Assignment of Infrared-Active Combination Bands in the Vibrational

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Article Cite This: J. Phys. Chem. A 2019, 123, 5613−5620

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Assignment of Infrared-Active Combination Bands in the Vibrational Spectra of Protonated Molecular Clusters Using Driven Classical Trajectories: Application to N4H+ and N4D+ Reagan Hooper, Dalton Boutwell, and Martina Kaledin* Department of Chemistry & Biochemistry, Kennesaw State University, 370 Paulding Avenue NW, Box # 1203, Kennesaw, Georgia 30144, Unites States Downloaded via NOTTINGHAM TRENT UNIV on August 13, 2019 at 12:45:28 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: We investigate the utility of the driven molecular dynamics (DMD) approach to complex molecular vibrations by applying it to linear clusters with several degenerate vibrational modes and infrared (IR) intense combination bands. Here, the prominent features in N4H+ and N4D+ IR spectra, reported and described by others previously, have been characterized for the first time by DMD using recently published high-level potential and dipole moment surfaces. Namely, the calculations closely correlate the parallel proton stretch vibration in N4H+, at 750 cm−1, with the one observed experimentally at 743 cm−1. Second, the intense IRactive combination bands found in experimental spectra within 900−1100 cm−1 have been properly recovered by DMD at 950 cm−1 as strongly IR-active and confirmed as consisting of H+ asymmetric stretch and N2···N2 intermolecular symmetric stretch modes. Furthermore, we show that certain combination bands involving overtone transitions may be recovered by DMD using a hard-driving regime, such as the 1409 cm−1 band measured in N4H+, revealed by DMD at 1375 cm−1, and assigned to a progressive combination of the parallel H+ stretch and two quanta of N2···N2 stretch, in agreement with quantum mechanical studies reported previously by others.

1. INTRODUCTION Gas-phase molecular synthesis in interstellar clouds is believed to occur via ion−molecule reactions.1 Over 160 molecular species have been identified in the interstellar medium.2 Characterization of ion−molecule complexes using molecular spectroscopy facilitates their detection. Infrared spectroscopy has contributed significantly to understanding the structure and chemical bonding properties of molecular ions. In this spirit, studies of vibrational transitions allow the identification of reaction intermediates and provide detailed information about the types and strengths of the chemical bonds. For moderate-size molecules, theoretical simulations of vibrational spectra are computationally feasible and may yield information in the spectral ranges that are not directly accessible experimentally. An excellent example of such species is N4H+ and its deuterium substituted isotopologue. The first high-resolution infrared (IR) spectrum of N4H+ was reported by Linnartz et al.3 They assigned the asymmetric NN stretching vibration at 2352.2 cm−1 and concluded that N4H+ has a centrosymmetric linear structure whose equilibrium dissociation energy De for fragmentation into N2 and N2H+ was estimated to be 5911 cm−1 at the CCSD(T)/aug-ccpV5Z level of theory.3 The follow-up theoretical investigations of a series of proton-bound cluster ions by Botschwina et al.4 predicted the potential energy surface (PES) of N4H+ to be strongly nonharmonic, especially so with respect to parallel proton stretching motion. According to their two-dimensional © 2019 American Chemical Society

(2D), three-dimensional reduced dimensionality quantum mechanical model, the H+ stretching vibration occurs at 875 cm−1 (783 cm−1), whereas the corresponding normal mode, i.e., harmonic, frequency is only 99 cm−1 (see below). Using a more sensitive rare-gas tagging technique, argontagged infrared spectra of protonated nitrogen dimer and its deuterium isotopologue in the 700−4000 cm−1 range were characterized by Duncan et al.5 One of the more intense spectral features, at 743 cm−1, was assigned to the parallel proton stretch (ν4) vibration. The corresponding absorption frequency for the deuterium isotopologue was found at 547 cm−1. The most prominent band at 2349 cm−1 in the N4H+·Ar experimental spectrum was shown to correlate closely with the NN asymmetric stretch motion (ν3), which was also predicted by Linnartz et al.3 Another intense feature at 1051 cm−1 and a weaker one at 1144 cm−1 were tentatively assigned by Duncan et al.5 to the in-plane (ν6) and out-of-plane (ν6′) perpendicular proton bending modes, respectively. The 1051 cm−1 feature, however, was alternatively proposed to be a combination band of parallel H+ motion and the symmetric N2···N2 stretch.5 In the Ar-tagged experiment, the assignment of the weak feature at 1409 cm−1 was uncertain. Duncan et al.5 speculated that this feature, similar to its bright 1051 cm−1 companion, was either a Received: May 10, 2019 Revised: June 8, 2019 Published: June 10, 2019 5613

DOI: 10.1021/acs.jpca.9b04480 J. Phys. Chem. A 2019, 123, 5613−5620

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H3O2− 18). We demonstrate this here on more challenging N4H+ and N4D+ ions with a linear geometry and degenerate bending modes.

combination band involving the perpendicular proton stretch (ν6) with the N2···N2 intermolecular symmetric stretch (ν2) vibration or an IR progression ν4 + nν2 (n = 0, 1, 2) involving parallel proton stretch and N2···N2 symmetric intermolecular stretch modes. Terrill and Nesbitt6 reported calculations of anharmonic frequencies for strongly coupled symmetric and asymmetric proton stretching modes in isoelectronic OC−H+ −CO and N2−H+−N2 complexes using a 2D reduced dimensionality model involving two coordinates: large-amplitude asymmetric proton stretch and symmetric heavy diatom−diatom stretch coordinates. The symmetric and asymmetric stretch fundamental frequencies for N2−H+−N2 were predicted at 387 and 849 cm−1, respectively, similar to the previous theoretical study by Botschwina et al.,4 but were overestimated compared to the experimental values.5 Lee et al. investigated the vibrational modes of N4H+/N4D+ complexes experimentally using p-H2 and n-D2 matrix isolation IR absorption spectroscopies.7 Also, they carried out discrete-variable representation (DVR) calculations of the IR spectra based on a CCSD/aug-ccpVDZ potential and dipole and an approximate, i.e., normal mode, Hamiltonian.7 The used level of electron correlation, however, did not yield the correct symmetric (D∞h) linear structure for the N4H+ complex, which may be attributed to the missing triple excitations in the CC expansion. Nevertheless, the DVR calculations provided useful assignments of certain combination bands N−H+−N/N2···N2, ν4 + nν2 (n = 1, 2). On the other hand, some low-frequency N2···N2 bending modes and high-frequency N−N stretch modes were notably overestimated compared to their experimental observations,7 VCI/VSCF quantum studies,8 and Duncan et al. measurements.5 The latter issue, while potentially nonimportant for the high-frequency modes, may reflect the neglect of vibration− rotation coupling of the normal mode Hamiltonian in the lower-frequency modes. A semiglobal full-dimensional CCSD(T)-F12b/aug-ccpVTZ potential energy and corresponding MP2/aug-ccpVTZ dipole moment surfaces (DMSs) have been published for N4H+.8 Variational basis set calculations8 of the vibrational spectra using the VSCF/VCI method9−12 and a six-mode potential representation yielded the asymmetric proton stretch at 759 cm−1 and H+ bending modes at 1165 cm−1. These calculations also found a weak feature at 1014 cm−1, which was assigned to a combination band consisting of the proton asymmetric stretch and N2···N2 trans bending modes (ν4 + ν5). In the present paper, the authors report new classical trajectory calculations of the IR spectra, specifically, in the near-infrared range, and a novel way to make spectral assignment using driven classical trajectories. The driven MD method was used recently to interpret some weakly IR-active modes in H7O3+ and H9O4+, although in the terahertz region.13 Equilibrium MD provides a reasonable estimate of the IR spectrum14,15 (and we use it too in our calculations), including fundamentals and possibly some combinations; examples include H5O2+, where we observed a combination in MD spectra in good agreement with the experiment.16,17 However, the intensities of combinations are severely underestimated due to the nonlinearity of dipole and the sampling of the dipole surface. Thus, many combinations may appear missing in MD. However, driven molecular dynamics (DMD) solves this problem by coupling dipole derivatives directly to nuclear motion and doing the correct sampling by letting the molecule execute motion far beyond the local minimum (see H5O2+,16,17

2. COMPUTATIONAL METHODS All trajectory calculations for N4H+ and N4D+ were done using highly accurate interaction potential and dipole moment surfaces in the analytical forms at the CCSD(T)-F12b/augcc-pVTZ and MP2/aug-cc-pVTZ levels of theory, respectively,8 while those for the Ar-tagged species were done using the direct MP2/aug-cc-pVDZ level of theory. All electronic structure calculations reported in this work were done using Gaussian 09.19 MD trajectories for N4H+ and N4D+ complexes were run at constant energy (NVE) and zero total angular momentum. In total, 20 trajectories were generated randomly and propagated up to 20 ps using the velocity-Verlet integrator with a time step of 0.5 fs at energies correlating to temperatures 50 and 100 K. The IR spectra were calculated by the Fourier transform of the dipole−dipole correlation functions recorded along the trajectories and time-averaged16 to yield a better-converged spectrum 1 1 Re ∞ I(ω) = ∫ dt eiωt ⟨μ0 ·μt ⟩ (1) π 0 To better describe peak intensity in the higher-frequency regions, in which proton motion is also involved, the classically derived spectral function, I (eq 1), was corrected by a quantum mechanical frequency-dependent factor20 equal to ω/[1 − exp(−ω/kT)], where ω is the frequency. The full-nonharmonic analysis was performed with the DMD method.21−23 In DMD, an external, sinusoidal electric field is applied to cause resonant absorptions of a molecule. The time-dependent Hamiltonian thus consists of the molecular Hamiltonian, H0, and a time-dependent driving term, U(q,t;ω) H(p, q, t ; ω) = H0(p, q) + U (q, t ; ω)

(2)

where q and p represent the 3N atomic Cartesian coordinates and momenta, respectively, ω is the driving frequency, and t is the time. The time-dependent term 1

1

U (q, t ; ω) = μ (q) ·ε (t ; ω)

(3)

1

is the molecule’s dipole μ (q) energy in the oscillating electric 1 1 field, given by ε (t;ω) = ε0 sin(ωt), whose direction and 1

strength are determined by ε0 . The equations of motion are appropriately modified for the driving term, as follows 1 p ∂H 1 qi̇ = 1 = i ∂pi mi 1̇

pi = −

∂H ⎯⇀

∂ qi

⎯⇀

= fi −

i = 1, 2, ... N

⎯⇀ ⎯

∂μ

⎯⇀ ⎯⇀ ε0

sin(ωt )

∂ qi

(4)

qi̇ and 1 where 1 pi ̇ represent time derivatives of atomic Cartesian 1 coordinates and momenta, respectively, and fi is the force. The dipole derivatives and the forces are computed along the trajectory. In our approach, a DMD trajectory starts at the 5614

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3. RESULTS AND DISCUSSION We first identified the two main stationary points on the PES: the linear symmetric minimum structure and the T-shaped N2 rotation transitional state, shown in Figure 1. The linear

global minimum on the potential energy surface with zero velocities, and thus the zero total angular momentum condition is enforced. The magnitude of the external field is used to calibrate the timescale of the molecule’s response to the driving force. It has been well documented that at resonant absorption, the average internal energy of the molecule rapidly increases, while off resonance, it is relatively small and oscillatory.16 For example, at a resonant driving frequency (ω = ωn), the molecular motion induced by a weak force will correspond to normal mode n, before a significant amount of energy has been absorbed, while a stronger driving force causes rapid absorption of energy and induces anharmonic motion.16 Infrared activity is measured as the total, averaged, absorbed energy along a trajectory, as follows IDMD = ⟨H0⟩ = [1/t ]

∫0

t

H0(q(t ′), p(t ′))dt ′

(5)

The DMD simulations were run up to 5 ps with the 0.5 fs time step in the frequency range from 200 to 1300 cm−1 with the frequency step 25 cm−1 and for all N4H+ harmonic frequencies. Spatial averaging was done to reflect the molecule’s arbitrary orientation in the laboratory frame.23 This required integrating several dipole-driven trajectories with the electric field direction sampled on a spherical polar grid. Due to high molecular symmetry, a coarse grid of two polar and three azimuthal angles was used resulting in six different orientations weighted accordingly. In specific cases, however, the controlled orientation of the field vector in the DMD simulations enabled us to distinguish between the stretching modes (along the molecular axis) and bending modes, and combination bands as a mixture of stretch/bending modes as allowed by molecular symmetry. Additional calibration of field magnitude revealed that 25 mV/bohr resulted in the moderate amplitude of motion of protonated nitrogen dimer and a considerable amount of energy being absorbed; thus, this was the choice for the majority of our DMD simulations, except certain instances, which will be mentioned separately. In addition to the set of the normal coordinates, we defined a set of bond-angle valued coordinates, which were used previously.8 The symmetric internal coordinates, s, were monitored along the DMD trajectories to visualize and assign the vibrational modes

Figure 1. N4H+ linear minimum (upper) and T-shape transition-state (lower) molecular geometry.

structure of N4H+ is favored over the T-shaped structure due to the anisotropic charge distribution in the N2 molecule.24 N2 shows negative electrostatic potential (ESP) at bond ends and positive ESP around the cylindrical bond surface.24 Therefore, the linear structure is the most stable since the electrostatically negative surface at the bond end in N2 favorably interacts with H+. The T-shaped structure represents the transition state for N2 rotation in N4H+. The electrostatic potential maps are shown in the Supporting Information (Figure 1S). Our calculations using the CCSD(T)/aug-cc-pVTZ level of theory find the barrier to N2 rotation at 5028 cm−1 (zero-point energy-corrected value) above the minimum. This is 1470 cm−1 below the dissociation limit (D0 = 6498 cm−1), yet probably too high to yield clearly measurable tunneling splittings. We also found no evidence for strong N2 rotational excitation in our trajectory simulations. Nonharmonicity of the shared proton stretch vibration of protonated water clusters has been a subject of numerous theoretical and experimental studies, including our work on H+(H2O)n (n = 2−4).13−17,22,25,26 Previous studies established that Ar atom perturbs the symmetrical structure of the isolated H5O2+ complex.16,26 The bridging proton stretch in H5O2+ at 1000 cm−1 was blue-shifted by about 100 cm−1 in the argontagged complex H5O2+·Ar.16 The binding energy of argon to H5O2+ is slightly higher, 1121 cm−1, compared to the binding energy of argon to N4H+, 836 cm−1, calculated at the CCSD(T)/aug-cc-pVTZ level of theory (Table S1). Table 1 summarizes vibrational frequencies obtained from the high-level full-dimensional PES and DMS surfaces8 using the normal mode analysis and DMD, VSCF/VCI,8 DVR7 methods, and available experimental measurements.5,7 The averaged dipole spectra of N4H+/N4D+ corrected by the quantum effect factor20 are shown in Figure 2. For comparison, Figure 3 shows the IR spectra for bare N4H+/N4D+ ions and Ar-tagged complexes. The sticks in the spectra are the harmonic frequencies. The asymmetric-stretch-shared proton vibration, ν4 (σu) in N4H+ is strongly anharmonic due to the shape of the potential energy surface.3,8 The harmonic frequency is 99 cm−1 (Table 1), while the accurate quantum studies predict this mode to be

s1(σg) = r(N1 − N3) + r(N2 − N4)

s2(σu) = r(N1 − N3) − r(N2 − N4) s3(σg) = r(H5 − N3) + r(H5 − N4) s4(σu) = r(H5 − N3) − r(H5 − N4) s5,6(πg , xz , yz) = a(N1 − N3 − H)y , x + a(N2 − N4 − H)y , x

s7,8(πu , xz , yz) = a(N3 − H − N4)y , x

s9,10(πu , xz , yz) = a(N1 − N3 − H)y , x − a(N2 − N4 − H)y , x

(6) 5615

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The Journal of Physical Chemistry A Table 1. N4H+-Calculated and Experimental Vibrational Frequencies (in cm−1)a this work harmonic ν1 ν3 ν6 ν4 ν2 ν5 ν7 2ν2 ν5 + ν7 ν2 + ν4 ν4 + ν5 ν6 + ν7 ν6 + ν5 2ν2 + ν4 ν2 + ν6

DMD

b

2412 2376 1223 99 436b 264b 141

theory8

this work

1225 775

125

VSCF/VCI 2335, 2376 2355.79 1165.8 758.84 385.6 260.4 146 780.3

325 950 1014.1 1329.5 1375 1510.2

theory7

exp.5

exp.7

DVR

N4H ·Ar

N4H+/p-H2

+

c

2360 2423 1144 763 378 296 240 739

2228 2350 1144 743 381c 240c 154c 780

1080 1026

1051 983 1300 1357 1409

1426 1505

2352.7 1129.6 715

762 1030

1395.5

a

The frequency labels (νi) correspond to the experimental work.5 bIR-inactive frequencies. cThese frequencies were not directly measured.

50 and 100 K, respectively (Figure 2), since higher temperatures may result in Ar dissociation. In the N4H+ spectrum, the shared proton stretch spectral region spans between 500 and 800 cm−1 showing significant anharmonicity and strong coupling with the other modes. At the lower temperature, 50 K, the most prominent peak is found at 600 cm−1, while at the higher temperature, 100 K, the spectral feature broadens up to 750 cm−1, which is in very good agreement with the experimental value 743 cm−1.5 Visual inspection of the MD-generated spectra suggests that the N−H+−N double-degenerate bending vibration (ν6) appears at 1225 cm−1, for which the corresponding harmonic value is 1223 cm−1. This double-degenerate bending mode in N4H+ is split into in-plane (a1) and out-of-plane (b1) components due to the presence of argon (Figure 3). Quantum calculations8 at the VSCF/VCI level of theory and full-dimensional potential energy and dipole surfaces, same as in the present calculations, place the N−H+−N bending vibration (ν6) at 1165.8 cm−1 in N4H+. Besides this, there are multiple peaks in the experimental spectrum5 between 780 and 1409 cm−1. Duncan et al. assigned the 780 and 1340 cm−1 peaks to overtones 2ν2 and 2ν4, respectively. The 983 cm−1 (ν4 + ν5), 1205 cm−1 (ν6 + ν7), 1300 cm−1 (ν6′ + ν7), 1357 cm−1 (ν6′ + ν5), and 1409 cm−1 (ν6 + ν2 or ν4 + 2ν2) peaks were assigned to various combination bands. Lee et al.7 measurements and mode assignment using the DVR calculations are listed in Tables 1 and 2. To clarify the spectral assignments mentioned above, extensive DMD probes of the spectral features were carried out by scanning the 75−1300 cm−1 range (Figure 4). The analysis reveals that the DMD calculations correlate, with remarkable accuracy, the strongly nonharmonic parallel proton stretch ν4 vibration in N4H+, found at 775 cm−1, with the one observed experimentally at 743 cm−1. More interestingly, the intense IR-active feature originally reported in the experimental spectrum measured by Duncan et al. at 1051 cm−1 and provisionally assigned to either a N−H+−N bend fundamental or a N−H+−N/N2···N2 stretch combination is recovered by DMD at ∼950 cm−1. The 950 cm−1 feature is barely noticeable in the equilibrium MD spectra at 50 and 100 K (Figures 2 and 3), although at the higher temperature, the activity appears to increase. We note that the MD-generated spectra using eq 1

Figure 2. Equilibrium MD analytical PES dipole spectra of N4H+ and N4D+ at 50 K (in blue) and 100 K (in red). A semiglobal fulldimensional potential energy surface and corresponding dipole moment surface were used from reference.8 The harmonic frequencies are shown as sticks.

Figure 3. Direct equilibrium MD MP2/AVDZ dipole spectra of N4H+ and N4H+. Ar and their deuterium analogues at 50 K (in blue) and 100 K (in red). The harmonic frequencies are shown as sticks.

at 758 cm−1 and the experimental Ar-tagged value is 743 cm−1.5 The MD simulations for bare ions N4H+/N4D+ presented in this work were obtained at two temperatures, 5616

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The Journal of Physical Chemistry A Table 2. N4D+-Calculated and Experimental Vibrational Frequencies (in cm−1)a this work harmonic ν1 ν3 ν6 ν4 ν2 ν5 ν7 2ν2 ν5 + ν7 ν2 + ν4 ν4 + ν5 v6 + ν7 ν6 + ν5 2ν2 + ν4

this work DMD

theory7 DVR

b

2412 2376 893 70 436b 264b 137

exp.5 +

N4D .Ar

exp.7 N4D+/n-D2

c

875 525

2425, 2435 845 499 377

125

2230 2349 817, 853 547 312c 251c 150c

2356.2 825.5 494

739.1 325 700

833

840.7

Figure 5. Average absorbed energy (in cm−1) and symmetric internal coordinates s1−10 along the N4H+ DMD trajectories for ν4 = 775 cm−1. The intensity of the electric field was 25 mV/bohr.

967 1068 1100

1168

a

The frequency labels (νi) correspond to the experimental work.5 b IR-inactive frequencies. cThese frequencies were not directly measured.

Figure 6. Average absorbed energy (in cm−1) and symmetric internal coordinates s1−10 along the N4H+ DMD trajectories for ν2 + ν4 = 950 cm−1. The intensity of the electric field was 25 mV/bohr.

executing only small displacements (s1−s4), but after 1 ps, the energy was absorbed rapidly and N2···N2 displacements (s3) were prominent, while those of the bending coordinates remained relatively small. This time delay observed above is typical for combination bands.13,17 We conclude that the 950 cm−1 mode is a combination band consisting of H+ asymmetric stretch and N2···N2 intermolecular symmetric stretch modes. Lee et al.7 also observed this band at 1030 cm−1 and computed at 1080 cm−1 by the DVR method (Table 1). VSCF/VCI quantum studies8 found a weak band at 1014 cm−1 assignable to parallel H+ stretch and N2···N2 trans bending modes (ν4 + ν5). To further elucidate the nature of the 775/950 cm−1 features and to address the issue of the weak IR activity in the MD calculations reported in the present work, we examine the dipole derivative along the resonant trajectory for N4H+ at 950 cm−1. In Figure 7, we show the magnitude of dipole’s first derivative vector with respect to proton’s coordinates (the dominant motion at this frequency). As evident from the plot, the derivative’s magnitude is strongly oscillatory. This indicates that the dipole function itself is highly nonlinear, i.e., having a substantial contribution from quadratic, cubic, etc. terms, and, moreover, the nonlinear terms appear to dominate its surface as oscillation increases with the absorbed energy, which is to say with displacement from the global minimum. Since the dipole’s derivative directly couples to atomic velocities (see eqs

Figure 4. Driven MD simulations: average absorbed energy of N4H+ and N4D+ as a function of driven frequency. The spectrum was scanned from 75 to 1300 cm−1 with a frequency step of 25 cm−1. The intensity of the electric field was 25 mV/bohr. The harmonic frequencies are shown as sticks.

may reveal true combination bands, as was demonstrated for H5O2+.17 The atomic motion was monitored along the DMD trajectories in terms of the four stretching s1−s4 and six bending s5−s10 coordinates (eq 6) and mode assignment made based on their time evolution, as shown in Figures 5 and 6. The identified positions of the maxima of corresponding peaks in the N4H+ DMD spectra are at 775 and 950 cm−1 (Figure 4). These frequencies absorbed a significant amount of energy, 800 and 500 cm−1, respectively, leading to large atomic displacements. The internal coordinate profiles for the trajectories driven at 775 and 950 cm−1 exhibit large N2···N2 intermolecular and N−H+−N parallel displacements (s3 and s4 coordinates). Based on the atomic coordinates for the driven trajectories, it can be concluded that both 775 and 950 cm−1 resonant frequencies have a significant asymmetric H+ stretch component. The 775 cm−1 driven trajectory absorbed energy rapidly (Figure 5), and after 3 ps, the shared proton executed both parallel stretch and bending motion. The trajectory driven at 950 cm−1 did not absorb energy up to 1 ps (Figure 6), 5617

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⎯⇀

Figure 7. Dipole derivatives for 775 and 950 cm−1 vibrations. The electric field (ε0 = 25 mV/bohr) was oriented along the molecular axis.

two quanta of N2···N2 intermolecular symmetric stretch modes. Our assignment is consistent with the DVR calculations. IR spectra were also reported for the D-substituted isotopologue by Duncan et al.5 and tentatively assigned using the normal mode analysis. Only two vibrational modes were notably affected by the H+/D+ isotopic substitution: the shared proton vibration in the parallel (H+ stretch) and perpendicular directions (H+ bend). The MD spectra presented in Figure 2 of N4D+ display the N−D+−N bending mode at 865 cm−1, and the isotopic shift is about 335 cm−1. The broad spectral region that corresponds to shared proton vibration is red-shifted by about 200 cm−1 with the maximum at 550 cm−1. The corresponding experimental value was derived from the combination band (ν3 + ν4) as 547 cm−1.5 The H+/D+ isotopic shift is well described by MD. The N4D+ fundamental asymmetric proton stretch (ν4) and bending (ν6) modes were found at 525 and 875 cm−1, respectively, in the DMD scan (Figure 4). The combination band (ν2 + ν4) assigned to N−H+−N/N2···N2 stretch was recovered at 700 cm−1. Additional scan between 1000 and 1200 cm−1 using higher electric field strength, 75 mV/bohr, confirmed the combination band (2ν2 + ν4) at 1100 cm−1. The SI document provides additional information (Figures 2S−6S) to support the mode assignment listed in Table 2. The N4H+·Ar experimental work5 offers multiple values for low frequencies derived from combination bands. Lowfrequency modes corresponding to the N2···N2 intramolecular symmetric stretch (σg), N2···N2 symmetric bend (trans, πg), and antisymmetric bend (cis, πu) modes were assigned using the harmonic analysis and compared to the experiment.5 The intense peak at 325 cm−1 in the N4H+ MD spectrum does not shift upon deuteration (Figure 2). Its intensity decreases with temperature. DMD scans revealed the spectral feature at 325 cm−1 with a smaller intensity (Figure 4). We speculate that this feature consists of N2···N2 (cis/trans) bending modes ν5 + ν7 due to large bending displacements (s6−s10) (Figure 9). Neither the quantum calculations7,8 nor experiment5,7 described this low-frequency mode, leaving this region of the spectrum open to interpretation.

2−4) and is the cause of resonant activity, it is understandable why the 950 cm−1 peak is strongly resonant in the DMD calculations. For this reason, the weak activity captured in MD is plausibly explained by the much smaller displacements from the minimum of the NVE ensembles at the thermal energies of 313 and 626 cm−1 corresponding to temperatures 50 and 100 K and consequently insufficient sampling of the DMS surface. The assignment of the weak feature in the experimental spectrum of N4H+·Ar at 1409 cm−1 remains uncertain. This feature was not IR-active in the VSCF/VCI calculations.8 The DVR calculations assigned this spectral feature to a combination band consisting of H+ asymmetric stretch and two quanta of N2···N2 symmetric stretch. The DMD simulations described here with the 25 mV/bohr field strength show no discernible absorption of energy in the region between 1300 and 1550 cm−1. However, additional scans with the field strength of 75 mV/bohr revealed absorption at 1375 cm −1 (Figure 8). Analysis of the symmetric internal

Figure 8. Average absorbed energy (in cm−1) and symmetric internal coordinates s1−10 along the N4H+ DMD trajectories for 2ν2 + ν4 = 1375 cm−1 frequency. The intensity of the electric field was 75 mV/ bohr.

coordinates identified large N−H+−N/N2···N2 stretch displacements, while all of the bending internal coordinates were relatively small. At such high intensity of the electric field, the molecule absorbed energy rapidly, leading to dissociation of the N4H+ complex to N2H+ and N2 (see s3 and s4 coordinates). Based on this, we conclude that the 1375 cm−1 mode is a combination band consisting of H+ asymmetric stretch and

4. SUMMARY In this paper, equilibrium and driven MD simulations of IR spectra for N4H+ and N4D+ are reported using highly accurate PES and DMS surfaces. The equilibrium MD simulations 5618

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Martina Kaledin: 0000-0003-1763-3552 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.K. thanks Prof. Joel Bowman and Dr. Qi Yu for providing the codes for the analytical potential energy and dipole surfaces. M.K. also thanks Advanced Computer Services at Kennesaw State University for providing a high-performance computing platform and the College of Science and Math at Kennesaw State University for providing support under Research Stimulus Program (RSP) Incentive Funding.

Figure 9. Average absorbed energy (in cm−1) and symmetric internal coordinates s1−10 along the N4D+ DMD trajectories for ν5 + ν7 = 325 cm−1 frequency. The intensity of the electric field was 25 mV/bohr ⎯⇀ (ε = 0.0158, 0.0, 0.0194).

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identify the parallel proton stretch vibration in N4H+ at 750 cm−1, which is in good agreement with the experimental observation of 743 cm−1. The intense IR-active mode in the DMD spectrum at 950 cm−1 has been identified as a bright mode, as observed experimentally at 10515 and 1030 cm−1,7 respectively, and assigned using the driven MD approach to a combination band consisting of H+ asymmetric stretch and N2···N2 intermolecular symmetric stretch modes. DMD simulations executed in a hard-driving regime revealed another combination band at 1375 cm−1 assigned to a progressive combination of the parallel H+ transition and two quanta of N2···N2, in agreement with DVR calculations.7 The corresponding combination modes in the N4D+ spectrum were found at 700 and 1100 cm−1, respectively, and assigned using the internal symmetric coordinate displacements. These combination modes are both strongly nonharmonic involving large-amplitude motion, and their dipole transitions are highly nonlinear, which make it a challenging case for conventional approaches, while DMD is able to recover these effects by virtue of coupling dipole’s derivative directly to the nuclear motion via an applied external field. This is important from both practical and purely theoretical standpoints, whereby we propose that dipole-driven molecular dynamics, in conjunction with analytic high-level ab initio PES and DMS functions, is capable of describing a certain type of IR activity involving low-frequency vibrational modes coupled with highly fluxional modes, such as H+ transfer, which may be inaccessible to both high-dimensionality quantum basis set calculations and equilibrium MD simulations. Further investigations of this phenomenon for related molecular ions using both DMD and its 2D-IR variant23 are currently being explored in our lab.

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REFERENCES

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.9b04480. Dissociation energies (Table S1); interatomic distances and harmonic vibrational frequencies (Tables S2 and S3); harmonic vibrational frequencies (Tables S4 and S5); interatomic distances R; rotational energy barrier and its zero-point energy-corrected value (Table S6) (PDF) 5619

DOI: 10.1021/acs.jpca.9b04480 J. Phys. Chem. A 2019, 123, 5613−5620

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