating framework for increasing the timestep in molecular dynamics

In molecular dynamics (MD) simulations, the Newtonian equations of motion are solved numerically, and a space/time trajectory of the molecular system is obtained [1,2]. Typically, explicit integration algorithms are used: new positions and velocities for all atoms are computed in closed form through simple relations involving positions and velocities at previous steps. Standard explicit schemes are simple to formulate and fast to propagate, but they impose a severe restriction on the integration timestep size: Δt must resolve the most rapid vibrational mode [3]. This generally limits Δt to the femtosecond (10−15 s) range and the trajectory length to the nanosecond (10−9 s) range. This feasible simulation range is still very short relative to motions of significant biological interest.

Van der Waals vibrations and isomers of 2,3-dimethylnaphthalene·Ne: Experiment and quantum three-dimensional calculations

We report a combined experimental and theoretical study of the van der Waals isomers and intermolecular vibrations of the 2,3‐dimethylnaphthalene⋅Ne complex in the S1 electronic state. The two‐color resonant two‐photon ionization spectrum exhibits eight bands within ≊40 cm−1 of the electronic origin. Theoretical considerations in combination with hole‐burning spectroscopic measurements show that the transition closest to the electronic origin (at 000+5 cm−1) arises from an isomer which is different from that responsible for the other seven bands in the spectrum. The latter involve excitations of the intermolecular vibrations of the main isomer of 2,3‐dimethylnaphthalene⋅Ne. Accurate three‐dimensional quantum calculations of the van der Waals vibrational levels of the complex were performed using a discrete variable representation method. Combination of theory and experiment led to a complete assignment as well as to a quantitative theoretical reproduction of the experimental intermolecular vibrational lev...

Quantum three‐dimensional calculation of endohedral vibrational levels of atoms inside strongly nonspherical fullerenes: Ne@C70

Detailed results of the quantum 3D calculation of the intermolecular vibrational levels of the endohedral fullerene complex Ne@C70, for the total angular momentum J=0, are presented. They elucidate, for the first time, the nature of the endohedral vibrations of an atom inside a strongly nonspherical fullerene. The calculations were performed using our recently developed method for accurate highly excited 3D intermolecular vibrational states of atom–large molecule complexes [J. Chem. Phys. 98, 7165 (1993)]. The treatment of the coupled endohedral vibrations of Ne@C70 involves no dynamical approximations, apart from taking the fullerene to be rigid, producing eigenstates which are essentially exact for the intermolecular potential energy surface (PES) employed. The 3D endohedral PES for Ne@C70, modeled as a sum of atom–atom Lennard‐Jones pair potentials, is anharmonic, especially in the direction of the long (z) axis of C70. The endohedral vibrational energy level structure of Ne@ C70 which emerged from our...

Three-dimensional discrete variable representation for accurate Van der Waals vibrational states of complexes between atoms and large molecules, including fullerenes

We discuss the recently developed method for accurate quantum three-dimensional (3D) calculation of excited Van der Waals (VdW) vibrational levels of floppy atom–large-molecule complexes. This method is designed primarily for highly anisotropic complexes, in which the radius of the molecule exceeds the equilibrium atom–molecule separation. The 3D discrete variable representation (DVR), in Cartesian coordinates, is used for all three intermolecular degrees of freedom. The quantum dynamics of coupled anharmonic VdW vibrations are treated exactly. Our 3D DVR computational methodology is well suited for VdW states delocalized over intermolecular potentials with multiple minima. The scope of its applicability is broad, and includes endohedral complexes of atoms inside strongly non-spherical fullerene cages. The method is used to calculate VdW vibrational levels of 2,3-dimethylnaphthalene · Ar (2,3-DMN · Ar) up to ca. 60–70 cm–1 above the ground VdW state. This enabled assignment of the experimentally observed VdW bands and refinement of the intermolecular potential-energy surface for the S1 state of 2,3-DMN · Ar. Using the same 3D DVR code, we also performed the first quantum 3D calculation of the VdW vibrational states of the endohedral fullerene complex Ne@C70. The regular nodal patterns of the VdW wavefunctions inspected so far suggest weak coupling of the endohedral vibrational modes of Ne@C70.

Spectroscopy and quantum dynamics of the 1,2-dimethylnaphthalene·Ar van der Waals complex

We report a detailed experimental and theoretical study of the intermolecular vibrational levels of the 1,2‐dimethylnaphthalene⋅Ar van der Waals complex in the S1 electronic state. Due to the low symmetry of the aromatic molecular substrate, excitations in all three van der Waals modes (two in‐plane, one out‐of‐plane) are allowed in the electronic spectrum, leading to the most complete data set of intermolecular vibrational transitions measured so far for an atom‐large molecule complex. Two‐color resonant two‐photon ionization spectra reveal twelve bands within ≊95 cm−1 of the electronic origin. Accurate quantum three‐dimensional calculations of the van der Waals vibrational levels were performed, using a method based on the 3D discrete variable representation. Combination of theory and experiment allowed a complete and quantitative interpretation of the level structure, as well as an accurate parametrization of the intermolecular potential energy surface (PES), modeled as sum of atom–atom Lennard‐Jones p...