Computing Bulk Phase Raman Optical Activity ... - ACS Publications

Letter pubs.acs.org/JPCL

Computing Bulk Phase Raman Optical Activity Spectra from ab initio Molecular Dynamics Simulations Martin Brehm* and Martin Thomas Institut für Chemie - Theoretische Chemie, Martin-Luther-Universität Halle-Wittenberg, Von-Danckelmann-Platz 4, 06120 Halle (Saale), Germany S Supporting Information *

ABSTRACT: We present our novel methodology for computing Raman optical activity (ROA) spectra of liquid systems from ab initio molecular dynamics (AIMD) simulations. The method is built upon the recent developments to obtain magnetic dipole moments from AIMD and to integrate molecular properties by using radical Voronoi tessellation. These techniques are used to calculate optical activity tensors for large and complex periodic bulk phase systems. Only AIMD simulations are required as input, and no timeconsuming perturbation theory is involved. The approach relies only on the total electron density in each time step and can readily be combined with a wide range of electronic structure methods. To the best of our knowledge, these are the first computed ROA spectra for a periodic bulk phase system. As an example, the experimental ROA spectrum of liquid (R)-propylene oxide is reproduced very well.

ibrational spectroscopy has been an important field of chemistry and physics for a very long time. The first “infrared spectrum” (albeit of the Earth’s atmosphere instead of a prepared sample) was recorded by Herschel in 1840, and the Raman effect was predicted by Smekal 94 years ago.1 More recently, the chiral variants of these two techniques have been introduced experimentally, namely, vibrational circular dichroism (VCD)2,3 and Raman optical activity (ROA) spectroscopy.4−7 With the rise of computational chemistry, it became possible to predict vibrational spectra by quantum chemical methods. In the beginning, these were based on the doubleharmonic approximation, resulting in static vibrational spectra. Static infrared8−15 and Raman8,10,12−19 spectra have been available for several decades in quantum chemistry software packages, and static VCD2,13,15,20−27 and ROA10,14−16,19,28−30 spectra can also be computed since many years. A lot of effort was put into going beyond the harmonic approximation, and more complex approaches were introduced to account for anharmonicity effects.10,15,31−34 However, a full representation of bulk phase and solvent effects was still not feasible. To tackle this shortcoming, a completely new class of methods for the prediction of vibrational spectra was developed, which is based on the evaluation of ab initio molecular dynamics (AIMD) simulations instead of static calculations. With this class of methods, periodic bulk phase systems can be treated natively, and even anharmonic effects are covered to a certain extent, as line shapes, overtones, and combination bands are reproduced in a qualitatively correct manner.35,36 This has been shown in the literature numerous times by the very good agreement of simulated infrared36−51 and Raman36,43,46,48,51−57 spectra with experimental data. However, concerning the chiral variants of

V

© XXXX American Chemical Society

these techniques, a similar progress could not be observed for a long time. Last year, M.T. et al. published the first computed periodic bulk phase VCD spectra,58 which are based on a classical approach to obtain the electric current density from Born− Oppenheimer molecular dynamics (MD). Shortly after, another bulk phase VCD spectrum based on AIMD was published,59 obtained by utilizing nuclear velocity perturbation theory (NVPT). A few months ago, the first method for computing ROA spectra from AIMD appeared in the literature,60 which is based on density functional perturbation theory. The predicted ROA spectrum of a single molecule in a nonperiodic cell is presented therein. Some derivations have explicitly been conducted under the assumption of a nonperiodic system, and the author concludes that the application to periodic bulk phase systems remains an open project for the future. Following this outline, there exist ab initio methods to compute infrared, Raman, and VCD spectra of periodic bulk phase systems today, which are in very good agreement with experimental data. However, we are not aware of any simulation of periodic bulk phase ROA spectra until now. In this letter, we present our novel methodology for computing ROA spectra from bulk phase AIMD simulations, thus providing an important extension of the techniques to simulate the vibrational spectra of liquid systems. When computing static spectra within the harmonic approximation, the intensities of the modes are obtained by differentiating the relevant properties with respect to the Received: June 23, 2017 Accepted: July 7, 2017 Published: July 7, 2017 3409

DOI: 10.1021/acs.jpclett.7b01616 J. Phys. Chem. Lett. 2017, 8, 3409−3414

Letter

The Journal of Physical Chemistry Letters

tessellation, as we have proposed before.51 In the general case (i.e., charged molecules), pMol is dependent on the choice of the coordinate origin; similarly, QMol depends on the origin if the dipole moment is nonzero. For each molecule, we use the center of mass as the coordinate origin when performing these computations. In order to also obtain magnetic dipole moments, we apply the purely classical approach presented by M.T. et al. last year58 to approximate the electric current density j(r) from the change in the total electron density between successive time steps. Subsequently, the molecular magnetic dipole moment mMol is computed by the classical expression

corresponding normal mode displacement vector. When the spectra shall be obtained from an MD simulation instead, the system is not situated in a local minimum of the potential energy surface, and normal modes are not known inherently. Instead, time correlation functions of the same relevant properties are considered in that case. Taking the Fourier transform of these correlation functions directly yields the spectrum.36,46 For example, the infrared spectrum of a system can be obtained from an MD simulation by autocorrelating the derivative of the system’s dipole moment vector with respect to the simulation time, and applying a Fourier transform to the resulting autocorrelation function afterward. In the case of Raman optical activity, the required approach is slightly more involved, as the relevant properties are three different polarizability tensors of the system (also known as optical activity tensors).61 These are the electric dipole−electric dipole polarizability tensor α, the electric quadrupole−electric dipole polarizability tensor A, and the magnetic dipole−electric dipole polarizability tensor G′. The main challenge in computing ROA spectra from MD simulations is to obtain these tensors in each simulation time step in order to compute the required time correlation functions. This can be achieved, e.g., by applying perturbation theory,60 which requires, however, significant amounts of computer resources to solve the resulting perturbation equations. Our approach is based on a purely classical approximation to these tensors. Only the coordinates ri of the nuclei and the total electron density ρ(r) on a three-dimensional grid are required as input in each time step. Based on this information, we compute the molecular dipole moment vector pMol and the trace-free molecular quadrupole moment tensor QMol for each molecule by the classical expressions p Mol =

NMol

∑ qn rn − ∫

rn δij)

∫Mol ρ(r)(3rri j −

2

r δij)d3r

(2)

where rn and qn denote the position and core charge of the nth nucleus, respectively, and NMol represents the number of atoms within the molecule. The volume in space over which ρ is integrated for each molecule is determined by a radical Voronoi ∞

aG′(ν)̃ = 2πcνiñ

∫−∞

n=1

1 2

∫Mol r × j(r)d3r

(3)

tensors required for ROA, we use the relations AMol = (Mol and G′ Mol = −(.′ Mol)T .61 The Mol superscript will be omitted in the following, but all quantities are still molecular quantities. The ROA spectrum consists of three invariants, aG′, γ2G′, and 2 γA. In static ROA calculations, these are computed from the derivatives of the polarizability tensor elements along each normal mode.61 In our new approach, we calculate the invariants as the Fourier transform of cross-correlation functions between the time series of certain molecular quantities along the trajectory. These quantities are the tensor G′ as well as the time derivatives α̇ and Ȧ of the tensors defined above. Only quantities from one molecule at a time are considered; cross-terms between different molecules are not included. Following this approach, the ROA invariants are functions of the wavenumber ν̃ rather than scalar values as in the static case:

n=1

−

∑ qn(rn × vn) −

d

2

∑ qn(3rn,irn,j −

NMol

electric quadrupole polarizability tensor (Mol = dE QMol , and the molecular electric dipole−magnetic dipole polarizability d tensor .′ Mol = dE m Mol . In order to finally determine the

(1)

NMol

Q ijMol =

1 2

where vn denotes the velocity of the nth nucleus, and the molecular center of mass is used as coordinate origin again. To obtain the corresponding polarizabilities from pMol, QMol, and mMol, we apply an external homogeneous electric field E in each spatial direction to the simulation frame under consideration. From a simple finite differences scheme, we obtain the molecular electric dipole−electric dipole polard izability tensor α Mol = dE p Mol , the molecular electric dipole−

ρ(r)rd3r

Mol

n=1

m Mol =

̇ (τ ) + αyy ̇ (τ ) + αzz ̇ (τ ) G′xx (τ + t ) + G′ yy (τ + t ) + G′zz (τ + t ) αxx 3

3

3410

·exp(− 2π icνt̃ )dt τ

(4)

DOI: 10.1021/acs.jpclett.7b01616 J. Phys. Chem. Lett. 2017, 8, 3409−3414

Letter

The Journal of Physical Chemistry Letters

γG2′(ν)̃ = 2πcνiñ

∞

⎡

∫−∞ ⎢⎣ 12 ⟨(αxẋ (τ) − αyẏ (τ))(G′xx (τ + t ) − G′yy (τ + t ))⟩τ

1 1 ̇ (τ ) − αzz ̇ (τ ))(G′ yy (τ + t ) − G′zz (τ + t ))⟩τ + ⟨(αzz ̇ (τ ) − αxx ̇ (τ ))(G′zz (τ + t ) − G′xx (τ + t ))⟩τ ⟨(αyy 2 2 3 3 ̇ (τ )(G′xy (τ + t ) + G′ yx (τ + t ))⟩τ + ⟨αyz ̇ (τ )(G′ yz (τ + t ) + G′zy (τ + t ))⟩τ + ⟨αxy 2 2 ⎤ 3 ̇ (τ )(G′zx (τ + t ) + G′xz (τ + t ))⟩τ ⎥ exp(− 2π icνt̃ )dt + ⟨αzx ⎦ 2

+

γA2(ν)̃ = πcνiñ

(5)

∞

∫−∞ [⟨(αyẏ (τ) − αxẋ (τ))Ȧz ,xy (τ + t )⟩τ + ⟨(αxẋ (τ) − αzż (τ))Ȧy ,zx (τ + t )⟩τ + ⟨(αzż (τ) − αyẏ (τ))Ȧx ,yz (τ + t )⟩τ

̇ (τ )(Ȧ y , yz (τ + t ) − Ȧ z , yy (τ + t ) + Ȧ z , xx (τ + t ) − Ȧ x , xz (τ + t ))⟩τ + ⟨αxy ̇ (τ )(Ȧ z , zx (τ + t ) − Ȧ x , zz (τ + t ) + Ȧ x , yy (τ + t ) − Ȧ y , yx (τ + t ))⟩τ + ⟨αyz ̇ (τ )(Ȧ y , zz (τ + t ) − Ȧ z , zy (τ + t ) + Ȧ x , xy (τ + t ) − Ȧ y , xx (τ + t ))⟩τ ]·exp( −2π icνt̃ )dt +⟨αzx

where ν̃in denotes the wavenumber of the incident laser light. The final ROA spectrum ΔI(ν̃) is assembled as a linear combination of these three invariants:61 ΔI(ν)̃ =

300 K for a physical time of 32.5 ps using density functional theory with the BLYP-D3 exchange−correlation functional, as implemented in the CP2k program package.62 As explained above, each frame was recalculated with external electric fields along each of the three cell vectors in order to obtain the polarizabilities. The computational details as well as a list of all program packages and methods used in this work are given in the Supporting Information. As discussed above, it is necessary to compute, among others, the electric dipole moment p, the magnetic dipole moment m, and the electric dipole−electric dipole polarizability tensor α in each time step to predict an ROA spectrum. Therefore, the infrared, Raman, and VCD spectra of the system can be obtained as a byproduct without any additional effort.46,58 We compare the computed depolarized Raman spectrum to an experimental spectrum63 of liquid (R)-propylene oxide in Figure 1. In order to emphasize the important fingerprint region, we show only a subset of the full frequency range here; the complete spectrum can be found in the Supporting Information. It can be seen that the experiment is reproduced by the simulation very well. All features of the experimental

(νiñ − ν)̃ 4 h · 8ε02ckBT ν ̃ 1 − exp − hcν̃ kT

(

( )) B

1 (X ·aG′(ν)̃ + Y ·γG2′(ν)̃ + Z ·γA2(ν)) × ̃ 90

(7)

where the values of the coefficients X, Y, and Z depend on the experimental setup for which the spectrum shall be predicted. The values of the coefficients for common scattering geometries are taken from the literature61 and shown in Table 1. Table 1. Coefficients in Eq 7 for ICP, SCP, DCPin Operating Modes and Several Scattering Geometriesa scattering angle 0° 0° 90° 90° 90° 180° 180°

polarization ⊥

∥

ΔI = ΔI ΔI ΔI⊥ ΔI∥ ΔI ΔI⊥ = ΔI∥ ΔI

X

Y

Z

360 720 180 0 180 0 0

8 16 28 24 52 48 96

−8 −16 4 −8 −4 16 32

(6)

a

Polarization rel. to scattering plane; 0° = forward, 180° = backward scattering.

These values are applicable to the following experimental operating modes: Incident circularly polarized radiation (ICP), scattered circularly polarized radiation (SCP), and in-phase dual circularly polarized radiation (DCPin). In the case of outof-phase dual circularly polarized radiation (DCPout), no signal is obtained within this approximation. The frequency-dependent prefactor in eq 7 ensures that the correct absolute intensity values are obtained. In order to validate the methodology, an ab initio molecular dynamics simulation containing 32 molecules of (R)-propylene oxide in the liquid state was performed at a temperature of

Figure 1. Comparison of experimental63 (red) and computed (black) depolarized Raman spectrum of liquid (R)-propylene oxide. 3411

DOI: 10.1021/acs.jpclett.7b01616 J. Phys. Chem. Lett. 2017, 8, 3409−3414

Letter

The Journal of Physical Chemistry Letters

previous work on infrared, Raman, and VCD spectroscopy,46,48,51,58 we further extended the methodology for the simulation of vibrational spectra by AIMD. A broad variety of spectra types is routinely accessible for complex periodic bulk phase systems now. It is important to note that our approach is not restricted to a particular electronic structure method, such as density functional theory in this work, but can be combined with a wide range of quantum chemical methods that are able to provide the total electron density of the system.

spectrum can be found in the predicted spectrum, and also the intensity ratios match very well for most bands. Most peaks appear at lower frequencies in the computed spectrum. This effect is well-known and was observed in comparable Raman studies of propylene oxide before.56 It is therefore not related to our method for ROA presented herein, and could be cured by using a higher-level theory for performing the electron structure calculations in the AIMD. As already mentioned, our approach can, in principle, be coupled to any electron structure method that is able to provide the total electron density. The computed ROA spectrum is compared with an experimental spectrum64 of liquid (R)-propylene oxide in Figure 2. The above-mentioned red-shift of the vibrational

■

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b01616. Computational details and complete spectra (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Martin Brehm: 0000-0002-6861-459X Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS M.B. acknowledges financial support by the DFG through project Br 5494/1-1. We thank Daniel Sebastiani for providing the computer time for the computations presented herein.

■

Figure 2. Comparison of experimental64 (red) and computed (black) ROA spectrum of liquid (R)-propylene oxide.

REFERENCES

(1) Smekal, A. Zur Quantentheorie der Dispersion. Naturwissenschaften 1923, 11, 873−875. (2) Stephens, P. J. Theory of Vibrational Circular Dichroism. J. Phys. Chem. 1985, 89, 748−752. (3) Nakanishi, K.; Berova, N.; Woody, R. W. Circular Dichroism: Principles and Applications; Wiley-VCH: Weinheim, Germany, 2000. (4) Atkins, P. W.; Barron, L. D. Rayleigh Scattering of Polarized Photons by Molecules. Mol. Phys. 1969, 16, 453−466. (5) Barron, L. D.; Buckingham, A. D. Rayleigh and Raman Scattering from Optically Active Molecules. Mol. Phys. 1971, 20, 1111−1119. (6) Barron, L. D.; Bogaard, M. P.; Buckingham, A. D. Raman Scattering of Circularly Polarized Light by Optically Active Molecules. J. Am. Chem. Soc. 1973, 95, 603−605. (7) Hug, W.; Kint, S.; Bailey, G.; Scherer, J. R. Raman Circular Intensity Differential Spectroscopy. Spectra of (−)-alpha-pinene and (+)-alpha-phenylethylamine. J. Am. Chem. Soc. 1975, 97, 5589−5590. (8) Neugebauer, J.; Reiher, M.; Kind, C.; Hess, B. A. Quantum Chemical Calculation of Vibrational Spectra of Large Molecules− Raman and IR Spectra for Buckminsterfullerene. J. Comput. Chem. 2002, 23, 895−910. (9) Pawłowski, F.; Halkier, A.; Jørgensen, P.; Bak, K. L.; Helgaker, T.; Klopper, W. Accuracy of Spectroscopic Constants of Diatomic Molecules from ab initio Calculations. J. Chem. Phys. 2003, 118, 2539−2549. (10) Danȩcě k, P.; Kapitán, J.; Baumruk, V.; Bednárová, L., Jr.; Kopecký, V.; Bouř, P. Anharmonic Effects in IR, Raman, and Raman Optical Activity Spectra of Alanine and Proline Zwitterions. J. Chem. Phys. 2007, 126, 224513. (11) Ovsyannikov, R. I.; Thiel, W.; Yurchenko, S. N.; Carvajal, M.; Jensen, P. PH3 revisited: Theoretical Transition Moments for the Vibrational Transitions Below. J. Mol. Spectrosc. 2008, 252, 121−128. (12) Jacob, C. R.; Reiher, M. Localizing Normal Modes in Large Molecules. J. Chem. Phys. 2009, 130, 084106. (13) Neese, F. Prediction of Molecular Properties and Molecular Spectroscopy with Density Functional Theory: From Fundamental

frequencies is inherent to the system, so it appears in the same way as in the Raman spectrum. Apart from that, the simulated ROA bands are in very good agreement with the experimentally observed pattern of positive and negative peaks. For each signal in the experiment, the simulation shows a corresponding counterpart, and also the relative intensity ratios agree very well. The calculated spectrum would easily allow one to identify the correct enantiomer of propylene oxide, since the other enantiomer possesses all bands with opposite sign. Compared to other approaches, the total computational time used in this project is moderate; it accounts to 2350 ch (core hours; Intel Xeon “Haswell” @ 2.4 GHz) for the equilibration, 25 500 ch for the production run of 4 trajectories with/without external field, and 2000 ch to solve the partial differential equation for the electric current in all time steps (see Supporting Information for computational details). This means that the spectra presented in this Letter can be obtained within 3 weeks on a 64 core small desktop server, which is available for less than 10 000 USD today. Apart from the resource usage, we would like to emphasize that only opensource software has been used within this work. All necessary methods are implemented in our freely available open-source program package TRAVIS.65 By using our novel method, it is now possible to compute ROA spectra of periodic bulk phase systems. This has not been achieved before to the best of our knowledge, so this constitutes an important contribution to the field of computational vibrational spectroscopy. The calculated ROA spectrum for the example system chosen in this Letter is in very good agreement with the experimental reference. Together with our 3412

DOI: 10.1021/acs.jpclett.7b01616 J. Phys. Chem. Lett. 2017, 8, 3409−3414

Letter

The Journal of Physical Chemistry Letters Theory to Exchange-Coupling. Coord. Chem. Rev. 2009, 253, 526−563. Theory and Computing in Contemporary Coordination Chemistry (14) Weymuth, T.; Haag, M. P.; Kiewisch, K.; Luber, S.; Schenk, S.; Jacob, C. R.; Herrmann, C.; Neugebauer, J.; Reiher, M. MOVIPAC: Vibrational Spectroscopy with a Robust Meta-Program for Massively Parallel Standard and Inverse Calculations. J. Comput. Chem. 2012, 33, 2186−2198. (15) Bloino, J.; Biczysko, M.; Barone, V. Anharmonic Effects on Vibrational Spectra Inten- sities: Infrared, Raman, Vibrational Circular Dichroism, and Raman Optical Activity. J. Phys. Chem. A 2015, 119, 11862−11874. PMID: 26580121 (16) Pecul, M.; Rizzo, A.; Leszczynski, J. Vibrational Raman and Raman Optical Activity Spectra of d-Lactic Acid, d-Lactate, and dGlyceraldehyde: Ab Initio Calculations. J. Phys. Chem. A 2002, 106, 11008−11016. (17) Mroginski, M. A.; Mark, F.; Thiel, W.; Hildebrandt, P. Quantum Mechanics/Molecular Mechanics Calculation of the Raman Spectra of the Phycocyanobilin Chromophore in α-C-Phycocyanin. Biophys. J. 2007, 93, 1885−1894. (18) Lee, J. J.; Höfener, S.; Klopper, W.; Wassermann, T. N.; Suhm, M. A. Origin of the Argon Nanocoating Shift in the OH Stretching Fundamental of n-Propanol: A Combined Experimental and Quantum Chemical Study. J. Phys. Chem. C 2009, 113, 10929−10938. (19) Luber, S.; Reiher, M. Intensity-Carrying Modes in Raman and Raman Optical Activity Spectroscopy. ChemPhysChem 2009, 10, 2049−2057. (20) Nafie, L. A.; Freedman, T. B. Vibronic Coupling Theory of Infrared Vibrational Transitions. J. Chem. Phys. 1983, 78, 7108−7116. (21) Nafie, L. A. Adiabatic Molecular Properties beyond the BornOppenheimer Approximation. Complete Adiabatic Wave Functions and Vibrationally Induced Electronic Current Density. J. Chem. Phys. 1983, 79, 4950−4957. (22) Stephens, P. J. Gauge Dependence of Vibrational Magnetic Dipole Transition Moments and Rotational Strengths. J. Phys. Chem. 1987, 91, 1712−1715. (23) Buckingham, A.; Fowler, P.; Galwas, P. Velocity-dependent Property Surfaces and the Theory of Vibrational Circular Dichroism. Chem. Phys. 1987, 112, 1−14. (24) Cheeseman, J.; Frisch, M.; Devlin, F.; Stephens, P. Ab initio Calculation of Atomic Axial Tensors and Vibrational Rotational Strengths using Density Functional Theory. Chem. Phys. Lett. 1996, 252, 211−220. (25) Nicu, V. P.; Neugebauer, J.; Wolff, S. K.; Baerends, E. J. A Vibrational Circular Dichroism Implementation within a Slater-typeorbital based Density Functional Framework and its Application to Hexa- and Hepta-helicenes. Theor. Chem. Acc. 2008, 119, 245−263. (26) Scherrer, A.; Vuilleumier, R.; Sebastiani, D. Nuclear Velocity Perturbation Theory of Vibrational Circular Dichroism. J. Chem. Theory Comput. 2013, 9, 5305−5312. PMID: 26592268. (27) Scherrer, A.; Agostini, F.; Sebastiani, D.; Gross, E. K. U.; Vuilleumier, R. Nuclear Velocity Perturbation Theory for Vibrational Circular Dichroism: An Approach based on the Exact Factorization of the Electron-Nuclear Wave Function. J. Chem. Phys. 2015, 143, 074106. (28) Bieler, N. S.; Haag, M. P.; Jacob, C. R.; Reiher, M. Analysis of the Cartesian Tensor Transfer Method for Calculating Vibrational Spectra of Polypeptides. J. Chem. Theory Comput. 2011, 7, 1867−1881. PMID: 26596448 (29) Cheeseman, J. R.; Shaik, M. S.; Popelier, P. L. A.; Blanch, E. W. Calculation of Raman Optical Activity Spectra of Methyl-β-D-Glucose Incorporating a Full Molecular Dynamics Simulation of Hydration Effects. J. Am. Chem. Soc. 2011, 133, 4991−4997. PMID: 21401137 (30) Luber, S. Solvent Effects in Calculated Vibrational Raman Optical Activity Spectra of α-Helices. J. Phys. Chem. A 2013, 117, 2760−2770. PMID: 23527877 (31) Neugebauer, J.; Hess, B. A. Fundamental Vibrational Frequencies of small polyatomic Molecules from Density-Functional Calculations and Vibrational Perturbation Theory. J. Chem. Phys. 2003, 118, 7215−7225.

(32) Hrenar, T.; Werner, H.-J.; Rauhut, G. Accurate Calculation of Anharmonic Vibrational Frequencies of Medium Sized Molecules using Local Coupled Cluster Methods. J. Chem. Phys. 2007, 126, 134108. (33) Kumarasiri, M.; Swalina, C.; Hammes-Schiffer, S. Anharmonic Effects in Ammonium Nitrate and Hydroxylammonium Nitrate Clusters. J. Phys. Chem. B 2007, 111, 4653−4658. PMID: 17474693. (34) Heislbetz, S.; Rauhut, G. Vibrational Multiconfiguration Selfconsistent Field Theory: Implementation and Test Calculations. J. Chem. Phys. 2010, 132, 124102. (35) Wang, H.; Agmon, N. Reinvestigation of the Infrared Spectrum of the Gas-Phase Protonated Water Tetramer. J. Phys. Chem. A 2017, 121, 3056−3070. PMID: 28351145 (36) Thomas, M. Theoretical Modeling of Vibrational Spectra in the Liquid Phase; Springer International Publishing: Cham, Switzerland, 2017. (37) Silvestrelli, P. L.; Bernasconi, M.; Parrinello, M. Ab initio Infrared Spectrum of Liquid Water. Chem. Phys. Lett. 1997, 277, 478− 482. (38) Pasquarello, A.; Car, R. Dynamical Charge Tensors and Infrared Spectrum of Amorphous SiO2. Phys. Rev. Lett. 1997, 79, 1766−1769. (39) Zhu, Z.; Tuckerman, M. E. Ab Initio Molecular Dynamics Investigation of the Concentration Dependence of Charged Defect Transport in Basic Solutions via Calculation of the Infrared Spectrum. J. Phys. Chem. B 2002, 106, 8009−8018. (40) Gaigeot, M. P.; Vuilleumier, R.; Sprik, M.; Borgis, D. Infrared Spectroscopy of N-Methylacetamide Revisited by ab initio Molecular Dynamics Simulations. J. Chem. Theory Comput. 2005, 1, 772−789. PMID: 26641894. (41) Iftimie, R.; Tuckerman, M. E. The Molecular Origin of the Continuous Infrared Absorption in Aqueous Solutions of Acids: A Computational Approach. Angew. Chem., Int. Ed. 2006, 45, 1144− 1147. (42) Gaigeot, M.-P.; Martinez, M.; Vuilleumier, R. Infrared Spectroscopy in the Gas and Liquid Phase from First Principle Molecular Dynamics Simulations: Application to Small Peptides. Mol. Phys. 2007, 105, 2857−2878. (43) Pagliai, M.; Cavazzoni, C.; Cardini, G.; Erbacci, G.; Parrinello, M.; Schettino, V. Anharmonic Infrared and Raman Spectra in CarParrinello Molecular Dynamics Simulations. J. Chem. Phys. 2008, 128, 224514. (44) Chen, W.; Sharma, M.; Resta, R.; Galli, G.; Car, R. Role of Dipolar Correlations in the Infrared Spectra of Water and Ice. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 245114. (45) Heyden, M.; Sun, J.; Funkner, S.; Mathias, G.; Forbert, H.; Havenith, M.; Marx, D. Dissecting the THz Spectrum of Liquid Water from First Principles via Correlations in Time and Space. Proc. Natl. Acad. Sci. U. S. A. 2010, 107, 12068−12073. (46) Thomas, M.; Brehm, M.; Fligg, R.; Vohringer, P.; Kirchner, B. Computing Vibrational Spectra from ab initio Molecular Dynamics. Phys. Chem. Chem. Phys. 2013, 15, 6608−6622. (47) Sieffert, N.; Bühl, M.; Gaigeot, M.-P.; Morrison, C. A. Liquid Methanol from DFT and DFT/MM Molecular Dynamics Simulations. J. Chem. Theory Comput. 2013, 9, 106−118. PMID: 26589014 (48) Thomas, M.; Brehm, M.; Hollóczki, O.; Kelemen, Z.; Nyulászi, L.; Pasinszki, T.; Kirchner, B. Simulating the Vibrational Spectra of Ionic Liquid Systems: 1-Ethyl-3-methylimidazolium Acetate and its Mixtures. J. Chem. Phys. 2014, 141, 024510. (49) Sun, J.; Niehues, G.; Forbert, H.; Decka, D.; Schwaab, G.; Marx, D.; Havenith, M. Understanding THz Spectra of Aqueous Solutions: Glycine in Light and Heavy Water. J. Am. Chem. Soc. 2014, 136, 5031− 5038. PMID: 24606118 (50) Luber, S. Local Electric Dipole Moments for Periodic Systems via Density Functional Theory Embedding. J. Chem. Phys. 2014, 141, 234110. (51) Thomas, M.; Brehm, M.; Kirchner, B. Voronoi Dipole Moments for the Simulation of Bulk Phase Vibrational Spectra. Phys. Chem. Chem. Phys. 2015, 17, 3207−3213. 3413

DOI: 10.1021/acs.jpclett.7b01616 J. Phys. Chem. Lett. 2017, 8, 3409−3414

Letter

The Journal of Physical Chemistry Letters (52) Putrino, A.; Parrinello, M. Anharmonic Raman Spectra in HighPressure Ice from Ab Initio Simulations. Phys. Rev. Lett. 2002, 88, 176401. (53) Souza, I.; Iñ́ iguez, J.; Vanderbilt, D. First-Principles Approach to Insulators in Finite Electric Fields. Phys. Rev. Lett. 2002, 89, 117602. (54) Umari, P.; Pasquarello, A. Ab initio Molecular Dynamics in a Finite Homogeneous Electric Field. Phys. Rev. Lett. 2002, 89, 157602. (55) Wan, Q.; Spanu, L.; Galli, G. A.; Gygi, F. Raman Spectra of Liquid Water from Ab Initio Molecular Dynamics: Vibrational Signatures of Charge Fluctuations in the Hydrogen Bond Network. J. Chem. Theory Comput. 2013, 9, 4124−4130. PMID: 26592405 (56) Luber, S.; Iannuzzi, M.; Hutter, J. Raman Spectra from ab initio Molecular Dynamics and its Application to Liquid (S)-methyloxirane. J. Chem. Phys. 2014, 141, 094503. (57) Ikeda, T. Infrared Absorption and Raman Scattering Spectra of Water under Pressure via First Principles Molecular Dynamics. J. Chem. Phys. 2014, 141, 044501. (58) Thomas, M.; Kirchner, B. Classical Magnetic Dipole Moments for the Simulation of Vibrational Circular Dichroism by ab Initio Molecular Dynamics. J. Phys. Chem. Lett. 2016, 7, 509−513. PMID: 26771403 (59) Scherrer, A.; Vuilleumier, R.; Sebastiani, D. Vibrational Circular Dichroism from ab initio Molecular Dynamics and Nuclear Velocity Perturbation Theory in the Liquid Phase. J. Chem. Phys. 2016, 145, 084101. (60) Luber, S. Raman Optical Activity Spectra from Density Functional Perturbation Theory and Density-Functional-TheoryBased Molecular Dynamics. J. Chem. Theory Comput. 2017, 13, 1254−1262. PMID: 28218847 (61) Long, D. A. The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules; John Wiley & Sons Ltd.: Chichester, U.K., 2002. (62) Hutter, J.; Iannuzzi, M.; Schiffmann, F.; VandeVondele, J. Atomistic Simulations of Condensed Matter Systems. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2014, 4, 15−25. (63) Polavarapu, P. L.; Hecht, L.; Barron, L. D. Vibrational Raman Optical Activity in Substituted Oxiranes. J. Phys. Chem. 1993, 97, 1793−1799. (64) Šebestík, J.; Bouř, P. Raman Optical Activity of Methyloxirane Gas and Liquid. J. Phys. Chem. Lett. 2011, 2, 498−502. (65) Brehm, M.; Kirchner, B. TRAVIS - A free Analyzer and Visualizer for Monte Carlo and Molecular Dynamics Trajectories. J. Chem. Inf. Model. 2011, 51, 2007−2023.

3414

DOI: 10.1021/acs.jpclett.7b01616 J. Phys. Chem. Lett. 2017, 8, 3409−3414