^{1}, Joshua K. Carr

^{2}, Michael Göllner

^{1}, Peter Hamm

^{3,a)}and Markus Meuwly

^{1,b)}

### Abstract

Using classical molecular dynamics simulations, the 2D infrared (IR) spectroscopy of CN− solvated in D2O is investigated. Depending on the force field parametrizations, most of which are based on multipolar interactions for the CN− molecule, the frequency-frequency correlation function and observables computed from it differ. Most notably, models based on multipoles for CN− and TIP3P for water yield quantitatively correct results when compared with experiments. Furthermore, the recent finding that T 1 times are sensitive to the van der Waals ranges on the CN− is confirmed in the present study. For the linear IR spectrum, the best model reproduces the full widths at half maximum almost quantitatively (13.0 cm−1 vs. 14.9 cm−1) if the rotational contribution to the linewidth is included. Without the rotational contribution, the lines are too narrow by about a factor of two, which agrees with Raman and IR experiments. The computed and experimental tilt angles (or nodal slopes) α as a function of the 2D IR waiting time compare favorably with the measured ones and the frequency fluctuation correlation function is invariably found to contain three time scales: a sub-ps, 1 ps, and one on the 10-ps time scale. These time scales are discussed in terms of the structural dynamics of the surrounding solvent and it is found that the longest time scale (≈10 ps) most likely corresponds to solvent exchange between the first and second solvation shell, in agreement with interpretations from nuclear magnetic resonance measurements.

The authors gratefully acknowledge financial support from the Swiss National Science Foundation (NSF(CH)) through the NCCR-MUST (to M.M. and P.H.) and grant 200021-117810 (to M.M.). The research at the University of Wisconsin was supported in part by National Science Foundation (NSF) Grant No. CHE-0840494. The authors thank Professor J. L. Skinner for insightful discussions, and M.M. thanks the Chemistry Department of the University of Wisconsin for hospitality during the time in which part of this work has been carried out.

I. INTRODUCTION

II. COMPUTATIONAL METHODS

A. 2D IR spectra

B. Cumulant approximation

C. Non-cumulant treatment

III. RESULTS

A. Linear spectra

B. 2D spectra and tilt angles

C. Solventdynamics

IV. DISCUSSION AND CONCLUSIONS

### Key Topics

- Infrared spectra
- 33.0
- Solvents
- 24.0
- Molecular dynamics
- 16.0
- Infrared spectroscopy
- 12.0
- Correlation functions
- 10.0

## Figures

The simulation system used in the present work. The C and N atoms of the cyanide ion are displayed as van der Waals spheres. The atoms of the water molecules whose oxygen atoms are within 4 Å (1st solvation shell) from the center of the cyanide ion are shown as red spheres and those between 4 and 6 Å (2nd solvation shell) as green spheres. Other water molecules are depicted as lines.

The simulation system used in the present work. The C and N atoms of the cyanide ion are displayed as van der Waals spheres. The atoms of the water molecules whose oxygen atoms are within 4 Å (1st solvation shell) from the center of the cyanide ion are shown as red spheres and those between 4 and 6 Å (2nd solvation shell) as green spheres. Other water molecules are depicted as lines.

Electrostatic potential obtained from the SCF density of the DFT calculation (blue), MTP parameters (red), and 3-point charge model parameters (green). The geometric center of CN− is at the origin and the atoms are placed at zero radial coordinate. The C atom is along the negative axis and the N atom is along the positive axis.

Electrostatic potential obtained from the SCF density of the DFT calculation (blue), MTP parameters (red), and 3-point charge model parameters (green). The geometric center of CN− is at the origin and the atoms are placed at zero radial coordinate. The C atom is along the negative axis and the N atom is along the positive axis.

1D IR spectra for various models computed with cumulant approximation (label CA, upper panel) or without cumulant approximation (label NCA, lower panel). Rotational contribution of CN− has been incorporated in the spectra for CA and NCA. M0 is shown in black, M2 in green, M4 in red, and M6 in magenta. FWHMs (in cm−1) are 8.5 (M0), 9.0 (M1), 12.8 (M2), 8.6 (M4), 7.4 (M5), and 6.8 (M6) for CA and 9.2 (M0), 9.4 (M1), 13.3 (M2), 9.2 (M4), 7.4 (M5), and 7.1 (M6) for NCA. The experimental FWHM 27 is shown as a gray bar at height 0.5 and the gray solid line represents the experimental spectrum with water background removed.

1D IR spectra for various models computed with cumulant approximation (label CA, upper panel) or without cumulant approximation (label NCA, lower panel). Rotational contribution of CN− has been incorporated in the spectra for CA and NCA. M0 is shown in black, M2 in green, M4 in red, and M6 in magenta. FWHMs (in cm−1) are 8.5 (M0), 9.0 (M1), 12.8 (M2), 8.6 (M4), 7.4 (M5), and 6.8 (M6) for CA and 9.2 (M0), 9.4 (M1), 13.3 (M2), 9.2 (M4), 7.4 (M5), and 7.1 (M6) for NCA. The experimental FWHM 27 is shown as a gray bar at height 0.5 and the gray solid line represents the experimental spectrum with water background removed.

The FFCFs from 0 to 1.5 ps obtained from the simulations of 13C15N− in D2O with M0 (black), M2 (green), M4 (red), and M5 (blue). All frequencies were computed with water molecules within 5 Å from CN−. The inset shows FFCFs in the range of 0–5 ps on a logarithmic scale.

The FFCFs from 0 to 1.5 ps obtained from the simulations of 13C15N− in D2O with M0 (black), M2 (green), M4 (red), and M5 (blue). All frequencies were computed with water molecules within 5 Å from CN−. The inset shows FFCFs in the range of 0–5 ps on a logarithmic scale.

Fitting of Eq. (9) or (10) to the FFCFs obtained from the trajectories of 13C15N− in D2O with models 0 (upper panel) and 4 (lower panel). Logarithmic scale is used for the vertical axis. Raw FFCFs are shown in solid lines, fitting with Eq. (9) in dashed lines, and fitting with Eq. (10) in dotted lines. In the inset of the lower panel, FFCFs obtained from the frequency calculation of CN− with water molecules within 3 Å (violet), 5 Å (red), and ∞ (green) from CN− are compared.

Fitting of Eq. (9) or (10) to the FFCFs obtained from the trajectories of 13C15N− in D2O with models 0 (upper panel) and 4 (lower panel). Logarithmic scale is used for the vertical axis. Raw FFCFs are shown in solid lines, fitting with Eq. (9) in dashed lines, and fitting with Eq. (10) in dotted lines. In the inset of the lower panel, FFCFs obtained from the frequency calculation of CN− with water molecules within 3 Å (violet), 5 Å (red), and ∞ (green) from CN− are compared.

The 2D IR spectra of 13C15N− in D2O using model M0 computed using the cumulant approximation with numerically integrated g(t) (1st row) and avoiding the cumulant approximation (2nd row). Waiting times are 100 fs (1st column), 1 ps (2nd column), and 10 ps (3rd column).

The 2D IR spectra of 13C15N− in D2O using model M0 computed using the cumulant approximation with numerically integrated g(t) (1st row) and avoiding the cumulant approximation (2nd row). Waiting times are 100 fs (1st column), 1 ps (2nd column), and 10 ps (3rd column).

Comparison of tilt angles as a function of mixing time t 2. Left panel shows α(t 2) determined using the cumulant approximation with the line shape functions g(t) obtained from FFCFs by numerical integration (solid lines). The inset compares the tilt angles from the numerical (solid circle) and the analytical line shape functions obtained from fitting of Eq. (9) to the FFCF (open circle) for M0. Black curve is from M0, cyan from M1, green from M2, red from M4, and blue from M5. Right panel shows α(t 2) determined by avoiding the cumulant approximation and the inset compares the tilt angles computed with (solid circle) and without (open circle) using the cumulant approximation for M0. The color scheme for M0, M2, M4, and M5 is the same as the left panel and M6 is shown in magenta. For comparison, tilt angles from experiment 28 are shown in gray in both panels.

Comparison of tilt angles as a function of mixing time t 2. Left panel shows α(t 2) determined using the cumulant approximation with the line shape functions g(t) obtained from FFCFs by numerical integration (solid lines). The inset compares the tilt angles from the numerical (solid circle) and the analytical line shape functions obtained from fitting of Eq. (9) to the FFCF (open circle) for M0. Black curve is from M0, cyan from M1, green from M2, red from M4, and blue from M5. Right panel shows α(t 2) determined by avoiding the cumulant approximation and the inset compares the tilt angles computed with (solid circle) and without (open circle) using the cumulant approximation for M0. The color scheme for M0, M2, M4, and M5 is the same as the left panel and M6 is shown in magenta. For comparison, tilt angles from experiment 28 are shown in gray in both panels.

(a) The distribution of water molecules around CN− computed from the simulations with M0. The geometric center of CN− is at the origin, and the probability of finding water oxygen atoms at certain axial and radial distances from CN− is displayed in red contour. The maximum around R ≈ 3 Å is labeled as “R3” and the maximum around R ≈ 4 Å as “R4.” The probability of hydrogen atoms is displayed in green. The van der Waals radii of carbon and nitrogen atoms are shown in black semicircles. (b) The distance of the first radial minimum from the origin as a function of the angle with respect to the axial coordinate, computed from the distribution of water molecules around CN−. The result from M0 is shown in black and that from M4 in red.

(a) The distribution of water molecules around CN− computed from the simulations with M0. The geometric center of CN− is at the origin, and the probability of finding water oxygen atoms at certain axial and radial distances from CN− is displayed in red contour. The maximum around R ≈ 3 Å is labeled as “R3” and the maximum around R ≈ 4 Å as “R4.” The probability of hydrogen atoms is displayed in green. The van der Waals radii of carbon and nitrogen atoms are shown in black semicircles. (b) The distance of the first radial minimum from the origin as a function of the angle with respect to the axial coordinate, computed from the distribution of water molecules around CN−. The result from M0 is shown in black and that from M4 in red.

The occupation fluctuation correlation function C n (t) of δn(t) as a function of time. The solid lines are from M0 and the dotted lines from M4 for oxygen (green) and deuterium (blue) atoms with cutoff radius of 4 Å. The inset shows the occupation correlation function C H (t) of δH(t) as a function of time for M4.

The occupation fluctuation correlation function C n (t) of δn(t) as a function of time. The solid lines are from M0 and the dotted lines from M4 for oxygen (green) and deuterium (blue) atoms with cutoff radius of 4 Å. The inset shows the occupation correlation function C H (t) of δH(t) as a function of time for M4.

(a) Analysis of the jump angle between cyanide and the neighboring water at the carbon-end of CN−. θ is the angle between the rotating O*H* bond and the bisector plane of the CO*O′ angle, where O′ is the new H-bond acceptor. 73 (b) The change of direction of CN− measured by for 50 ps.

(a) Analysis of the jump angle between cyanide and the neighboring water at the carbon-end of CN−. θ is the angle between the rotating O*H* bond and the bisector plane of the CO*O′ angle, where O′ is the new H-bond acceptor. 73 (b) The change of direction of CN− measured by for 50 ps.

## Tables

Parameters of CN− for (1) the multipole model and (2) the 3-point charge model. The reference data of CN− were obtained from B3LYP/aug-cc-pVQZ around the equilibrium bond length. Each multipole component is denoted by Q u , where u represents angular momentum labels (00, 10, 11c, 11s, 20, 21c, 21s, 22c, and 22s). The molecular axis is oriented along the z-axis, and only nonzero components are shown. For the 3-point charge model, charges on the C and N atoms are fitted to a function of the form q = a 0 + a 1 r + a 2 r 2 + a 3 r 3, where r is the bond distance of CN−. The parameters of the fits are given in the last 4 columns.

Parameters of CN− for (1) the multipole model and (2) the 3-point charge model. The reference data of CN− were obtained from B3LYP/aug-cc-pVQZ around the equilibrium bond length. Each multipole component is denoted by Q u , where u represents angular momentum labels (00, 10, 11c, 11s, 20, 21c, 21s, 22c, and 22s). The molecular axis is oriented along the z-axis, and only nonzero components are shown. For the 3-point charge model, charges on the C and N atoms are fitted to a function of the form q = a 0 + a 1 r + a 2 r 2 + a 3 r 3, where r is the bond distance of CN−. The parameters of the fits are given in the last 4 columns.

Parameters for water potential reported in the work of Kumagai et al. 55 and used in this work. Atomic units are used for D, β, r 0, f k , r m , and g r . θ0 is given in degrees.

Parameters for water potential reported in the work of Kumagai et al. 55 and used in this work. Atomic units are used for D, β, r 0, f k , r m , and g r . θ0 is given in degrees.

Water and cyanide models used in this study. The combination of them are called models 0 through 6. V bond represents bonded interactions and V es electrostatic interactions. q is electric charges, μ dipole moments, and Θ quadrupole moments. r min = r UFF is used for CN− in the case of M5, whereas r min = 1.075r UFF is used for all other models. “SHAKE” refers to simulations in which SHAKE is applied to all water molecules, as is typically done in biomolecular simulations. All models were run for 20 ns.

Water and cyanide models used in this study. The combination of them are called models 0 through 6. V bond represents bonded interactions and V es electrostatic interactions. q is electric charges, μ dipole moments, and Θ quadrupole moments. r min = r UFF is used for CN− in the case of M5, whereas r min = 1.075r UFF is used for all other models. “SHAKE” refers to simulations in which SHAKE is applied to all water molecules, as is typically done in biomolecular simulations. All models were run for 20 ns.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content