Computing Bulk Phase Resonance Raman Spectra from ab Initio

Letter Cite This: J. Chem. Theory Comput. 2019, 15, 3901−3905

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Computing Bulk Phase Resonance Raman Spectra from ab Initio Molecular Dynamics and Real-Time TDDFT Martin Brehm* and Martin Thomas Institut für Chemie - Theoretische Chemie, Martin-Luther-Universität Halle-Wittenberg, Von-Danckelmann-Platz 4, 06120 Halle (Saale), Germany

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S Supporting Information *

ABSTRACT: We present our novel approach for computing resonance Raman (RR) spectra of periodic bulk phase systems from ab initio molecular dynamics, including solvent influence and some anharmonic effects. Based on real-time timedependent density functional theory, we obtain the RR spectra for all laser wavelengths in one pass. We compute the RR spectrum of uracil in aqueous solution, which is in good agreement with experiment. This is the first simulation of a bulk phase RR spectrum.

fields of medicine7 and electrochemistry8 and to study drug binding,9 solar cells,10 photosynthesis,11 nanoparticles,12 and water splitting.13 Following the rise of computational chemistry, it became possible to predict vibrational spectra by quantum chemical methods. In the beginning, the approaches were based on the double-harmonic approximation, resulting in static vibrational spectra. Static infrared14−18 and Raman14−20 spectra have been available for many decades in quantum chemistry software packages. Considerable effort was put into going beyond the harmonic approximation, and more complex approaches were introduced to account for some anharmonic effects.15,18,21−23 However, a full representation of bulk phase and solvent effects was still not in reach. To further advance in this direction, a completely new class of methods for predicting spectra was developed, which is based on ab initio molecular dynamics (AIMD) simulations instead of static calculations. With this class of methods, periodic bulk phase systems could be treated natively, and some anharmonic effects (such as line broadening, overtones, and combination bands) were covered. Numerous investigations based on this new approach have been published in the literature both for infrared24−29 and Raman30−37 spectra, which are often in very good agreement with experimental data. Predicting resonance Raman spectra turns out to be more involved. As the resonance Raman effect involves electronic excitation of the sample, it is in general not sufficient to solve the time-independent Schrödinger equation to obtain the scattering intensities. Several approaches to compute these

A

mong the methods available in modern analytical chemistry, vibrational spectroscopy is of special importance due to its high spectral resolution and sensitivity for the chemical environment of a sample molecule. Within these methods, Raman spectroscopy is of particular popularity. It offers several striking advantages, such as the ability to measure biological samples in aqueous solution and a very high spatial resolution which even gave rise to methods such as Raman microscopy.1 The most prominent limitation of Raman-based methods, however, is their low sensitivity. Typically, less than one out of 1 million incident photons undergo Raman scattering, which leads to a very weak signal. The Raman effect was first predicted by Smekal already 96 years ago,2 and the first experimental applications followed several years later,3 but only the advent of the laser in the 1960s led to the final breakthrough of Raman spectroscopy. In the same decade, it was discovered that the intensity of the Raman scattering drastically increases if the incident laser wavelength is close to the energy of an electronic excitation in the sample, which was termed as the resonance Raman effect.4−6 Apart from the overall increase in intensity, also the intensity ratio of the spectral bands changes−vibrational modes which displace atoms involved in the electronic excitation show larger gains of Raman intensity. With the low sensitivity of Raman spectroscopy in mind, the discovery of the resonance Raman effect was an important advance in the field, and the increased signal intensity allowed for higher resolution and shorter acquisition times. Moreover, as the signal increase only occurs for molecules which are electronically excited by the laser, it became possible to measure very dilute solutions−a reasonable choice of laser wavelength amplifies the bands of the solute but not those of the solvent. Resonance Raman spectroscopy was recently applied in the © 2019 American Chemical Society

Received: May 26, 2019 Published: June 25, 2019 3901

DOI: 10.1021/acs.jctc.9b00512 J. Chem. Theory Comput. 2019, 15, 3901−3905

Letter

Journal of Chemical Theory and Computation intensities have been presented in the literature. Many of them are based on the vibronic theory of Albrecht and coworkers38−40 or on the time-dependent formalism of Heller and co-workers.41−43 Another method, based on linear response time-dependent density functional theory (LRTDDFT), was published by Jensen and Schatz.44,45 Scattering intensities obtained from these methods have been used in many studies in the literature.46−50 Recently, a different approach which uses real-time timedependent density functional theory (RT-TDDFT)51 to obtain the dynamic polarizability of the sample appeared in the literature.52 In contrast to the methods mentioned before, the real-time approach offers the advantage of including all electronic excitations into the calculation, such that the full frequency range is covered and no subset of low-lying excitations needs to be selected. Furthermore, this approach intrinsically includes nonlinear effects which are neglected in perturbative methods such as LR-TDDFT. Within the last years, a few studies on computing resonance Raman scattering intensities from RT-TDDFT were published.53−55 However, all spectra presented in these studies were based on static− harmonic frequency calculations of isolated molecules in vacuum and therefore lack solvent influence and anharmonic effects as discussed above. To the best of our knowledge, a predicted resonance Raman spectrum of a bulk phase system has not been published yet. In this Letter, we introduce our novel methodology for computing bulk phase resonance Raman spectra based on Born−Oppenheimer molecular dynamics (BOMD) and RTTDDFT. To validate our approach, we computed the resonance Raman spectrum of uracil in aqueous solution, which shows a good agreement with experiment. This is the first predicted resonance Raman spectrum of a bulk phase system to appear in the literature. We show that our method yields the resonance Raman spectra for all possible laser wavelengths (including the nonresonant Raman spectrum) in one pass.

Note that we use a Gaussian window function with parameter c for the Fourier transform of the RT-TDDFT time series. T is the total RT-TDDFT simulation time, μ0,j(t) denotes the initial molecular dipole moment at BOMD time t after wave function optimization under external electric field in the j direction, and |E| is the absolute value of the external electric field. Also note that the dynamic polarizability tensor obtained from eq 1 is complex-valued, with dispersion as real part and absorption as imaginary part. An example of the dynamic polarizability is shown in Figure S1 in the SI. Based on the dynamic polarizability tensor, the resonance Raman spectrum for any incident laser wavelength can be computed as Fourier transform of autocorrelation functions along the BOMD time series, as discussed in the literature for nonresonant Raman spectra before.33 We obtain the two Raman invariants, namely the isotropic polarizability a2p(ν̃,ω) and the anisotropy γ2p(ν̃,ω), as follows: ap2(∼ ν , ω) =

T̂

∫0 19 ⟨(αxẋ (ω , τ) + αyẏ (ω , τ) + αzż (ω , τ))· ∼

̇ (ω , τ + t ) + αyy ̇ (ω , τ + t ) + αzz ̇ (ω , τ + t ))⟩τ e−iν t dt (αxx (2) γp2(∼ ν , ω) ÄÅ T̂ ÅÅÅÅ ÅÅ 1 ÅÅ ⟨(αxx = ̇ (ω , τ ) − αyy ̇ (ω , τ ))·(αxx ̇ (ω , τ + t ) − αyy ̇ (ω , τ + t ))⟩τ 0 Å ÅÅÅ 2 ÅÇ 1 + ⟨(αyy ̇ (ω , τ ) − αzz ̇ (ω , τ ))·(αyy ̇ (ω , τ + t ) − αzz ̇ (ω , τ + t ))⟩τ 2 1 + ⟨(αzz ̇ (ω , τ ) − αxx ̇ (ω , τ ))·(αzz ̇ (ω , τ + t ) − αxx ̇ (ω , τ + t ))⟩τ 2

∫

+ 3⟨αxy ̇ (ω , τ )·αxy ̇ (ω , τ + t )⟩τ + 3⟨αxz ̇ (ω , τ )·αxz ̇ (ω , τ + t )⟩τ ÑÉÑ ÑÑ ÑÑ ∼ + 3⟨αyz ̇ (ω , τ )·αyz ̇ (ω , τ + t )⟩τ ÑÑÑe−iν t dt ÑÑ ÑÑ ÑÖ

(3)

The integrals run over the total BOMD simulation time T̂ . Taking the time derivative α̇ of the dynamic polarizability tensor α is equivalent to a factor of ν̃2 outside of the Fourier transform.33 The complex autocorrelation function can be expressed in terms of real autocorrelations, as shown in eq 2 in the SI. Finally, the resonance Raman spectrum I(ν̃,ω) at laser frequency ω can be expressed as a linear combination of the two invariants a2p(ν̃,ω) and γ2p(ν̃,ω), where the coefficients X and Y depend on the scattering geometry and polarization and can be found in the literature. Common choices for (X;Y) are (0;3) for orthogonal polarization, (45;4) for parallel polarization, and (45;7) for unpolarized setups.57

1. METHOD Our newly proposed method is based on a BOMD simulation of the bulk phase system of interest. Along the BOMD trajectory, snapshots of the system are stored in equidistant intervals. For each of those snapshots, a separate RT-TDDFT calculation is started. The initial wave function is optimized under the influence of an external periodic electric field, which is switched off in the beginning of the RT-TDDFT run, so that the electron density starts to fluctuate (step response). During the RT-TDDFT run, the temporal development of the total electron density is stored in compressed BQB format56 and subsequently processed with our Voronoi integration scheme36 to yield time series of molecular electric dipole vectors μ(τ,t) with BOMD time t and RT-TDDFT time τ. The Fourier transform of the three dipole vector components yields three entries of the molecular dynamic polarizability tensor. To obtain the full dynamic polarizability tensor αij(ω,t) for each molecule (with ω the incident laser frequency and t the time along the BOMD trajectory), three RT-TDDFT runs are performed from initial wave functions optimized under external fields in X, Y, and Z directions: T τ 2 1 αij(ω , t ) = (μi (τ , t ) − μi0, j (t ))e(−c T ) e−iωτ dτ ∫ |E| 0

I(∼ ν , ω) =

(ω − ∼ ν )4 h · hc∼ ν 8ε02ckBT ∼ ν 1 − exp − k T

(

( ))

·

B

1 (X ·ap2(∼ ν , ω) + Y ·γp2(∼ ν , ω)) 45

(4)

As the RT-TDDFT run yields the dynamic polarizability tensor over the full frequency range (see eq 1), we obtain the resonance Raman spectra for all possible laser wavelengths ω from eq 4 in one pass. This is a clear advantage over other methods, where the resonance Raman intensities are often computed for a single laser wavelength per pass. The low-

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DOI: 10.1021/acs.jctc.9b00512 J. Chem. Theory Comput. 2019, 15, 3901−3905

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Journal of Chemical Theory and Computation frequency part of the polarizability is correctly reproduced and matches the static polarizability obtained via finite electric field differences. Therefore, also the nonresonant Raman spectrum is correctly obtained from our approach. We implemented the methodology in our freely available open-source program package TRAVIS.58

2. RESULTS AND DISCUSSION To validate our methodology, we performed ab initio molecular dynamics simulations of several systems using density functional theory with the BLYP-D3 exchange− correlation functional, as implemented in the CP2k program package.59 The computational details as well as computed fullrange spectra (Figures S2−S5) can be found in the SI. A worthwhile model system for resonance Raman spectroscopy is uracil. It is commonly found in biological samples, possesses electronic excitations of relatively low energy, and offers several hydrogen bond donor and acceptor positions to interact with solvent molecules. Therefore, we employ an aqueous solution of uracil as an example system here. To demonstrate the importance of the solvent effect for this system, we also performed a simulation of uracil in gas phase. All computed spectra are presented without any empirical scaling or shifting. In Figure 1, we compare our nonresonant AIMD-based spectra of uracil in gas phase and aqueous solution to a

Figure 2. AIMD-based resonance Raman spectrum of uracil in gas phase and water compared to experiment61 (AIMD at 3.65 eV/340 nm, experiment at 4.66 eV/266 nm, experimental spectrum in arbitrary units). Note the increased absolute intensity compared to Figure 1.

hybrid functionals, where the agreement between experimental and computed excitation energies is known to be far better. Similarly to the nonresonant case above, the predicted spectrum of the gas phase system (green curve in Figure 2) shows some significant deviations from experiment (red curve), while the bulk phase simulation (black curve) is in very good agreement with the experimental spectrum. We conclude that for both nonresonant and resonance Raman spectra, it is definitely required to take the solvent influence explicitly into account in the case of uracil. When comparing the ordinate axes of Figures 1 and 2, it is visible that the absolute signal intensity is increased by around 3 orders of magnitude due to the resonance Raman effect, as also observed in experiment.61 In addition to uracil, we computed resonance Raman spectra for o-nitrophenol in gas phase. Resonance Raman spectra of this system have been investigated in the literature before,49,53 in particular also by means of RT-TDDFT within the staticharmonic approximation.53 In the upper panel of Figure S6 in the SI, we compare the spectra from our approach to these previously reported results. As explained above, our method does not require a set of laser energies as input but yields the resonance Raman spectra for all possible laser energies in one pass. In the lower panel of Figure S6 in the SI, we present the set of all such spectra for o-nitrophenol, with the laser energy on the ordinate axis, and the vibrational frequency shown on the abscissa. Such a contour plot of all resonance Raman spectra is very helpful to understand the coupling between vibrational and electronic modes and maybe even to design more insightful resonance Raman experiments by selectively choosing certain laser energies.

Figure 1. AIMD-based nonresonant Raman spectrum of uracil in gas phase and water compared to experiment60 (all three at 1.17 eV/1060 nm; experimental spectrum in arbitrary units).

nonresonant Raman experiment.60 While the gas phase simulation (green curve) deviates strongly from the experimental spectrum (red curve), the bulk phase system (black curve) shows a nice agreement with experiment. Even if resonance effects do not play a role, it is therefore mandatory to perform bulk phase simulations in order to correctly predict the Raman spectrum of uracil. As the next step, we discuss the resonance Raman spectrum. In Figure 2, we show the AIMD-based spectra of uracil in gas phase and aqueous solution together with an experimental resonance Raman spectrum.61 While the experiment was conducted with a laser energy of 4.66 eV/266 nm, we used a value of 3.65 eV/340 nm in our prediction. This difference can be explained by the fact that GGA functionals often underestimate electronic excitation energies and is therefore not related to our method. Our approach works also with

3. CONCLUSION By using our novel approach, it is now possible to directly compute resonance Raman spectra of bulk phase systems. This has not been achieved before to the best of our knowledge, therefore constituting an important contribution to the field of computational vibrational spectroscopy. In contrast to existing methods, our approach includes the full solvent influence and some anharmonic effects. We have computed the resonance Raman spectrum of an aqueous solution of uracil and find that 3903

DOI: 10.1021/acs.jctc.9b00512 J. Chem. Theory Comput. 2019, 15, 3901−3905

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(10) Gao, Y.; Martin, T. P.; Thomas, A. K.; Grey, J. K. Resonance Raman Spectroscopic- and Photocurrent Imaging of Polythiophene/ Fullerene Solar Cells. J. Phys. Chem. Lett. 2010, 1, 178−182. (11) Zedler, L.; Guthmuller, J.; Rabelo de Moraes, I.; Kupfer, S.; Krieck, S.; Schmitt, M.; Popp, J.; Rau, S.; Dietzek, B. ResonanceRaman Spectro-Electrochemistry of Intermediates in Molecular Artificial Photosynthesis of Bimetallic Complexes. Chem. Commun. 2014, 50, 5227−5229. (12) Faust, A.; Amit, Y.; Banin, U. Phonon-Plasmon Coupling and Active Cu Dopants In. Indium Arsenide Nanocrystals Studied by Resonance Raman Spectroscopy. J. Phys. Chem. Lett. 2017, 8, 2519− 2525. (13) Friebel, D.; Louie, M. W.; Bajdich, M.; Sanwald, K. E.; Cai, Y.; Wise, A. M.; Cheng, M.-J.; Sokaras, D.; Weng, T.-C.; Alonso-Mori, R.; Davis, R. C.; Bargar, J. R.; Nørskov, J. K.; Nilsson, A.; Bell, A. T. Identification of Highly Active Fe Sites in (Ni,Fe)OOH for Electrocatalytic Water Splitting. J. Am. Chem. Soc. 2015, 137, 1305−1313. (14) 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. (15) Daněcě k, P.; Kapitán, J.; Baumruk, V.; Bednárová, L.; Kopecký, V., Jr; Bouř, P. Anharmonic Effects in IR, Raman, and Raman Optical Activity Spectra of Alanine and Proline Zwitterions. J. Chem. Phys. 2007, 126, 224513. (16) Jacob, C. R.; Reiher, M. Localizing Normal Modes in Large Molecules. J. Chem. Phys. 2009, 130, 084106. (17) 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. (18) Bloino, J.; Biczysko, M.; Barone, V. Anharmonic Effects on Vibrational Spectra Intensities: Infrared, Raman, Vibrational Circular Dichroism, and Raman Optical Activity. J. Phys. Chem. A 2015, 119, 11862−11874. (19) 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. (20) Luber, S.; Reiher, M. Intensity-Carrying Modes in Raman and Raman Optical Activity Spectroscopy. ChemPhysChem 2009, 10, 2049−2057. (21) 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. (22) 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. (23) Heislbetz, S.; Rauhut, G. Vibrational Multiconfiguration SelfConsistent Field Theory: Implementation and Test Calculations. J. Chem. Phys. 2010, 132, 124102. (24) Silvestrelli, P. L.; Bernasconi, M.; Parrinello, M. Ab Initio Infrared Spectrum of Liquid Water. Chem. Phys. Lett. 1997, 277, 478− 482. (25) Pasquarello, A.; Car, R. Dynamical Charge Tensors and Infrared Spectrum of Amorphous SiO2. Phys. Rev. Lett. 1997, 79, 1766−1769. (26) Bernasconi, M.; Silvestrelli, P. L.; Parrinello, M. Ab Initio Infrared Absorption Study of the Hydrogen-Bond Symmetrization in Ice. Phys. Rev. Lett. 1998, 81, 1235−1238. (27) Handgraaf, J.-W.; Meijer, E. J.; Gaigeot, M.-P. DensityFunctional Theory-Based Molecular Simulation Study of Liquid Methanol. J. Chem. Phys. 2004, 121, 10111−10119.

it is in very good agreement with experiment. On the other hand, a predicted gas phase spectrum of uracil strongly deviates from the experimental spectrum, emphasizing the importance of explicitly including solvent interactions. Our approach does not require a set of laser energies as an input but yields the resonance Raman spectra for all possible laser energies in one pass. Furthermore, our methodology is not limited to GGA functionals. As it is known that GGA functionals underestimate electronic excitation energies, an even better agreement to experimental results can be expected from using hybrid functionals. Only open-source software has been used within this work; all presented methods have been implemented in our freely available open-source program package TRAVIS.58 A tutorial on computing bulk phase resonance Raman spectra is available at https://brehm-research.de/spectroscopy.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jctc.9b00512.

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Computational details, full-range spectra, and discussion of o-nitrophenol (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

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

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.B. acknowledges financial support by the DFG through project Br 5494/1-1.

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