# DFT Computed Dielectric Response and THz Spectra of Organic Co-Crystals and Their Constituent Components

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results and Discussion

#### 2.1. Co-Crystals

#### 2.2. Improving Agreement with Experiment

## 3. Materials and Methods

#### 3.1. Pellet Fabrication

#### 3.2. Dielectric Measurements

#### 3.3. Terahertz Spectroscopy

#### 3.4. Computational Details

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Shown here are the co-crystal components (

**a**) BPE, (

**b**) BPEth, and (

**c**) SA. Atoms of carbon, hydrogen, nitrogen, and oxygen are depicted as black, light pink, light blue, and red spheres, respectively. Dashed lines represent the crystallographic axes of the primitive lattice unit cell for each of the components.

**Figure 2.**Comparisons of the computed phonon modes (black solid curves) to experimentally obtained THz spectra (solid blue curves) of BPE using (

**a**) DFT and (

**b**) DFT-D. Dashed black vertical lines are the normalized phonon mode intensity used to obtain the phonon density of states (DOS). All measurements are given in arbitrary units.

**Figure 3.**Depicted here are the DFT-D computed IR active vibrational modes of BPE that occur at (

**a**) 105.6 cm

^{−1}(along the x-direction) and (

**b**) 106.4 cm

^{−1}(along the y-direction. Color scheme is the same as before, but red arrows indicate relative atomic displacements. The displacements of H atoms are not shown for clarity.

**Figure 4.**Same description as in Figure 2, but for 1,2-bis(4-pyridyl)ethane (BPEth).

**Figure 5.**Depicted here are the DFT-D computed IR active vibrational modes of BPEth that occur at (

**a**) 61.2 cm

^{−1}(along the y-direction) and (

**b**) 70.9 cm

^{−1}(along the x-direction).

**Figure 6.**Same description as in Figure 2, but for salicylic acid (SA).

**Figure 7.**Shown here are the DFT-D computed IR active modes of SA that occur at (

**a**) 37.9 cm

^{−1}(along y); (

**b**) 76.1

^{−1}(along xz); and (

**c**) 92.3

^{−1}(along y).

**Figure 8.**Shown here are the co-crystals (

**a**) 2(SA)·BPE-I; (

**b**) 2(SA)·BPE-II; and (

**c**) 2(SA)·BPEth. Color scheme is as before in Figure 1.

**Figure 9.**Shown here are comparisons of the computed phonon modes (black solid curves) to experimentally obtained THz spectra (solid blue curves) of (

**a**) 2(SA)·BPE-I; (

**b**) 2(SA)·BPE-II; and (

**c**) 2(SA)·BPEth using DFT-D. Dashed black vertical lines are the normalized phonon mode intensity used to obtain the phonon density of states (DOS). All measurements are given in arbitrary units.

**Figure 10.**Comparisons of the Experimental THz spectra (

**top**) and DFT-D computed phonon modes (

**bottom**) of (

**left**) 2(SA)·BPE-I (solid yellow line) and 2(SA)·BPE-II (dash-dotted purple line), and (

**right**) 2(SA)·BPE-II (dash-dotted purple line) and 2(SA)·BPEth (solid orange line).

**Figure 11.**Shown here are the DFT-D computed IR active modes of 2(SA)·BPEth that occur at (

**a**) 77.7 cm

^{−1}(along xz); (

**b**) 79.9 cm

^{−1}(along y); (

**c**) 89.8 cm

^{−1}(along xz); (

**d**) 91.3 cm

^{−1}(along y); and (

**e**) 93.2 cm

^{−1}(along xz).

**Figure 12.**Plotted here are the DFT-D computed IR active modes of 2(SA)·BPE-I that occur at (

**a**) 28.9 cm

^{−1}(along xz); (

**b**) 33.9 cm

^{−1}(along xz); (

**c**) 34.9 cm

^{−1}(along y); (

**d**) 69.8 cm

^{−1}(along y); and (

**e**) 70.3 cm

^{−1}(along xz).

**Figure 13.**Depicted here are the DFT-D computed IR active modes of 2(SA)·BPE-II that occur at (

**a**) 42.3 cm

^{−1}(along xz); (

**b**) 68.5 cm

^{−1}(along z); (

**c**) 69.1 cm

^{−1}(along y); (

**d**) 92.3 cm

^{−1}(along xz); and (

**e**) 102.9 cm

^{−1}(along xz).

**Figure 14.**For co-crystal components (

**a**) BPE; (

**b**) BPEth; and (

**c**) SA, we vary s

_{6}from 0 to 1 to determine how DFT-D computed lattice parameters a, b, c, and β will be affected when compared to experimentally determined lattice parameters. The same tests for co-crystal 2(SA)·BPEth yield a similar range of s

_{6}in which lattice constant underestimation may be minimized. Brown dashed lines denote ±4% error with respect to experimentally determined lattice parameters.

**Table 1.**Lattice parameters of co-crystal components BPE, BPEth, and SA, using DFT (top) and DFT-D (bottom). All lattice constants are reported in units of Å, and both the experimental value and % deviation from experimentally determined values are given in parentheses.

${\mathit{a}}_{\mathbf{DFT}}$ | ${\mathit{b}}_{\mathbf{DFT}}$ | ${\mathit{c}}_{\mathbf{DFT}}$ | ${\mathit{\beta}}_{\mathbf{DFT}}$ | |
---|---|---|---|---|

(Å) | (Å) | (Å) | ||

BPE | 11.00 (7.82, +40.66) | 10.38 (10.56, −1.70) | 6.89 (5.77, +19.41) | 116.89 (92.68, +26.12) |

BPEth | 5.69 (5.56, +2.33) | 9.64 (8.16, +18.14) | 11.33 (11.35, −0.18) | 99.26 (100.73, −1.45) |

SA | 5.20 (4.89, +6.38) | 11.02 (11.20, −1.64) | 14.83 (11.24, +31.94) | 75.39 (92.49, −18.49) |

BPE | 7.30 (7.82, −6.66) | 10.51 (10.56, −0.50) | 5.56 (5.77, −2.87) | 90.39 (92.68, −2.47) |

BPEth | 5.31 (5.56, −4.53) | 7.80 (8.16, −4.38) | 11.11 (11.35, −2.16) | 98.73 (100.73, −1.99) |

SA | 4.85 (4.89, −0.78) | 11.02 (11.20, −1.64) | 11.27 (11.24, +0.23) | 93.54 (92.49, +1.14) |

**Table 2.**Comparison of experimentally determined dielectric constant, $\u03f5$, to the isotropically averaged values computed using DFT and DFT-D for the co-crystal components BPE, BPEth, and SA. Percent deviation from experiment is shown in parenthesis for DFT and DFT-D.

Experiment | DFT | DFT-D | |
---|---|---|---|

BPE | 3.43 ± 0.08 | 2.68 (−21.87) | 3.92 (+14.29) |

BPEth | 3.13 ± 0.15 | 2.68 (−14.38) | 3.25 (+3.83) |

SA | 3.09 ± 0.04 | 3.70 (+19.74) | 2.79 (−9.71) |

**Table 3.**Mode-by-mode analysis of the directional components of the IR active response of BPE for DFT (top) and DFT-D (bottom) for the THz frequency range of 20–110 cm${}^{-1}$. $\omega $ are given in units of cm${}^{-1}$ and all $\u03f5$ are unitless. Asterisks (*) are next to the frequencies with high contributions to ${\u03f5}_{\mu}$, and are shown in Figure 3. The two final rows in each of the DFT and DFT-D calculations are the total ionic portion of the dielectric response per direction x, y, z per mode $\mu $ (denoted as ${\u03f5}_{\mu}$), and the directionally decomposed electronic contribution of the dielectric response ${\u03f5}_{\infty}$.

Method | $\mathit{\omega}$ | ${\mathit{\u03f5}}_{\mathit{x}}$ | ${\mathit{\u03f5}}_{\mathit{y}}$ | ${\mathit{\u03f5}}_{\mathit{z}}$ |
---|---|---|---|---|

DFT | 31.1 | - | 0.29 | - |

47.2 | - | 0.01 | - | |

47.5 | - | 0.03 | - | |

55.2 | 0.02 | - | 0.03 | |

65.8 | - | 0.07 | - | |

70.5 | 0.01 | - | 0.03 | |

81.9 | 0.02 | - | 0.00 | |

92.0 | - | 0.06 | - | |

97.0 | 0.02 | - | 0.00 | |

${\u03f5}_{\mu}$ | 0.12 | 0.55 | 0.15 | |

${\u03f5}_{\infty}$ | 1.97 | 2.86 | 2.40 | |

DFT-D | 67.6 | - | 0.02 | - |

69.5 | 0.01 | - | 0.00 | |

105.6 * | 0.15 | - | 0.00 | |

106.4 * | - | 0.15 | - | |

${\u03f5}_{\mu}$ | 0.44 | 0.30 | 0.14 | |

${\u03f5}_{\infty}$ | 2.63 | 4.63 | 3.62 |

Method | $\mathit{\omega}$ | x | y | z |
---|---|---|---|---|

DFT | 31.8 | - | 0.11 | - |

32.5 | - | 0.10 | - | |

41.6 | 0.10 | - | 0.16 | |

54.8 | - | 0.03 | - | |

60.5 | - | 0.06 | - | |

68.8 | 0.10 | - | 0.01 | |

70.8 | - | 0.11 | - | |

${\u03f5}_{\mu}$ | 0.26 | 0.48 | 0.22 | |

${\u03f5}_{\infty}$ | 2.20 | 2.18 | 2.69 | |

DFT-D | 45.4 | - | 0.06 | - |

53.9 | 0.03 | - | 0.00 | |

61.2 * | - | 0.08 | - | |

70.9 * | 0.13 | - | 0.04 | |

93.8 | - | 0.01 | - | |

108.9 | 0.00 | - | 0.01 | |

${\u03f5}_{\mu}$ | 0.24 | 0.43 | 0.13 | |

${\u03f5}_{\infty}$ | 2.97 | 2.55 | 3.43 |

Method | $\mathit{\omega}$ | x | y | z |
---|---|---|---|---|

DFT | 30.8 | - | 0.04 | - |

37.0 | 0.02 | - | 0.00 | |

42.2 | - | 0.02 | - | |

42.3 | 0.02 | - | 0.00 | |

58.9 | 0.03 | - | 0.00 | |

63.0 | - | 0.22 | - | |

71.3 | 0.03 | - | 0.00 | |

79.2 | - | 0.04 | - | |

79.5 | 0.09 | - | 0.00 | |

${\u03f5}_{\mu}$ | 0.79 | 1.01 | 0.44 | |

${\u03f5}_{\infty}$ | 3.00 | 3.11 | 2.73 | |

DFT-D | 37.9 * | - | 0.29 | - |

49.7 | 0.05 | - | 0.00 | |

66.5 | - | 0.04 | - | |

76.1 * | 0.07 | - | 0.03 | |

78.4 | - | 0.02 | - | |

92.3 * | - | 0.09 | - | |

100.2 | 0.03 | - | 0.01 | |

${\u03f5}_{\mu}$ | 0.55 | 0.69 | 0.28 | |

${\u03f5}_{\infty}$ | 2.19 | 2.32 | 2.34 |

**Table 6.**Lattice parameters of co-crystals using DFT (top) and DFT-D (bottom). All lattice constants are reported in units of Åand % deviation from experimentally determined values are given in parentheses after the experimentally determined values.

Co-Crystal | ${\mathit{a}}_{\mathbf{DFT}}$ | ${\mathit{b}}_{\mathbf{DFT}}$ | ${\mathit{c}}_{\mathbf{DFT}}$ | ${\mathit{\beta}}_{\mathbf{DFT}}$ |
---|---|---|---|---|

(Å) | (Å) | (Å) | ||

2(SA)·BPE-I | 13.48 (11.93, +12.99) | 4.89 (4.87, +0.45) | 20.71 (20.25, −2.27) | 99.81 (106.92, −6.65) |

2(SA)·BPE-II | 9.12 (8.76, +4.11) | 6.48 (6.81, −4.85) | 24.65 (19.66, +25.38) | 110.86 (105.34, +5.24) |

2(SA)·BPEth | 9.25 (8.63, +7.18) | 6.49 (6.86, −5.39) | 22.35 (19.55, +14.32) | 91.94 (101.36, −9.29) |

2(SA)·BPE-I | 11.76 (11.93, −1.41) | 4.89 (4.87, +0.45) | 19.89 (20.25, −1.08) | 108.07 (106.92, +1.08) |

2(SA)·BPE-II | 8.73 (8.76, −0.34) | 6.87 (6.81, +0.91) | 18.06 (19.66, −8.15) | 105.91 (105.34, +0.54) |

2(SA)·BPEth | 8.61 (8.63, −0.26) | 6.88 (6.86, +0.34) | 17.98 (19.55, −8.02) | 102.92 (101.36, +1.54) |

**Table 7.**Experimentally determined THz frequencies for the co-crystals 2(SA)·BPE form I and II, and 2(SA)·BPEth, given in units of cm${}^{-1}$. Values are partitioned to highlight similarities and differences.

2(SA)·BPE-I | 29.5 | 33.5 | 38.8 | 44.9 | 54.6 | 68.1 | 73.7 | 92.7 | 99.6 | 102.4 | ||

2(SA)·BPE-II | 24.9 | 35.4 | 42.8 | 60.8 | 84.0 | 108.7 | ||||||

2(SA)·BPEth | 35.2 | 43.6 | 61.6 | 83.4 | 110.7 |

**Table 8.**Mode-by-mode analysis of the directional components of the IR active response of 2(SA)·BPEth co-crystal using DFT-D for the THz frequency range of 20–110 cm${}^{-1}$. $\omega $ are given in units of cm${}^{-1}$ and all $\u03f5$ are unitless. Asterisks are next to the frequencies that have high contributions to ${\u03f5}_{\mu}$ and are plotted in Figure 11. The final two rows are the total ionic portion of the dielectric response per direction (x, y, z) per mode $\mu $ (denoted as ${\u03f5}_{\mu}$), and the directionally decomposed electronic contribution of the dielectric response ${\u03f5}_{\infty}$.

System | $\mathit{\omega}$ | x | y | z |
---|---|---|---|---|

2(SA)·BPEth | 38.5 | 0.00 | - | 0.05 |

44.5 | - | 0.01 | - | |

56.0 | - | 0.01 | - | |

77.7 * | 0.09 | - | 0.05 | |

79.9 * | - | 0.15 | - | |

89.8 * | 0.22 | - | 0.06 | |

91.3 | - | 0.08 | - | |

93.2 * | 0.02 | - | 0.10 | |

96.6 * | 0.12 | - | 0.01 | |

98.9 | - | 0.01 | - | |

${\u03f5}_{\mu}$ | 0.99 | 1.57 | 0.85 | |

${\u03f5}_{\infty}$ | 3.02 | 3.19 | 2.71 |

2(SA)·BPE-I | 28.9 * | 0.00 | - | 0.08 |

33.9 * | 0.01 | - | 0.12 | |

34.9 * | - | 0.15 | - | |

48.5 | - | 0.01 | - | |

50.9 | 0.01 | - | 0.02 | |

51.1 | - | 0.01 | - | |

61.5 | 0.02 | - | 0.02 | |

69.8 * | - | 0.13 | - | |

70.3 * | 0.06 | - | 0.02 | |

87.8 | 0.01 | - | 0.03 | |

109.5 | 0.06 | - | 0.02 | |

${\u03f5}_{\mu}$ | 0.58 | 2.19 | 1.66 | |

${\u03f5}_{\infty}$ | 2.86 | 3.16 | 3.14 | |

2(SA)·BPE-II | 41.5 | - | 0.01 | - |

42.3 * | 0.02 | - | 0.28 | |

47.3 | - | 0.04 | - | |

68.5 * | 0.00 | - | 0.11 | |

69.1 * | - | 0.19 | - | |

88.4 | 0.07 | - | 0.03 | |

90.9 | - | 0.02 | - | |

92.3 * | 0.19 | - | 0.02 | |

102.9 * | 0.24 | - | 0.02 | |

103.9 | - | 0.04 | - | |

110.2 | - | 0.02 | - | |

${\u03f5}_{\mu}$ | 0.79 | 1.01 | 0.64 | |

${\u03f5}_{\infty}$ | 3.44 | 3.72 | 2.83 |

**Table 10.**Experimentally determined $\u03f5$ of co-crystals compared to the isotropically averaged $\u03f5$ computed using DFT-D. Percent deviation from experiment is in parentheses.

Experiment | DFT-D | |
---|---|---|

2(SA)·BPE-I | 6.13 ± 0.19 | 4.53 (−26.10) |

2(SA)·BPE-II | 4.89 ± 0.05 | 4.14 (−15.34) |

2(SA)·BPEth | 7.82 ± 0.15 | 4.11 (−47.44) |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Bennett, J.W.; Raglione, M.E.; Oburn, S.M.; MacGillivray, L.R.; Arnold, M.A.; Mason, S.E.
DFT Computed Dielectric Response and THz Spectra of Organic Co-Crystals and Their Constituent Components. *Molecules* **2019**, *24*, 959.
https://doi.org/10.3390/molecules24050959

**AMA Style**

Bennett JW, Raglione ME, Oburn SM, MacGillivray LR, Arnold MA, Mason SE.
DFT Computed Dielectric Response and THz Spectra of Organic Co-Crystals and Their Constituent Components. *Molecules*. 2019; 24(5):959.
https://doi.org/10.3390/molecules24050959

**Chicago/Turabian Style**

Bennett, Joseph W., Michaella E. Raglione, Shalisa M. Oburn, Leonard R. MacGillivray, Mark A. Arnold, and Sara E. Mason.
2019. "DFT Computed Dielectric Response and THz Spectra of Organic Co-Crystals and Their Constituent Components" *Molecules* 24, no. 5: 959.
https://doi.org/10.3390/molecules24050959