Letter pubs.acs.org/JPCL
Coupling of Low- and High-Frequency Vibrational Modes: Broadening in the Infrared Spectrum of F−(H2O)2 Eugene Kamarchik*,† and Joel M. Bowman*,‡ †
Combustion Research Facility, Sandia National Laboratories, Livermore, California 94551, United States Cherry L. Emerson Center for Scientific Computation, Department of Chemistry, Emory University, Atlanta, Georgia, 30322, United States
‡
ABSTRACT: We present ab initio calculations of the infrared (IR) spectra of the strongly anharmonic clusters F−(H2O) and F−(H2O)2 using fulldimensional potential energy and dipole moment surfaces. The fulldimensional F−(H2O)2 potential energy surface is composed of previously published one- and two-body water potentials, a two-body F−H2O potential, and a new three-body F−(H2O)2 potential. The three-body water−fluoride potential is a fit to 16 111 second-order Møller−Plesset perturbation theory (MP2/aug-cc-pVTZ) energies using permutationally invariant polynomials. The IR spectrum of F−(H2O)2 is computed using 6-, 8-, 10-, and 13dimensional VSCF/VCI in order to illustrate the effects of mode coupling and intensity borrowing between the high-frequency intramolecular modes and the low-frequency intermolecular modes. Comparisons with Ar-tagged action spectra are also made. SECTION: Spectroscopy, Photochemistry, and Excited States mong the halogens, complexes of the fluoride anion (F−) with water represent a unique class of strongly hydrogenbonded systems. The ion−water interaction results in significant elongation of the hydrogen-bonded OH in both F−(H2O) and F−(H2O)2; this induces large red shifts in the corresponding infrared (IR) vibrational spectra. Additionally, the coupling of the hydrogen-bonded stretches to the other vibrational modes of the cluster may be important for the study of vibrational energy transfer.1−4 Harmonic vibrational frequencies for both clusters5−8 severely overestimate the experimentally measured fundamental frequencies,9,10 which is indicative of strong anharmonic effects. Previous theoretical studies have highlighted the need for accurate potential energy surfaces (PESs) and for a full treatment of the coupled motions in both of these complexes.6,11−14 While these studies have provided a detailed description of the F−(H2O) spectroscopy, certain features of the F−(H2O)2 spectrum remain unexplored. In this Letter, a new PES for the F−(H2O)2 complex is presented, and vibrational self-consistent field/vibrational configuration interaction (VSCF/VCI) calculations are performed in order to elucidate the underlying vibrational dynamics. The full-dimensional PES for F−(H2O)2 is a fit to 16 111 electronic energies obtained with second-order Møller−Plesset perturbation theory (MP2/aug-cc-pVTZ) using the augmented correlation-consistent triple-ζ basis (aug-cc-pVTZ).15 All calculations were carried out using the MOLPRO suite of quantum chemistry programs.16 The approach used to fit the energies has been previously described and is based on the representation of the potential energy using permutationally invariant polynomials in Morse variables, e−αrij, where rij is the
internuclear distance between atoms i and j and α is a range parameter typically chosen to be 2 bohr−1.17 The configurations of the electronic energies were generated by performing molecular dynamics on water−fluoride clusters using a manybody potential that included one- two-, and three-body water terms and our previously published two-body water−fluoride potential. Because we plan to use the F−(H2O)2 in simulations of larger clusters in the future, we fit the intrinsic three-body potential
A
© 2013 American Chemical Society
Vthree‐body = V (0F , 1H2O , 2 H2O) − V (0F , 1H2O ) − V (0F , 2 H2O) − V (1H2O , 2 H2O) − V (0F) − V (1H2O ) − V (2 H2O)
(1)
where the first term on the right-hand side is the full electronic potential of F− with two H2O molecules, all in a given configuration. Then, the intrinsic three-body interaction is just this full interaction minus the various one- and two-body interactions indicated. The counterpoise correction was computed by calculating the two- and one-body terms with the missing species being replaced by the appropriate ghost atoms. The three-body intrinsic potential was fit using permutationally invariant polynomials in all 21 Morse variables with a total polynomial order less than or equal to 5, yielding 2625 unique terms. Within our set of data, the minimum energy obtained for Received: July 4, 2013 Accepted: August 15, 2013 Published: August 16, 2013 2964
dx.doi.org/10.1021/jz4013867 | J. Phys. Chem. Lett. 2013, 4, 2964−2969
The Journal of Physical Chemistry Letters
Letter
the intrinsic three-body potential was −4.38 kcal/mol, while its maximum value was 22.31 kcal/mol. The root-mean-square fitting error over all configurations was 0.02 kcal/mol. The full PES for F−(H2O)2 is thus a composite of several different potentials calculated at the highest level of theory feasible for each specified interaction
Again, 0F denotes the Cartesian coordinates of the fluoride anion, and 1H2O through NH2O denote the collective Cartesian coordinates of the first through the Nth water monomers. The (1) terms q(1) F (0F) and qH2O represent the one-body effective partial charges, which are q(1) F (0F) = −1 for the fluoride anion and obtained from a monomer DMS for water. The two-body corrections to the effective partial charges are labeled as (2) q(2) F (0F,iH2O) and qH2O(iH2O,jH2O) and are calculated from our F−(H2O) DMS and the previously published water dimer DMS.19 Note that, although we write the DMS as a function of Cartesian coordinates, it is in fact invariant with respect to overall rotation and translation. For the vibrational calculations, we obtain eigenfunctions and eigenvalues of the Watson Hamiltonian, for which the kinetic energy operator is20
2
V (0F , 1H2O , 2 H2O) = V (0F) +
∑ V (iH O) 2
i=1 2
+
∑ V (0F, iH O) + V (1H O , 2 H O) 2
2
2
i=1
+ V (0F , 1H2O , 2 H2O)
(2)
The one-body term, V(iH2O), is an accurate isolated water potential, the two-body term, Vtwo‑body(1H2O,2H2O), is a previously published fit of tens of thousands of CCSD(T) energies,18 and the two-body term, V(0F,iH2O), is the recent intrinsic two-body fluoride−water potential, which is based on fitting roughly 18 000 CCSD(T)/aug-cc-pVTZ energies.11,12 The dipole moment surface DMS for hydrated cluster F−(H2O)2 is represented as
1 2
T̂ =
1 2
−
3
1 μαβ (Jα̂ − Π̂α)(Jβ̂ − Π̂β) − 8 α ,β=1
∑
3N − 6
n
d (⃗ r1⃗ , ..., rn⃗ ) =
∑ qi( r1⃗ , ..., rn⃗ )· ri ⃗
where ri⃗ represents the Cartesian coordinates of the ith nucleus and the sum runs over all nuclei. We require the functions, qi, which can be viewed as effective partial charges. These are functions of all internuclear distances (again in Morse variables), and their properties are such that the dipole transforms covariantly under the interchange of like atoms. Using the effective partial charges, we can construct the DMS as
2
+
2
2
2
2
∑ ∑ ( sTi ,i′ + sVi ,i′)sai†̂ saî ′+ i,i′
( s , tTi , j , i ′ , j ′ +
∑ ∑ s
