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Modeling the Histidine−Phenylalanine Interaction: The NH···π Hydrogen Bond of Imidazole·Benzene Maria A. Trachsel,† Philipp Ottiger,† Hans-Martin Frey,† Chantal Pfaffen,† Angela Bihlmeier,‡ Wim Klopper,‡ and Samuel Leutwyler*,† †

Departement für Chemie und Biochemie, Universität Bern, Freiestrasse 3, CH-3012 Bern, Switzerland Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, D-76131 Karlsruhe, Germany

‡

S Supporting Information *

ABSTRACT: NH···π hydrogen bonds occur frequently between the amino acid side groups in proteins and peptides. Data-mining studies of protein crystals find that ∼80% of the T-shaped histidine···aromatic contacts are CH···π, and only ∼20% are NH···π interactions. We investigated the infrared (IR) and ultraviolet (UV) spectra of the supersonic-jet-cooled imidazole·benzene (Im·Bz) complex as a model for the NH···π interaction between histidine and phenylalanine. Ground- and excited-state dispersioncorrected density functional calculations and correlated methods (SCS-MP2 and SCS-CC2) predict that Im·Bz has a Cs-symmetric T-shaped minimum-energy structure with an NH···π hydrogen bond to the Bz ring; the NH bond is tilted 12° away from the Bz C6 axis. IR depletion spectra support the T-shaped geometry: The NH stretch vibrational fundamental is red shifted by −73 cm−1 relative to that of bare imidazole at 3518 cm−1, indicating a moderately strong NH···π interaction. While the S0(A1g) → S1(B2u) origin of benzene at 38 086 cm−1 is forbidden in the gas phase, Im·Bz exhibits a moderately intense S0 → S1 origin, which appears via the D6h → Cs symmetry lowering of Bz by its interaction with imidazole. The NH···π ground-state hydrogen bond is strong, De=22.7 kJ/mol (1899 cm−1). The combination of gas-phase UV and IR spectra confirms the theoretical predictions that the optimum Im·Bz geometry is T shaped and NH···π hydrogen bonded. We find no experimental evidence for a CH···π hydrogen-bonded ground-state isomer of Im·Bz. The optimum NH···π geometry of the Im·Bz complex is very different from the majority of the histidine·aromatic contact geometries found in protein database analyses, implying that the CH···π contacts observed in these searches do not arise from favorable binding interactions but merely from protein side-chain folding and crystal-packing constraints. The UV and IR spectra of the imidazole·(benzene)2 cluster are observed via fragmentation into the Im·Bz+ mass channel. The spectra of Im·Bz and Im·Bz2 are cleanly separable by IR hole burning. The UV spectrum of Im·Bz2 exhibits two 000 bands corresponding to the S0 → S1 excitations of the two inequivalent benzenes, which are symmetrically shifted by −86/+88 cm−1 relative to the 000 band of benzene.

1. INTRODUCTION The five-membered aromatic heterocycle imidazole (Im) is present in the side chain of the amino acid histidine (His). The intermolecular interactions of imidazole to the phenyl and indole moieties in the side chains of phenylalanine (Phe) and tryptophan (Trp) are believed to stabilize the structures of many peptides and proteins.1−7 Nonconventional hydrogen bonds between XH donors (X = N, O, S) and the π electrons of aromatic moieties are generally of significance in structural biology1−5,8 and well documented in structural organic chemistry.8,9 NH···π contacts have been found through datamining studies of protein crystal structures, in which amine (lysine, arginine), amide (asparagine, glutamine), or imidazole (histidine) side chains are found to closely approach to aromatic rings.1−7 About 40% of all side-chain interactions of histidine involve His·Phe contacts.2 Recently, Kadam et al.10 found 29 585 histidine−aromatic side chain contacts in the PDB database of which 634 are T-shaped structures. Interestingly, 78% of these structures are CH···π contacts, while only 22% are NH···π contacts. © 2015 American Chemical Society

Using coupled-cluster [CCSD(T)] calculations, Karthikeyan and Nagase identified two energetically low-lying T-shaped NH···π forms of imidazole·benzene, which they called BzImidaD-E and BzImidaD-F.11 They also found a CH···π isomer (BzImidaD-D), but this structure is less stable because the CH bond of imidazole is much less polar than its NH bond. Popov et al. also investigated Im·Bz dimers and found that the NH···π-bonded dimer is more stable than the CH···π-bonded one.12 Mignon et al. studied the interaction of imidazole with substituted benzenes in the T-shaped, parallel-displaced, and parallel-sandwich structures at the MP2/6-31G* level of theory.13 Fourier transform infrared (FTIR) spectroscopic experiments have been performed on imidazole and several of its complexes, both in supersonic jets and in noble-gas matrices: The imidazole·water complex is found to be H bonded.14−17 Received: December 22, 2014 Revised: May 28, 2015 Published: May 28, 2015 7778

DOI: 10.1021/jp512766r J. Phys. Chem. B 2015, 119, 7778−7790

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The Journal of Physical Chemistry B

The SCS-MP2 and SCS-CC2 harmonic vibrational frequencies were computed with the def2-QZVPP basis set using the Turbomole27 NumForce script with the options “−central” and “−d 0.05”. Since these NumForce results did not seem reliable, we discretized each normal mode using 9 grid points

The imidazole dimer exhibits an NH···π hydrogen bond from the “donor” imidazole to the acceptor moiety.11,18−20 The jetcooled imidazole·indole complex has been investigated as a model for the Trp−His interaction.21 It is mainly stabilized by (indole)NH···N(imidazole) hydrogen bonding plus weaker CH···π and π-stacking interactions, which is supported by the observation that the IR spectrum exhibits a “free” NH stretch of imidazole at 3516 cm−1, very close to that of bare imidazole at 3518 cm−1.21 Below, we present and analyze the UV vibronic and infrared (IR) spectra of the supersonic jet-cooled complexes imidazole· benzene and imidazole·(benzene)2, which were measured by mass-specific resonant two-photon ionization (R2PI) spectroscopy. Their respective IR spectra were measured by the IR/UV hole burning technique. The current computations and experiments are complemented with near basis-set-limit CCSD(T) calculations of the binding energy De in ref 22. Theory and experiment agree that the ground-state (S0) geometry of imidazole·benzene has a Cs-symmetric T-shaped structure with an NH···π bond from the imidazole NH to the benzene π-electron system.

xk =

⎛ kπ ⎞ 2kBT 1 sin⎜ ⎟ ω ⎝ 16 ⎠ μ

with k = −4 ,..., 4

Here, kB is Boltzmann’s constant and μ and ω are the reduced mass and the value of the frequency, respectively, as obtained from the NumForce script. The amplitude of the grid points was set by the “temperature” T = 10 K. The harmonic vibrational frequency was subsequently obtained from a polynomial fit to the 9 points. As discussed below, the imidazole·(benzene)2+ cluster ion fragments efficiently into Im·Bz+ + Bz, so that the UV spectra of Im·Bz and Im·Bz2 both appear in the Im·Bz+ mass channel. Therefore, the ground-state equilibrium geometry of Im·Bz2 was optimized with the SCS-MP2 method and the aug-ccpVTZ and def2-QZVPP basis sets. Structure optimizations were also carried out using the same DFT methods (M06-2X, B97-D, and B97-D3) and basis sets as above. The S1 excited state was optimized with the SCS-CC2 method and the def2QZVPP basis set. Normal-mode calculations of Im·Bz2 were done on the M06-2X-, B97-D-, and B97-D3-optimized geometries using the same basis sets as for the geometry optimizations. The calculations were performed using Turbomole 6.427,28 or Gaussian09.29

2. EXPERIMENTAL AND THEORETICAL METHODS 2.1. Experimental Methods. The imidazole·benzene (Im·Bz) complexes were synthesized and cooled in a pulsed supersonic jet using Ne (Linde, ≥99.995%) carrier gas at 1.2− 1.5 bar backing pressure. The sample of benzene (Fluka, 99%) was seeded into the carrier gas using an evaporator held at from −45 to −35 °C, corresponding to 0.9−1.9 mbar benzene partial pressure. Imidazole (Sigma, ≥99.5%) was placed within the nozzle and heated to 75−80 °C, corresponding to 0.4−0.6 mbar partial pressure or about 2−3 times less than the benzene partial pressure. When further raising the benzene pressure the Im·Bz and Im·Bz2 signals increased in both the mass spectra and the resonant two-photon ionization spectra, demonstrating the expected dependence on the benzene concentration. However, the simultaneous strong increase of larger Im·(Bz)n clusters which exhibit broad unstructured spectra and dissociate into the Im·Bz+ ion channel upon excitation/ionization cover up the highly resolved R2PI spectra of Im·Bz and Im·(Bz)2 discussed below. Mass- and isomer-selected resonance two-photon ionization (R2PI) spectra and infrared (IR) depletion spectra were measured over the 3300−3700 cm−1 range. Details are given in the Supporting Information. 2.2. Computational Methods. The ground-state equilibrium geometry of the Im·Bz complex was optimized with the resolution-of-identity (RI) second-order Møller−Plesset (MP2) method in its spin-component scaled (SCS) variant with the aug-cc-pVXZ (X = T, Q) and def2-QZVPP basis sets. For the S1 state the SCS approximate second-order coupled cluster (CC2) method was employed with the aug-cc-pVXZ (X = T, Q) and def2-QZVPP basis sets. For the SCS-MP2 and SCS-CC2 calculations, the like and unlike spin components of the MP2 and CC2 energies were scaled according to Grimme.23 With a view toward normal-mode vibrational calculations we also investigated the performance of several density functional (DFT) methods that have been developed to represent intermolecular interactions, i.e., the Minnesota functional M06-2X (using the 6-31+G(d,p) basis set) and the B97-D and B97-D3 functionals with Grimme’s dispersion corrections24−26 (using the def2-TZVPP basis set).

3. COMPUTATIONAL RESULTS 3.1. Geometry Optimization and Binding Energies. 3.1.1. Imidazole·Benzene. The S0-state geometry optimizations with both the SCS-MP2 and the dispersion-corrected DFT methods predict Cs-symmetric T-shaped structures that involve an NH···π hydrogen bond from the imidazole moiety to benzene (see Figure 1a). The NH bond axis of the imidazole moiety is slightly tipped relative to the surface normal of the benzene moiety, quantified by the tipping angle ω defined in Figure 1a. Nearly all methods predict that the S0 state of the Im· Bz complex exhibits only a single NH··· π isomer, with ωe in the range between 12° and 19° (isomer A, see Table 1). The SCSMP2 method with the aug-cc-pVTZ basis set and the M06-2X method predict a second isomer, denoted B, with a negative tipping angle ωe = −10° to −18° (see Table 1). The geometries of isomer A at the SCS-MP2 level in the def2-TZVPP, def2QZVPP, and aug-cc-pVQZ basis sets are very similar; in the following we will refer to the def2-QZVPP structure. Table 1 summarizes the calculated binding energies and key geometry parameters such as the tipping angle ωe, the vertical (Rvert) and horizontal (Rhoriz) distances between the centers of mass of Im and Bz, and the surface normal distances from the benzene ring to the N and H atoms of the NH group. For isomer A, the SCS-MP2/def2-QZVPP method predicts a minimum at ωe = 11.8°, a vertical distance between the two centers of mass Rvert of 4.35 Å, and a horizontal distance Rhoriz of 0.33 Å. As indicated in Figure 1a the NH···Bz distance is 2.27 Å. The B97-D and B97-D3 values are similar to the SCSMP2 values but slightly larger (see Table 1). The counterpoisecorrected SCS-MP2/def2-QZVPP binding energy of isomer A is 1722 cm−1, which is about 165 cm−1 smaller than the best estimate of ref 22. 7779

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0.06 and 0.16 Å, respectively. The N···Bz distance remains unchanged, but the H···Bz distance is increased by 0.06 Å. The imidazole moiety of isomer B is tipped in the opposite direction. While Rvert is 0.05 Å larger than in isomer A, Rhoriz is 0.08 Å smaller. The counterpoise-corrected excited-state binding energies of isomers A and B are 1564 and 1521 cm−1, respectively. For comparison, the SCS-MP2/aug-cc-pVTZ geometry parameters of the pyrrole·benzene (Py·Bz) complex are also listed in Table 1. One sees that the additional N atom and the different orientation of the dipole moment in imidazole induce relatively small geometry changes. The tipping angle of isomer A of Im·Bz in the S0 state is 2.2° larger than that in Py·Bz at the same level of theory. The binding energy of Im·Bz is about 185 cm−1 larger than that for Py·Bz. The two isomeric forms of Im·Bz predicted by the SCS-CC2 method are interconverted along the ω tipping vibration coordinate. Therefore, there is a double-minimum potential along the ω coordinate in the S1 state. In contrast to the double-minimum potentials along the δ and ω coordinates in 2-pyridone·benzene30 and Py·Bz,31 the S1 potential for Im·Bz is asymmetric due to the asymmetry of the imidazole moiety. Figure 2 displays schematic profiles of the S0- and S1-state potentials along the ω coordinate, based on the calculated energy difference between isomers A and B and the computed excited-state barrier between isomers A and B of 114 cm−1. This barrier height is an upper bound to the true computed value, because the barrier geometry of Im·Bz had to be optimized under the constraint that the N−H bond of imidazole is perpendicular to the Bz ring and pointing toward the center of mass of benzene. 3.1.2. Imidazole·(Benzene)2. S0-state geometry optimizations were performed for Im·Bz2 with the SCS-MP2, B97-D/D3, and M06-2X methods, which all predict a cyclic sequentially H-bonded NH··· π/CH··· π/CH··· π structure, as shown in Figure 3. Table S1 (Supporting Information) summarizes the geometry parameters for this structure, where ϕe are the angles

Figure 1. (a) SCS-MP2-optimized S0 state and (b) SCS-CC2 S1 excited-state geometries of imidazole·benzene using the def2-QZVPP basis set. Two stable isomers (A and B) exist in the S1 state but only one in the S0 state. NH···Bz distances are indicated in Angstroms. Red arrow in a indicates the direction of the calculated S0 → S1 electronic transition dipole moment, the coordinate system in b indicates the three rotational (inertial) axes.

The Cs symmetric T-shaped structure is retained upon electronic excitation to the S1 state, but all methods predict two S1-state isomers (A and B) (see Figure 1b). The tipping angle of isomer A increases to 22.3°, and Rvert and Rhoriz decrease by

Table 1. Calculated Geometry Parameters and Binding Energies De for Imidazole·Benzenea ωe

Rvert

Rhoriz

N···Bz

H···Bz

De

b DCP e

11.6 17.4 19.0 −18.4 12.7 −9.5 11.8

4.37 4.37 4.27 4.30 4.31 4.33 4.35

0.35 0.48 0.62 0.53 0.34 0.20 0.33

3.27 3.30 3.22 3.22 3.22 3.22 3.26

2.28 2.34 2.26 2.26 2.23 2.22 2.27

2090 2023 1973 1939 2307 2299 1898

1705 1697 1722

c

imidazole·benzene S0 B97-D/def2-TZVPP B97-D3/def2-TZVPP M06-2X/6-31+G(d,p) M06-2X/6-31+G(d,p) (B) SCS-MP2/aug-cc-pVTZ SCS-MP2/aug-cc-pVTZ (B) SCS-MP2/def2-QZVPP CCSD(T)/CBSd best estimate (A)e S1 TD-M06-2X/6-31+G(d,p) TD-M06-2X/6-31+G(d,p) (B) SCS-CC2/aug-cc-pVTZ SCS-CC2/aug-cc-pVTZ (B) SCS-CC2/def2-QZVPP SCS-CC2/def2-QZVPP (B) pyrrole·benzene S0 SCS-MP2/aug-cc-pVTZ best estimatee

1880.9 1897.6 19.1 −18.3 22.2 −20.8 22.3 −21.0

3.87 3.96 4.25 4.29 4.29 4.34

0.03 0.05 0.16 0.10 0.17 0.09

2.82 2.86 3.21 3.23 3.26 3.28

1.83 1.87 2.28 2.28 2.33 2.34

2173 2123 1755 1705

10.5

4.33

0.28

3.23

2.24

2123

1563 1521 1563 1521 1521 1705.3

Distances in Angstroms, ωe in degrees, binding energies De in cm−1. bCounterpoise-corrected binding energy cAll values refer to isomer A except those marked (B). dReference 11. eReference 22. a

7780

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Figure 3. Two views of the imidazole·(benzene)2 cyclic minimumenergy structure, calculated at the SCS-MP2/def2-QZVPP level. H···π hydrogen-bond distances to the respective benzene or imidazole molecular planes are given in Angstroms.

Figure 2. Scheme of the S0 and S1 states of imidazole·benzene along the ω tipping coordinate. Relative energies and curvatures at the SCSCC2/def2-QZVPP level. Isomer B is a local minimum in the S1 state that does not exist in the ground state. Curvature along the ω vibrational coordinate increases by ∼10 times upon S0 → S1 electronic excitation (see also Table 2).

between the donor and the acceptor planes and R are the distances between the centers of mass. The angle ϕe for Im−Bz1 (see Figure 3) is 72.1°, for Bz1−Bz2 55.8°, and for Bz2−Im 52.7° at the SCS-MP2/def2-QZVPP level. The DFT (B97-D, B97-D,3 and M06-2X) methods predict a 0.5−2.7° smaller value for ϕe(Im−Bz1), a 1.2−1.8° larger value for ϕe(Bz1−Bz2), and a similar value for ϕe(Bz2−Im). The NH···π distance is about 0.3 Å shorter than the CH···π distances. The SCS-MP2-predicted geometry is more compact (i.e., with the three moieties closer to each other) than those predicted by the B97-D, B97-D3, and M06-2X methods. With the B97-D3/def2TZVPP method a second minimum-energy structure of Im·Bz2 is predicted, which has a double T shape with Cs symmetry, but is 1380 cm−1 less stable. 3.2. Vibrational Normal Modes. The imidazole·benzene complex has six intermolecular modes, namely, the three hindered translations, denoted tilt δ, shear χ, and stretch σ, and three hindered rotations, denoted bend β, twist θ, and tipping ω. The excited-state normal-mode eigenvectors calculated at the SCS-CC2/def2-QZVPP level are shown in Figure 4. Table 2 lists the calculated frequencies for the intermolecular normal modes and the benzene intramolecular modes of isomers A and B in imidazole·benzene. Due to the 6-fold symmetry of the benzene moiety around its C6 rotational axis, one of the Im·Bz intermolecular vibrations is a hindered internal rotation with a 6-fold-symmetric potential. The corresponding V6 barriers are very low in both the S0 and

Figure 4. SCS-CC2/def2-QZVPP-calculated S1-state normal-mode eigenvectors and harmonic frequencies of the six intermolecular vibrations of isomer A of imidazole·benzene.

the S1 states (see section 4.4). For a small vibrational amplitude, the internal rotation correlates with the θ or “twist” normalmode vibration (see Figure 4). The large-amplitude internal rotation and its expected effects on the R2PI spectrum of Im·Bz are discussed in section 4.4. 3.3. Excitation Energies and Electronic Transition Dipole Moment. Table 3 lists the calculated adiabatic transition energies of benzene, of isomers A and B of imidazole· benzene, and of the cyclic imidazole·Bz2 structure. Since the S0 state was optimized with the SCS-MP2 method whereas the S1 state was optimized with the SCS-CC2 method, there are two ways to compute the adiabatic transition energy: (i) the SCSMP2+ΔE case, the SCS-CC2 excitation energy of the S1 state is 7781

DOI: 10.1021/jp512766r J. Phys. Chem. B 2015, 119, 7778−7790

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The Journal of Physical Chemistry B Table 2. Calculated S0- and S1-State Normal-Mode Frequencies (in cm−1) of Imidazole·Benzene isomer A

isomer B

S0

a

S1

S1

vibration

irrep. (in Cs)

SCS-MP2 def2-QZVPP

SCS-CC2 def2-QZVPP

θ δ ω β χ σ ν16b ν16a ν6a ν6b ν11 ν4 ν10b ν10a ν17b ν17a ν1 ν5 NH stretch

a″ a″ a′ a″ a′ a′ a′ a″ a′ a″ a′ a″ a″ a′ a′ a″ a′ a″ a′

5.6 25.4 12.5 62.1 65.3 74.4 409.0 410.2 609.5 611.5 701.8 703.0 879.6 880.2 999.0 999.5 1012.2 1018.9 3658.0

5.3 17.0 40.4 47.6 56.8 75.7 265.0 258.6 524.2 521.7 555.3 412.7 612.9 621.8 749.1 738.9 932.6 758.7 3628.9

exptl.

SCS-CC2 def2-QZVPP 2.1 9.9 35.9 44.9 53.3 74.7 260.8 256.4 524.0 521.9 548.7 409.6 617.1 605.7 744.5 730.6/738.0a 932.5 754.5 3629.6

21.2 24.2 46.8 43.8 75.7 239.7 244.7 523.0 518.2

925.4 3445b

exptl. 22.6 23.9 46.6

521.9 524.0

The ν17a vibration of benzene is coupled to an imidazole intramolecular out-of-plane vibration, giving rise to two fundamentals. bS0-state frequency.

Table 3. Adiabatic Electronic Transition Energiesa of Benzene, Imidazole·Benzene (Isomers A and B), and Imidazole· (Benzene)2 (in cm−1) SCS-MP2 benzene Im·Bz (A) Im·Bz (B) Im·Bz2 a

shift SCS-MP2b

SCS-CC2

shift SCS-CC2b

w/o ZPE

w/ZPE

w/o ZPE

w/ZPE

w/o ZPE

w/ZPE

w/o ZPE

w/ZPE

39760.8 39888.5 39933.1 39768.4

38484.1 38486.5 38499.2 38270.2

39604.3 39716.8 39767.3 39590.7

38327.6 38314.7 38333.4 38092.6

+127.7 +172.3 +7.6

+2.4 +15.1 −213.9

+112.5 +163.0 −13.6

−12.9 +5.8 −235.0

Computed in the def2-QZVPP basis set. bRelative to benzene.

added to the SCS-MP2 ground-state energy (in the S1 geometry) and the SCS-MP2 energy of the S0 ground state (in the S0 geometry) is then subtracted, or (ii) the SCS-CC2+ΔE case, the SCS-CC2 energy of the S0 state (in its SCS-MP2 optimized geometry) is subtracted from the SCS-CC2 energy of the S1 state (in its S1 geometry). In case i, both the A and the B isomers are slightly blue shifted compared to benzene by +2.4 and +15.1 cm−1, respectively. In case ii, isomer A is shifted by −12.9 cm−1 (to the red) and isomer B by +5.8 cm−1. The adiabatic excitation energy of Im·Bz2 is red shifted by −213.9 (case i) or −235.0 cm−1 (case ii). The SCS-CC2/def2-QZVPP-calculated vertical excitation energies for isomer A of Im·Bz and for Im·Bz2, including the oscillator strength and the fractional orbital excitation contributions, are summarized in Table S1 and Figure S1 (see the Supporting Information). The S0 → S1 transition of Im·Bz includes mainly a Bzπ → π* and a small Bzπ → Rydberg orbital contribution (see Figure 5).

in this range. Thus, the electronic transition is associated with the benzene S0 → S1 (1A1g → 1B2u) excitation, which is electricdipole forbidden in D6h symmetry; the transition only exhibits vibronically induced (Herzberg−Teller) bands.33−35 Figure 6 shows an overview of the one-color R2PI spectrum measured in the (Im·Bz)+ mass channel. The IR/UV depletion measurements in the N−H stretch region of imidazole (see below) reveal that the Im·Bz2 cluster fragments into the Im·Bz+ mass channel, giving rise to weaker bands in the range 38 000− 38 300 cm−1 and to broad features from larger Im·Bzn clusters extending from 38 600 to 38 850 cm−1 (see below). The R2PI spectrum of Im·Bz in Figure 6 exhibits a 000 band and a number of intramolecular vibronic excitations of the Bz moiety that are marked as 16a20/16b20, 6b10/6a10, and 110. These band assignments are based on their closeness to the respective S1-state vibrational frequencies of benzene and on the relative intensities. We distinguish two types of excitations. (1) Vibronically induced (Herzberg−Teller) bands that occur in the S0 → S1 spectrum of benzene,33−36 i.e., the 1620 overtone of the ν′16 (e2u) out-of-plane vibration and the 610 excitation of the in-plane ν6′ (e2g) mode.33−35 The benzene ν6a ′ /ν6b ′ and ν16a ′ /ν16b ′ S1-state normal-mode eigenvectors are shown in Figure S2 (Supporting Information). The 610 band is the so-called false origin

4. EXPERIMENTAL RESULTS 4.1. Resonant Two-Photon Ionization Spectra. Oneand two-color R2PI spectra were measured over the 37 900− 39 100 cm−1 range. The imidazole moiety does not absorb at wavelengths below 40 800 cm−1 32 nor do the calculations in section 3.3 predict any imidazole-centered electronic excitations 7782

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(16a20), 484.5 (16a1016b10), and 489.4 cm−1 (16b20). The harmonically derived fundamental frequencies are 239.7 (ν′16a) and 244.7 cm−1 (ν′16b); these are 2.2 and 7.2 cm−1 higher than ν16 ′ in benzene (237.5 cm−1).35 (2) Vibronic excitations that do not appear as in the S0 → S1 spectrum of Bz: The 110 excitation of the in-plane ν1′ vibration (a1g in Bz) is observed at 925.4 cm−1 (see Figure 6). Like the 000 band, ν′1 becomes optically allowed via the D6h → Cs symmetry lowering. The 110 frequency of Im·Bz lies 2.4 cm−1 above ν1′ in Bz (923.0 cm−1).35 The ν1′ normal-mode eigenvector is shown in Figure S2 (Supporting Information). In Figure 6 broad and structureless features are observed around 38 550, 38 750, and 38 750 cm −1, which dominate the spectrum if one considers the integral transition strengths. These arise from dissociation of larger Im·Bzn clusters into the Im·Bz+ mass channel. As noted in section 2.1, the broad features from larger Im·Bzn clusters completely cover the narrow-band spectrum if the Bz partial pressure is raised above 2 mbar or 0.13% mole fraction. The R2PI spectrum observed in the (Im·Bz2)+ mass channel is compared to Figure 6 in Figure S3 (Supporting Information). The broad bands in both the Im·Bz+ and the (Im·Bz2)+ mass channels are largely coincident; the spectroscopic assignments of the broad bands are given in Figure S3 (Supporting Information). 4.2. Infrared/UV Depletion Spectra. Figure 7 shows two UV-detected infrared (IR) depletion spectra in the 3300− 3700 cm−1 range. For the IR spectrum shown in Figure 7a the UV excitation laser was set to the lowest frequency sharp

Figure 5. Frontier orbitals of imidazole·benzene (isomer A) and their participation in the S0 → S1 (blue) and S0 → S2 (red) transitions (SCS-CC2/def2-QZVPP).

Figure 6. One-color resonant two-photon ionization spectrum measured in the (imidazole·benzene)+ mass channel, with superimposed spectra of imidazole·benzene and imidazole·(benzene)2. Assignments are discussed in the text. The (forbidden) S0 → S1 000 band of benzene at 38 086 cm−1 is marked by the red arrow.

of benzene: it gives rise to the most intense band system of Im·Bz (see Figure 6). The D6h → Cs symmetry lowering of the Bz moiety in Im·Bz splits the degeneracy of the ν′16 and ν′6 vibrations and hence the corresponding 1620 and 610 bands. The 6b10 and 6a10 sub-band frequencies in Im·Bz are 518.2 and 523.6 cm−1 and lie 2−3 cm−1 below/above the ν6′ frequency of bare benzene. The 1620 overtone splits into three sub-bands that lie at 479.3

Figure 7. UV-detected infrared depletion spectra of (a) imidazole· benzene and (b) imidazole·benzene2 in the NH stretch range of imidazole (for the assignment see text). IR spectrum a is measured by IR depletion while detecting at the UV 000 band marked a in the insert; IR spectrum b is measured while detecting at the broad band b in the IR spectrum. 7783

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The Journal of Physical Chemistry B

Figure 8. (a) Two-color R2PI (2C-R2PI) spectrum measured in the imidazole·benzene+ mass channel. 2C-R2PI spectrum (b) of imidazole·benzene and (c) of the imidazole·(benzene)2 cluster, which together contribute to the total R2PI spectrum shown in a. Spectra in panels b and c were separated by IR hole burning. The forbidden S0 → S1 electronic origin of benzene at 38 086 cm−1 is indicated by a vertical red line.

feature of the R2PI spectrum at 37 981 cm−1, marked a in the inset, while in Figure 7b the UV detection laser was centered in the higher lying and broader band at 38 174 cm−1, marked b in the inset. The IR band at 3445 cm−1, Figure 7a, is assigned to the NH stretch of the imidazole within the Im·Bz complex. The band at 3452 cm−1 in Figure 7b is assigned as the NH stretch of imidazole in the Im·Bz2 trimer. The reason for these assignments is that the species with the IR spectrum in Figure 7a exhibits one group of close-lying UV vibronic bands, whereas the carrier of the IR spectrum b exhibits two separate UV absorption band systems; these correspond to the electronic excitations of benzene-1 and benzene-2 in Im·Bz2, as will be discussed in section 4.3. The NH stretch frequencies provide a qualitative diagnostic of the NH···π interaction strength: The gas-phase NH stretch of free imidazole appears at 3518 cm−1. In the self-dimer (imidazole)2, the “free” NH stretch of the acceptor, appears at 3516 cm−1, while the H-bonded NH donor stretch frequency decreases to 3200 cm−1.19,37 The NH stretch in imidazole· benzene is shifted −73 cm−1 below that of bare imidazole. This is only 23% of the shift of the NH-donor stretch of Im2, indicating a much weaker NH···π interaction than in (imidazole)2. On the other hand, the shift in imidazole·benzene is similar to that in the T-shaped complex pyrrole·benzene, where the pyrrole NH stretch is shifted by −59 cm−1,31 and to 2-pyridone·benzene, where the 2-pyridone NH stretch is shifted by −56 cm−1.30 The slightly larger shift of the NH stretch in Im·Bz indicates that the imidazole NH···π interaction with benzene is slightly larger than that with the pyrrole and 2-pyridone donors.30,31 We note, however, that Suhm and co-workers performed FTIR supersonic jet experiments on pyrrole/benzene jet expansions and assigned the pyrrole·benzene NH stretch to a band at −46 cm−1, further IR bands with shifts of −60 and −67 cm−1 being assigned to the pyrrole·(benzene)2 and pyrrole·(benzene)3, respectively.38,39 The NH stretch of imidazole in Im·Bz2 is shifted by −66 cm−1 relative to bare imidazole, i.e., 7 cm−1 less than that of Im·Bz. This is consistent with the fact that in the trimer the NH···π

hydrogen bond is slightly distorted and therefore the intermolecular interaction is less strong. The calculated harmonic NH stretch frequencies of imidazole in Im·Bz and Im·Bz2 are higher than observed, both with the DFT and with the correlated ab initio methods. The B97-D and B97-D3 frequencies are lower than the M062X or SCS-MP2 values; the four harmonic frequencies are indicated by vertical lines in Figure 7. With all four methods, the imidazole NH stretch in Im·Bz2 is calculated to be 15−20 cm−1 lower than that of Im·Bz, which is contrary to observation. However, the additional calculated shift in Im·Bz2 is small. 4.3. IR Hole Burned UV Spectra. Figure 8a shows the 000 region of the two-color R2PI spectrum measured in the Im·Bz+ mass channel. Cluster-specific and mass-specific UV spectra were obtained by IR hole burning at the peaks of the IR bands shown in Figure 7a and 7b combined with subsequent twocolor R2PI: If the hole burning laser is set to the NH stretch at 3445 cm−1 (see Figure 7a), we obtain the UV spectrum shown in Figure 8b by subtracting the IR hole burned from the nonburned UV spectrum. This spectrum exhibits a group of narrow (1 cm−1 wide) bands, the lowest of which is shifted by −104 cm−1 below the 000 band of benzene at 38 086 cm−1. If the IR hole burning laser is fixed at the NH stretch at 3452 cm−1 (see Figure 7b), we obtain in an analogous manner the UV spectrum shown in Figure 8c. Note that while this spectrum partially overlaps that in Figure 8b, there are major differences: (1) It is less red shifted, starting −86 cm−1 below the 000 band of benzene; (2) it exhibits two distinct groups of bands, the lower frequency group exhibiting narrow bands of 1 cm−1 width, while the higher frequency group exhibits 4−8 cm−1 broad bands; (3) the lowest band of the broad-band group is shifted +88 cm−1 to the blue of the benzene 000 band. We assign the spectrum in Figure 8b to the 000 band of the Bz moiety in Im·Bz plus associated intermolecular vibrational bands; the latter are similar to those associated with the 000 bands of 2-pyridone·benzene and pyrrole·benzene.30,31 In contrast, the two band groups in Figure 8c are the electronic excitations of two benzene moieties, which correspond to the benzene-1 and benzene-2 moieties of Im·Bz2 (see Figure 2). 7784

DOI: 10.1021/jp512766r J. Phys. Chem. B 2015, 119, 7778−7790

Article

The Journal of Physical Chemistry B Hence, we assign the UV spectrum in Figure 8c to Im·Bz2. The ratio of the integrals of the band groups, taken from 38 000 to 38 090 cm−1 and from 38 150 to 38 270 cm−1 in Figure 8c is 1:2.9. This is in very good agreement with the ratio of the electronic oscillator strengths fel(S1):fel(S2) = 1:3.00 calculated at the SCS-CC2/def2-QZVPP level. The fact that the 000 band of Im·Bz is shifted by −104 cm−1 below that of Bz implies an increase of the imidazole·benzene dissociation energy D0 by the same amount upon electronic excitation. For Im·Bz2, the situation is complicated by the additional benzene−benzene interaction. The 000 bands of benzene-1 and benzene-2 are mainly split by the H bonding and positional inequivalence of the two Bz chromophores within the cluster. In the UV spectrum of the T-shaped benzene dimer, this inequivalence is denoted the site splitting.40,41 While the lower energy S0 → S1 transition of (benzene)2 has been repeatedly studied,40−46 the higher energy S0 → S2 transition is very weak and has only recently been identified ∼250 cm−1 above the S0 → S1 origin. The S0 → S1 and S0 → S2 origin bands of Im·Bz2 are split by 174 cm−1, which is similar to the S1/S2 splitting observed in (benzene)2. Furthermore the two origins are shifted by −86 and +88 cm−1, nearly symmetrically relative to the 000 band of benzene at 38 086 cm−1. The SCS-CC2-calculated transitions (ZPVE-corrected adiabatic energies) predict a red shift of −13 cm−1 for Im·Bz and −235 cm−1 for Im·Bz2. Qualitatively, the small red shifts agree with the experiment, but in quantitative terms, the calculated predicted red shift of Im·Bz is too small and that of Im·Bz2 is too large. 4.4. Internal Rotation of BenzeneThe θ Mode. Before assigning the Im·Bz spectrum in Figure 8b, we discuss the internal rotation of benzene relative to the imidazole moiety. When described as a completely rigid system, imidazole·benzene is an asymmetric top with its a inertial axis tilted by ∼5° relative to the normal of the benzene plane and with the b/c inertial axes nearly parallel to the benzene plane through the center of mass of the complex, as indicated in Figure 1b. However, the 6-fold V6 barrier that hinders the internal rotation of the benzene around its local C6 axis is low. As noted in section 3.2, this motion is the large-amplitude limit of the θ′ intermolecular normal mode. We computed the V6″(S0) and V6′ (S1) internal-rotation barriers at the SCS-MP2/def2-QZVPP and SCS-CC2/def2QZVPP levels, respectively. The unrelaxed barriers were obtained by rotating the benzene molecule by 30° about its C6 axis. The relaxed barriers were obtained from a geometry optimization in Cs symmetry following the 30° rotation. For isomer A, the unrelaxed barriers are V6″ = 2.8 cm−1 and V6′ = 11.7 cm−1, while the relaxed barriers are V6″ = 2.2 cm−1 and V′6 = 5.1 cm−1. For isomer B, which is a stable minimum in the S1 state only, the unrelaxed and relaxed barriers are V′6 = 8.9 cm−1 and V6′ = 4.4 cm−1, respectively. Figure 9 shows the relaxed S0- and S1-state V6(θ) potentials of isomer A. We determined the internal-rotation eigenfunctions and eigenvalues of imidazole−benzene by numerically solving the one-dimensional (1D) internal-rotation Hamiltonian

Figure 9. S0- (v = 0) and S1-state potentials for the internal rotation of imidazole·benzene (isomer A) with the relaxed barriers V6″ = 2.2 cm−1 and V′6= 5.1 cm−1. Vertical arrows in black refer to pure internalrotation transitions associated with the 000 band or to a′ vibrations such as ω′, σ′, or ν′1 of benzene. Transitions in red refer to combination excitations to internal-rotation plus a″ (antisymmetric) vibrations.

They assumed an ideal T-shaped structure, a reduced rotational constant for cap rotation as the sum of the monomer rotational constants, A + C = 0.2847 cm−1, and calculated a V6″ barrier of 6 cm−1.49,50 To check the accuracy of our IDL program, we repeated their model calculation of the (Bz)2 1D cap rotation and reproduced the energy levels of ref 49 within