Ab initio potential energy and dipole moment surfaces of the F−(H2O) complex

Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 119 (2014) 59–62

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Ab initio potential energy and dipole moment surfaces of the F(H2O) complex Eugene Kamarchik a, Daniele Toffoli b, Ove Christiansen c,⇑, Joel M. Bowman d a

Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551, USA Department of Chemistry, Middle East Technical University, 06531 Ankara, Turkey c Department of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark d Cherry L. Emerson Center for Scientific Computation, Department of Chemistry, Emory University, Atlanta, GA 30322, USA b

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

 We present full-dimensional ab initio

8000 7000 6000 -1

Energy (cm )

potential energy and dipole moment surfaces for the F(H2O) complex.  Vibrational self-consistent field/ vibrational configuration interaction (VSCF/VCI) calculations of energies and the IR-spectrum are presented.  A one-dimensional calculation of the splitting of the ground state, due to equivalent double-well global minima is reported.

5000 4000 3000 2000 1000 0 -1000 -150

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50

0

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q im

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Article history: Available online 30 April 2013 Keywords: Potential energy surfaces Anharmonic vibrations Ab initio calculations Complexes Hydrogen bonding IR spectra

a b s t r a c t We present full-dimensional, ab initio potential energy and dipole moment surfaces for the F(H2O) complex. The potential surface is a permutationally invariant fit to 16,114 coupled-cluster single double (triple)/aVTZ energies, while the dipole surface is a covariant fit to 11,395 CCSD(T)/aVTZ dipole moments. Vibrational self-consistent field/vibrational configuration interaction (VSCF/VCI) calculations of energies and the IR-spectrum are presented both for F(H2O) and for the deuterated analog, F(D2O). A onedimensional calculation of the splitting of the ground state, due to equivalent double-well global minima, is also reported. Ó 2013 Elsevier B.V. All rights reserved.

There is a long history to the study of ions within an aqueous environment, dating back well over 100 years [1,2]. This interest has been motivated by the realization that subtle ion and water and water-water non-covalent interactions can lead to substantial macroscopic effects [1,3,4]. In the development of rigorous theoretical models for hydrated ions, small gas-phase clusters provide an ideal proving ground for new potentials as well as new ideas. Since the development of high-resolution techniques for gas-phase infrared spectroscopy [1,5], small clusters offer the advantages of ⇑ Corresponding author. Tel.: +45 5152 6145. E-mail address: [email protected] (O. Christiansen). 1386-1425/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.saa.2013.04.076

being amenable to direct experimental observation. Additionally, the relatively small size of such clusters permits the use of high-level ab initio calculations from which the performance of the model can also be benchmarked. In aqueous systems, the hydrogen-bonded and/or ionic OH stretches are of particular interest since they provide a ‘‘signature’’ of specific interactions between ionic species and water molecules. In general, these vibrational transitions occur at approximately 3500 cm1, although the exact energy is highly sensitive to the strength of the hydrogen bond. They also have large oscillator strengths, which make them ideal targets for experimental observation. The ionic OH stretch in the H2O–F complex repre-

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sents a particularly challenging hydrogen-bonded stretch because of the unusually high anharmonicity of this vibrational mode. In fact, the red-shift induced by the hydrogen bonded between the F ion and water is so large that the fundamental is located at around 1500 cm1. This complex has been the object of number of experimental [6,7] and theoretical studies [8–11]. These studies have highlighted the need both for accurate potential energy surfaces (PESs) and for a full treatment of all the coupled motions of the complex [8]. Toffoli et al. used an n-mode representation of the PES [12] to perform essentially exact full-dimensional calculations of the fundamental and a number of overtone and combination states of this system. Agreement with experiment was very good, especially considering the rather low resolution of these challenging experiments. The n-mode representation of the PES makes use of grids of potential values and, as such, it is not a global or even semi-global PES. However, the electronic energies obtained on these grids, with some supplementation, can be used to generate a full-dimensional PES using a fit. We have done this and report the new PES here. In addition, new calculations were performed to obtain the dipole moment surface. Specifically, the full-dimensional PES for F(H2O) is a fit to 16,114 coupled-cluster with single, double, and perturbative triple excitations [CCSD(T)] using the augmented correlation-consistent triple f basis (aVTZ) [13,14]. All calculations were carried out using the MOLPRO suite of quantum chemistry programs [15]. The approach used to obtain the PES has been previously developed and applied to a large range of molecules, complexes, and reactive systems [16]. It is based on the representation of the potential energy using permutationally invariant polynomials in Morse variables, earij , where rij is the internuclear distance between atoms i and j and a is a range parameter typically chosen to be 1 Å1 [17]. The energies used to fit the surface are comprised of two data sets. The first, which includes approximately 10,000 points, describes the hydrogen-bonded interaction between the fluoride ion and the water and was obtained using the previous electronic energies obtained by Toffoli et al. [8]. The second, newly calculated set of 6000 points, describes the long-range interactions out to r(O–F) distances of 10 Å. The energies were fit to permutationally invariant polynomials of total order less than or equal to seven. The root-mean-square fitting error is 6.5 cm1 for configurations with energy less than 10,000 cm1 and 13.5 cm1 for configurations having energies between 10,000 cm1 and 20,000 cm1. We also constructed a full-dimensional dipole moment surface (DMS) for F(H2O) using a subset of 11,395 geometries from the PES. The DMS is fit to the three components of the dipole moment obtained at the CCSD(T)/aVTZ level of theory. The dipole is represented as

~ dð~ r1 ; . . . ;~ rn Þ ¼

n X r 1 ; . . . ;~ ri ; qi ð~ rn Þ  ~

PES has Cs symmetry with R(O  F) = 2.435 Å, ionic R(O  H) = 1.056 Å, free R(O  H) = 0.960 Å, h(HOH) = 101.9°, and h(OHF) = 177.0°. The PES also contains the saddle point corresponding to bending of the water monomer between the two equivalent minima. The optimized C2v saddle point has R(O  F) = 2.564 Å, h(HOH) = 89.8° and two equivalent O–H bonds with R(O  H) = 0.974 Å. Both of these structures are shown in Fig. 1 and are in excellent agreement with the structures obtained by direct optimization with CCSD(T)/aVTZ. As shown in Table 1, the PES harmonic frequencies are also in very good agreement with those from direct CCSD(T)/aVTZ calculations. The vibrational modes are labelled as the water-fluoride stretch, miw, the in-plane water rotation, mip, the out-of-plane water rotation, moop, the water bending mode, mb, the ionic hydrogen-bonded stretch, mihb, and the free OH stretch mf. Finally, the surface dissociates to a fluoride ion and a water molecule where the fragment water molecule has R(O  H) = 0.962 Å and h(HOH) = 103.9°. The relaxed potential at fixed R(O  F) distances is shown in Fig. 3. The PES De is 9698 cm1, in good agreement with the CCSD(T)/aVTZ value of 9734 cm1. For the F(H2O) cluster we performed full-dimensional vibrational self-consistent field/vibrational configuration interaction (VSCF/VCI) calculations, using algorithms which have been described in the literature previously [21,22]. The calculations employed the 4-mode coupling representation (4-MR) of the potential and the kinetic energy operator including vibrational angular momentum terms. At the level of 4-MR, the full-dimensional Hamiltonian is used, but the potential and kinetic energy intergrals are approximated by sums of functions depending on at most four normal coordinates [12]. The underlying basis for the calculation is a grid of 32 points in each dimension. The bounds on the one-dimensional grids were placed where the energy along the corresponding 1-d cut reached 20,000 cm1 or the cut reached a maximum displacement of 200 m1=2  bohr. The grids are used directly in the e VSCF calculation and then the resulting VSCF states, formed from linear combinations of the pseudospectral basis functions, are used as the basis for the VCI. The vibrational basis included all VSCF

ð1Þ

i¼1

ri represents the Cartesian coordinates of the ith nucleus and where ~ the sum runs over all nuclei. and the qi, which can be viewed as effective partial charges, are determined by fitting the dipole moment data. The qi are functions of all Morse variables and their properties are such that the dipole transforms covariantly under the interchange of like atoms [17]. This procedure has previously been proven effective in fitting the DMS of water and of other small ionic clusters [18–20]. The dipole was fit to polynomials having a total order less than or equal to five with a root-mean-square fitting error in the magnitude of the dipole moment of 0.004 D over all configurations (for reference, the dipole moment at the minimum energy configuration has a magnitude of 2.171 D). The PES yields an accurate description of the structure and frequencies of the F(H2O) complex. The optimized geometry on the

Fig. 1. The structures for the minimum (1) and the saddle point (1TS) for F(H2O).

Table 1 Comparison of harmonic vibrational frequencies for F(H2O). Cs minimum Mode

miw mip moop mb mihb mf

C2v saddle point

PES

CCSD(T)/aVTZ

383 576 1171 1718 2205 3857

387 580 1171 1723 2210 3856

Mode

mip miw moop mb mihb mf

PES

CCSD(T)/aVTZ

523i 271 849 1611 3670 3714

524i 276 843 1645 3664 3716

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E. Kamarchik et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 119 (2014) 59–62 Table 2 Comparison of selected VCI fundamentals and overtone excitation energies for F(H2O) and F(D2O) with previous theoretical [8] and experimental [7] results.

Mode

Toffoli et al.

miw 2miw 3miw mip 2mip moop 2moop mb 2mb mihb 2mihb 2miwmihb mf

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F(D2O) Exp.

426.65 829.10 1218.03 576.27 1200.75 1184.36 2352.42 1653.56 3281.94 1464.54 2915.91 2634.68 3689.00

VCI

433.24 836.86 1219.92 566.61 1169.81 1083–1250 1146.62 2314.56 1650 1623.25 3225.46 1430–1570 1456.71 2815–2930 2872.49 2561.36 3687 3660.70

Exp.

VCI

393.54 770.67 1131.41 408.88 834.12 815.15 1621.06 1184.95 2349.58 1160–1270 1168.46 2120–2263 2133.63

Energy (cm−1)

F(H2O)

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0 2698.78

2

3

4

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6

7

8

9

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11

r(O−F) ( ) Fig. 3. Relaxed potential for fixed values of the R(O– F) distance.

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states with 13 or fewer total excitations, yielding a Hamiltonian of dimension 27,132. The results of this calculation are shown in Table 2. A plot of the one-dimensional cut along qihb along with the first three vibrational levels in this mode is also shown in Fig. 2. There is reasonable agreement with the previously computed vibrational peaks of Toffoli et al. The differences between our values and theirs are likely the result of differences in the fitting procedure of the potential as well as their use of higher level CCSD(T)/ aVQZ calculations for the 1-mode grids. The use of a 4-MR rather than a 6-MR for the potential also may account for a slight shift, although for the majority of the results reported by Toffoli et al. the difference between 4-MR and 6-MR was less than 2 cm1. Also, Toffoli et al. employed an approximation, by evaluating the effective moment of inertia tensor at the equilibrium geometry and then treating the obtained value as a constant, in the vibrational angular momentum terms, which is expected to be quite accurate, but which could also contribute to some of the differences. In the current calculation, the effective moment of inertia tensor is treated as a variable, depending on displacements in up to four coordinates as per the 4-MR representation. As noted previously by Toffoli et al. there is reasonably good agreement with experiment. Also, note the large red-shift of the H-bonded OH-stretch fundamental, appearing at 1464 cm1, compared to the harmonic frequency of 2205 cm1. Analogous calculations have been performed for F(D2O), using the same parameters for the VSCF and VCI steps, and the frequencies are also shown in Table 2.

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Energy (cm ) Fig. 4. The calculated IR spectra for the F(H2O) cluster. Calculated peaks are convoluted with gaussians having a full-width half-maximum of 10 cm1, and both spectra have been normalized so that the maximum intensity is unity.

Expt. VCI

Intensity (arb. units)

Fig. 2. One dimensional potential along the normal mode coordinate corresponding to the ionic hydrogen-bonded stretch. For reference the density, jWj2, is plotted for the ground and first two vibrationally excited states.

500

1000

1500

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3500

4000

Energy (cm-1) Fig. 5. The calculated IR spectra for the F(D2O) cluster. Calculated peaks are convoluted with gaussians having a full-width half-maximum of 10 cm1, and both spectra have been normalized so that the maximum intensity is unity.

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Energy (cm-1)

6000 5000 4000 3000 2000 1000 0 -1000 -150

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qim (me1/2 bohr) Fig. 6. One dimensional relaxed potential following the imaginary frequency mode from the C2v saddle-point. The ground and first excited vibrational states along this coordinate are also shown for reference.

the neglect of this feature in earlier calculations. However, we estimate that the contribution of the tunneling to the spectra could become significant at around 3mip so any states which contain this character (or that of higher excitations in the in-plane bending motion) should be examined carefully. This estimation is based on a consideration of both the magnitude of the excited vibrational state splittings obtained for the one-dimensional calculation as well as consideration of the relative energies. At 3mip there is 1800 cm1 of energy in this mode and sufficient delocalization of the vibrational wave function to begin to allow the states corresponding to the separate wells to begin to couple. In summary, we presented a new full-dimensional PES and DMS of the F(H2O) complex that accurately reproduces both the complex region and the dissociation to F + H2O. We have validated the potential by comparing geometries and frequencies with direct ab initio results as well as by performing high-level VCI calculations. In addition, we have shown that the tunneling due to the two equivalent minima can be neglected in calculations of the fundamentals and first few vibrational overtones. Acknowledgments

The computed IR spectra for F(H2O) is shown in Fig. 4. As expected, the fundamental of the ionic OH stretch shows the greatest intensity with the other prominent peaks being the fundamental of the F–H2O stretch and the first overtone of the ionic OH stretch. Agreement with experiment is good. The computed IR spectra for F(D2O) is shown in Fig. 5, and again the overall agreement with experiment is quite good. Along with the prominent peaks corresponding to the fundamental and first overtone of the ionic OD stretch, the second overtone of the water-fluoride stretch also shows significant intensity due to strong coupling to the ionic stretch fundamental. Finally, as noted already there are two equivalent global minima separated by a C2v saddle-point, labelled as 1TS in Fig. 1. The energy of this saddle point is 2604 cm1 above the global minima. The expectation is that this high barrier effectively localizes the vibrational states in one or the other well and that was assumed in be true in the present and all previous vibrational calculations. In order to calculate the tunneling splitting, a one-dimensional relaxed potential was prepared starting from the C2v saddle-point and following the imaginary normal mode in either direction while relaxing the remaining 3N  7 coordinates. The potential that this generates is shown in Fig. 6. Solving the one-dimensional Schödinger equation with Hamiltonian

H ¼ p2im þ V relaxed ðqim Þ;

Financial support from the National Science Foundation (CHE1145227) and Department of Energy (DE DFG02-97ER14782) is gratefully acknowledged. This work is also supported by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, U.S. Department of Energy (DE-AC04-94AL85000). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]

ð2Þ

[16]

where qim is the imaginary normal mode at the 1TS geometry having unit reduced mass, yields a set of vibrational states along the imaginary frequency mode and the difference between the ground and first excited gives the ground state tunneling splitting. This calculation yields a tunneling splitting of only <0.1 cm1, which justifies

[17] [18] [19] [20] [21] [22]

W.H. Robertson, M.A. Johnson, Ann. Rev. Phys. Chem. 54 (2003) 173. K.D. Collins, Methods 34 (2004) 300. J. Heyda, T. Hrobarik, P. Jungwirth, J. Phys. Chem. A 113 (2009) 1969. C.G. Zhan, D.A. Dixon, J. Phys. Chem. A 108 (2004) 2020. C.S. Gudeman, R.J. Saykally, Annu. Rev. Phys. Chem. 35 (1984) 387. J.R. Roscioli, E.G. Diken, M.A. Johnson, S. Horvath, A.B. McCoy, J. Phys. Chem. A 110 (2006) 4943. S. Horvath, A.B. McCoy, J.R. Roscioli, M.A. Johnson, J. Phys. Chem. A 112 (2008) 12337. D. Toffoli, M. Sparta, O. Christiansen, Chem. Phys. Lett. 510 (2011) 36. B.F. Yates, H.F. Schaefer, T.J. Lee, J.E. Rice, J. Am. Chem. Soc. 110 (1988) 6327. G.M. Chaban, S.S. Xantheas, R.B. Gerber, J. Phys. Chem. A 107 (2003) 4952. J. Kim, H.M. Lee, S.B. Suh, D. Majumdar, O.K.S. Kim, J. Chem. Phys. 113 (2000) 5259. S. Carter, S. Culik, J. Bowman, J. Chem. Phys. 107 (1997) 10458. T.H. Dunning, J. Chem. Phys. 90 (1989) 1007. R.A. Kendall, T.H. Dunning, R.J. Harrison, J. Chem. Phys. 96 (1992) 6796. MOLPRO, A Package of Ab Initio Programs Designed by H.-J. Werner and P.J. Knowles, Version 2010.1. http://www.molpro.net. J.M. Bowman, B.J. Braams, S. Carter, C. Chen, G. Czako, B. Fu, X. Huang, E. Kamarchik, A.R. Sharma, B.C. Shepler, et al., J. Phys. Chem. Lett. 1 (2010) 1866. B.J. Braams, J.M. Bowman, Int. Rev. Phys. Chem. 28 (2009) 577. X. Huang, B.J. Braams, J.M. Bowman, J. Phys. Chem. A 110 (2006) 445. E. Kamarchik, Y. Wang, J.M. Bowman, J. Chem. Phys. 134 (2011) 114311. E. Kamarchik, J.M. Bowman, J. Phys. Chem. A 48 (2010) 12945. J.M. Bowman, J. Chem. Phys. 68 (1978) 608. J.M. Bowman, T. Carrington, H.-D. Meyer, Mol. Phys. 106 (2008) 2145.