Homogeneous and Heterogeneous Noncovalent Dimers of

Article pubs.acs.org/JPCA

Homogeneous and Heterogeneous Noncovalent Dimers of Formaldehyde and Thioformaldehyde: Structures, Energetics, and Vibrational Frequencies Eric Van Dornshuld, Christina M. Holy, and Gregory S. Tschumper* Department of Chemistry and Biochemistry, University of Mississippi, University, Mississippi 38677, United States S Supporting Information *

ABSTRACT: This work provides the first characterization of five stationary points of the homogeneous thioformaldehyde dimer, (CH2S)2, and seven stationary points of the heterogeneous formaldehyde/thioformaldehyde dimer, CH2O/CH2S, with correlated ab initio electronic structure methods. Full geometry optimizations and corresponding harmonic vibrational frequencies were computed with second-order Møller−Plesset perturbation theory (MP2) and 13 different density functionals in conjunction with triple-ζ basis sets augmented with diffuse and multiple sets of polarization functions. The MP2 results indicate that the three stationary points of (CH2S)2 and four of CH2O/ CH2S are minima, in contrast to two stationary points of the formaldehyde dimer, (CH2O)2. Single-point energies were also computed using the explicitly correlated MP2-F12 and CCSD(T)-F12 methods and basis sets as large as heavy-aug-cc-pVTZ. The (CH2O)2 and CH2O/CH2S MP2 and MP2-F12 binding energies deviated from the CCSD(T)-F12 binding energies by no more than 0.2 and 0.4 kcal mol−1, respectively. The (CH2O)2 and CH2O/CH2S global minimum is the same at every level of theory. However, the MP2 methods overbind (CH2S)2 by as much as 1.1 kcal mol−1, effectively altering the energetic ordering of the thioformaldehyde dimer minima relative to the CCSD(T)-F12 energies. The CCSD(T)-F12 binding energies of the (CH2O)2 and CH2O/CH2S stationary points are quite similar, with the former ranging from around −2.4 to −4.6 kcal mol−1 and the latter from about −1.1 to −4.4 kcal mol−1. Corresponding (CH2S)2 stationary points have appreciably smaller CCSD(T)-F12 binding energies ranging from ca. −1.1 to −3.4 kcal mol−1. The vibrational frequency shifts upon dimerization are also reported for each minimum on the MP2 potential energy surfaces.

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decreases by about 0.4−0.5 kcal mol−1 when zero-point vibrational energy (ZPVE) is included.18 Thioformaldehyde (CH2S), an isovalent analogue of formaldehyde (CH2O) and the simplest thiocarbonyl compound, is unstable with a short lifetime of only a few minutes at low pressures19 and readily polymerizes into a cyclic trimer.20−22 However, monomeric thioformaldehyde has been detected in both intellerstellar space23 and the Hale-Bopp comet.24 A number of experimental analyses25,26 have been performed on monomeric thioformaldehyde, to obtain the vibrational27−36 and rotational19,31,32,34,36−38 spectra of the ground electronic state as well as excited state properties.39−41 These efforts have been complemented by extensive ab initio studies of monomeric thioformaldehyde35,42−56 that have provided fundamental insight into the physical chemistry of thioformyl and similar sulfur-containing compounds, some which may have appreciable biological activities.57−59 Like the carbonyl functional group, thiocarbonyls can establish attractive inter- and intramolecular noncovalent interactions,46,48,50,51,54,55,60 ranging from hydrogen to chalcogen bonding (the latter of which can be classified more generally as σ-hole interactions).61 Recently, the influence of carbonyl−carbonyl interactions on the conformational prefer-

INTRODUCTION Noncovalent interactions between carbonyl groups may play an important role in protein structure, folding, and stability.1−4 These attractive forces between carbonyl groups in peptide backbones have been shown to affect the conformational preference of biological model systems.1,5−7 The formaldehyde dimer, (CH2O)2, is perhaps the simplest system that can model these interactions. This homogeneous dimer has been characterized in a wide range of theoretical and experimental studies.8−18 Two minima, denoted as structure I and structure II in Figure 1, have been identified with Cs and C2h symmetry, respectively. Structure I is characterized by an edge-to-face arrangement with a CH···O contact and a short O···C intermolecular distance. Structure II exhibits an edge-to-edge arrangement with two equivalent CH···O hydrogen bonds. The formaldehyde dimer has been experimentally observed in argon and nitrogen matrices using infrared (IR)8−10 and Raman8 spectroscopy. The characterization of the (CH2O)2 potential energy surface (PES) using second-order Møller−Plesset perturbation theory (MP2) indicated that structure I was the experimentally detected configuration based on its vibrational frequency shifts relative to the monomer.11 Structure I is the global minimum, lying 0.8 kcal mol−1 lower in energy than structure II at the CCSD(T) (i.e., the coupled-cluster method that includes all single and double substitutions as well as a perturbative treatment of the connected triple excitations) complete basis set (CBS) limit.11 This energy separation © 2014 American Chemical Society

Received: March 14, 2014 Revised: April 17, 2014 Published: April 28, 2014 3376

dx.doi.org/10.1021/jp502588h | J. Phys. Chem. A 2014, 118, 3376−3385

The Journal of Physical Chemistry A

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weakly bound complexes. For comparison, stationary points of (CH2O)2 are also characterized with the same procedures.

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THEORETICAL METHODS Full geometry optimizations and corresponding harmonic vibrational frequencies were computed with second-order Møller−Plesset perturbation theory (MP2)62−67 for each monomer and dimer configuration using the analytic gradients and Hessians available in Gaussian 09.68 The heavy-aug-ccpVTZ (haTZ) correlation consistent basis set69,70 was employed for these computations where the heavy (nonhydrogen) atoms are augmented with diffuse functions (i.e., ccpVTZ for H and aug-cc-pVTZ for all other atoms). Additionally, 13 density functional theory (DFT) methods were employed, as implemented in Gaussian 09,68 including B3LYP,71,72 B3LYP-D3, B3LYP-D3(BJ), TPSS,73 TPSS-D3, TPSS-D3(BJ), APF,74 APF-D,74 M06-2X,75 M06-2X-D3, N12SX,76 MN12SX,76 and VSXC.77 For TPSS, that functional was implemented for both the exchange and correlation part of the functional. The DFT-D3 schemes employ Grimme’s thirdgeneration dispersion correction with the original D3 damping function,78 whereas the DFT-D3(BJ) schemes employ the Becke−Johnson damping function.79 These functionals were chosen based on the availability of Grimme’s D3 dispersion correction78,79 and/or their ability to reliably describe noncovalent interactions in other systems.74,76,80,81 The 6-311+G(2df,2pd)82−86 and haTZ basis sets were used for all DFT computations. MP2 Binding energies, Ebind , were computed via the supermolecular approach by comparing the energy of each optimized dimer structure to the corresponding optimized monomer energies. Single-point energy computations were performed for all optimized structures using the explicitly correlated MP2-F12 [specifically MP2-F12 3C(FIX)87] and CCSD(T)-F12 [specifically CCSD(T)-F12a88 with unscaled triples contributions] methods with the haTZ basis set. Corresponding binding energies are denoted as EMP2‑F12 and ECC‑F12 bind bind , respectively. All explicitly correlated computations were performed with the haTZ basis set and include the default density fitting (DF) and resolution of the identity (RI) basis sets implemented in Molpro 2010.1.89 To estimate basis-set superposition error (BSSE),90,91 counterpoise (CP) corrections for EMP2‑F12 and bind ECC‑F12 were computed at the MP2-F12 and CCSD(T)-F12 bind level of theory with the haTZ basis set for the MP2 optimized structures using the method of Boys and Bernardi,90,92 for which a detailed tutorial is available in a review from this group.93 The computation of this correction factor is defined in eq 1.

Figure 1. (CH2O)2 structures and corresponding point group symmetries.

ences of simple biomolecules was found to be significantly enhanced when oxygen was replaced with sulfur.1 Interestingly, neither the homogeneous nor the heterogeneous sulfur analogues of the formaldehyde dimer model system have been examined. The (CH2O)2, CH2O/CH2S, and (CH2S)2 series provides a platform to compare and contrast the noncovalent interactions of carbonyl and thiocarbonyl groups. This paper presents the first detailed characterization of the stationary points of (CH2S)2 and CH2O/CH2S (i.e., full optimizations and harmonic vibrational frequency computations) with correlated ab initio electronic structure methods and density functional theory (DFT). For these systems, we examine configurations analogous to the extensively characterized stationary points of the formaldehyde dimer. Vibrational frequency shifts relative to the isolated monomers are reported for all minima to facilitate experimental identification of these

2 CP E bind = E(dimer) −

basis ∑ [E(fragmenti)dimer dimer geometry i=1

basis + E(fragmenti)fragment fragment geometry fragment basis − E(fragmenti)dimer geometry ]

(1)

Spherical harmonic 5d and 7f basis functions were used rather than their 6d and 10f Cartesian counterparts for all computations. The magnitudes of the components of the residual Cartesian gradients of all optimized structures were less than 1.77 × 10−5 Eh a−1 0 . A pruned numerical integration grid having 150 radial shells and 974 angular points per shell was employed for all DFT computations. The frozen core 3377



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approximation was invoked for all computations (1s, 2s, 2p-like orbitals on sulfur and 1s-like orbitals on oxygen and carbon). Minimum root-mean-square deviations (RMSD) between the unweighted Cartesian coordinates of the MP2- and DFToptimized geometries were computed with the SUPERPOSE program available in the TINKER94 software package.

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RESULTS AND DISCUSSION Structures and Energetics. Five stationary points of the formaldehyde dimer, (CH2O)2, seven newly identified stationary points of CH2O/CH2S, and five newly identified stationary points of the thioformaldehyde dimer, (CH2S)2, have been characterized with MP2 electronic structure theory. We adopt a structure labeling scheme based on the relative energies of the formaldehyde dimer. The (CH2O)2 and (CH2S)2 stationary points are shown in Figures 1 and 2, respectively, along with their point group symmetries (Cs for I, C2h for II and III, and C2v for IV and V). These structures are characterized by an edge-to-face (I), edge-to-edge (II), face-to-face (III), nonplanar head-to-tail (IV), and planar head-to-tail (V) alignment of the monomers. The (CH2O)2 and (CH2S)2 structures are qualitatively similar except structure III. The (CH2O)2 structure III is characterized by two antiparallel CH2O monomers in a near-stacked, face-to-face orientation containing two C···O interactions, while the two monomers in the corresponding (CH2S)2 dimer slip in an antiparallel direction forming a face-to-face alignment of the carbonyl centers. The CH2O/CH2S stationary points are shown in Figure 3 with corresponding point group symmetries (Cs for Ia, Ib, and II and C2v for IVa, IVb, Va, and Vb) and contain similar orientations to the corresponding (CH2O)2 and (CH2S)2 stationary points. Optimizations of CH2O/CH2S configurations comparable to (CH2O)2 or (CH2S)2 structure III collapsed to a head-to-tail arrangement. MP2/haTZ scans indicate that the stacked configurations are quite attractive with interaction energies approaching 2 kcal mol−1. In Cs symmetry, however, the molecular planes of the monomers are not constrained to be parallel, and there does not appear to be any energetic barrier to nonparallel orientations that collapse to head-to-tail arrangements. As such, a CH2O/CH2S structure III is not reported. The Hessian index (or number of imaginary modes of vibration denoted as ni) for the MP2 optimized structures is listed in Table 1. The (CH2O)2 structures I and II are the only minima on the MP2 PES, with ni = 0. Structure IV is a transition state (ni =1), while structures III and V are higherorder saddle points (ni >1). These results are consistent with MP2 computations, employing much smaller double-ζ quality basis sets.11,12 The CH2O/CH2S structures Ia, Ib, II, and Va are also minima, while IVa and IVb are transition states and Vb a higher-order saddle point. The (CH2S)2 structures I, II, and III are minima, while V is a transition state and IV a higher order saddle point. The intermolecular separations of (CH2O)2 with respect to the center of mass (COM) of each monomer (RCOM listed in Table 1) range from 2.89 Å (structure I) to 4.35 Å (structure V). These separations increase slightly in CH2O/ CH2S, ranging from 3.12 to 4.88 Å. In (CH2S)2, the range further increases from 3.42 to 5.22 Å. The MP2, MP2-F12, and CCSD(T)-F12 binding energies MP2‑F12 (EMP2 , and ECC‑F12 bind , Ebind bind , respectively), as well as higherorder correlation effects defined here as the energy difference between the EMP2‑F12 and ECC‑F12 to give δCC‑F12 bind bind MP2‑F12 of the MP2 optimized structures are also listed in Table 1. The values for

Figure 2. (CH2S)2 structures and corresponding point group symmetries. MP2‑F12 EMP2 are very similar, with differences growing no bind and Ebind larger than 0.13 kcal mol−1 for all stationary points. Good agreement is also typically observed between the explicitly correlated MP2-F12 and CCSD(T)-F12 methods with a −1 deviation (δCC‑F12 for the MP2‑F12) of no more than 0.20 kcal mol −1 (CH2O)2 stationary points and 0.37 kcal mol for the CH2O/ CH2S stationary points. However, this measure of higher-order correlation effects grows as large as 1.09 kcal mol−1 for structure I of (CH2S)2. Structure I is the global minimum for (CH2O)2 with a binding energy of −4.58 kcal mol−1. Structure Ia is the global minimum for CH2O/CH2S with a binding energy of −4.40 kcal mol−1. Both of these structures lie 0.81 kcal mol−1 lower in energy than the corresponding structure II of each system at the CCSD(T)-F12/haTZ level of theory. The energy difference for (CH2O)2 is in superb agreement with the previously

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Table 1. Number of Imaginary Vibrational Frequencies (ni), Intermolecular Separations (RCOM in Å), as well as the MP2, MP2-F12, and CCSD(T)-F12 Binding Energies (EMP2 bind , EMP2−F12 , and ECC−F12 ) Obtained with the haTZ Basis Set for bind bind the MP2/haTZ Optimized Structures in kcal mol−1 structure (CH2O)2 I II III IV V CH2O/CH2S Ia Ib II IVa IVb Va Vb (CH2S)2 I II III IV V

ni

RCOM

EMP2 bind

EMP2−F12 bind

ECC−F12 bind

δCC−F12 MP2‑F12

0 0 3 1 2

2.89 3.30 3.14 4.29 4.35

−4.62 −3.54 −2.65 −2.52 −2.39

−4.63 −3.57 −2.62 −2.43 −2.32

−4.58 −3.77 −2.63 −2.54 −2.44

+0.05 −0.20 −0.01 −0.11 −0.12

0 0 0 1 1 0 3

3.12 3.30 3.68 4.86 4.60 4.88 4.78

−4.74 −3.42 −3.43 −2.09 −1.35 −2.12 −1.15

−4.77 −3.40 −3.46 −1.97 −1.26 −2.00 −1.08

−4.40 −3.12 −3.59 −2.06 −1.24 −2.10 −1.11

+0.37 +0.28 −0.12 −0.09 +0.01 −0.10 −0.03

0 0 0 3 1

3.42 4.06 4.13 5.16 5.22

−4.13 −3.45 −2.10 −1.31 −1.35

−4.16 −3.49 −2.00 −1.18 −1.23

−3.07 −3.37 −1.50 −1.06 −1.15

+1.09 +0.12 +0.50 +0.12 +0.08

Table 2. Unscaled Harmonic MP2/haTZ Zero-Point Vibrational Energy Corrections (ΔEZPVE in kcal mol−1) to the electronic binding energies in Table 1 and an additive estimate of the CCSD(T)-F12/haTZ ZPVE corrected binding energy (E0bind in kcal mol−1) structure (CH2O)2 I II CH2O/CH2S Ia Ib II Va (CH2S)2 I II III

Figure 3. CH2O/CH2S structures and corresponding point group symmetries.

reported 0.80 kcal mol−1 electronic energy difference between structures I and II at the CCSD(T) CBS limit.18 The (CH2S)2 global minimum is structure II, according to the CCSD(T)F12/haTZ computations, in stark contrast to the corresponding MP2-F12 results where the relative energies of structures I and II shift, by roughly 1 kcal mol−1, and structure I lies at 0.67 kcal mol−1 below structure II. This suggests that the MP2 and CCSD(T) PESs may be qualitatively different for the thioformaldehyde dimer. The CP-corrected MP2-F12 and CCSD(T)-F12 binding energies obtained with the haTZ basis set for all optimized geometries are relegated to Table S2 of the Supporting Information. These binding energies indicate that BSSE is modest and grows no larger than 0.14 kcal mol−1 at the CCSD(T)-F12/haTZ level of theory. These corrections do not change the energetic ordering of the dimers. The effect of zero-point vibrational energy (ZPVE) on the energetics of the two lowest energy minima (edge-to-face and edge-to-edge) of the three dimer systems is quite consistent. Unscaled harmonic MP2/haTZ vibrational frequencies

ΔEZPVE

E0bind

+1.65 +0.97

−2.93 −2.80

+1.60 +1.27 +0.90 +0.38

−2.80 −1.85 −2.69 −1.72

+1.38 +0.86 +0.56

−1.69 −2.51 −0.94

(ΔEZPVE in Table 2) indicate that the ZPVE decreases the magnitude of Ebind by roughly 1.5 kcal mol−1 for the lowest lying edge-to-face minima (+1.65, +1.60, and +1.38 kcal mol−1 for structure I of the formaldehyde dimer, structure Ia of the mixed dimer, and structure I of the thioformaldehyde dimer, respectively). In contrast, the ZPVE correction is approximately 0.9 kcal mol−1 for the edge-to-edge minima (+0.98, +0.90, and +0.86 kcal mol−1 for structure II of the dimers with 0, 1, and 2 S atoms, respectively). Although the magnitude of the ZPVE correction decreases slightly as the number of S atoms increases, the net effect is the same. The edge-to-edge minima (structure II) are effectively stabilized relative to structure I (or Ia) by ca. 0.6 kcal mol−1 (i.e., by the difference between their ZPVE corrections). Additive estimates of the ZPVE-corrected CCSD(T)-F12/haTZ binding energies (E0bind) are reported in 3379



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experimental IR spectra. For example, both structures Ia and II exhibit large upfield shifts (greater than or equal to +20 cm−1) in the CH2 stretching modes with respect to the CH2O monomer as well as large upfield shifts in the CH2 rock and wag modes with respect to the CH2S monomer. However, these two structures differ in the CH2 stretching modes with respect to the CH2S monomer. The former has a modest downfield shift and a small upfield shift, while the latter exhibits one large upfield shift for these modes. Similarly, structures Ib and Va both have significant upfield shifts in the CH2 stretching modes with respect to the CH2S monomer. However, these two structures differ in the CH2 stretching modes with respect to the CH2O monomer as well as the CH2 rock and wag modes with respect to the CH2S monomer. A similar analysis could be applied to distinguish between structures I, II, and III of the thioformaldehyde dimer. Select (CH2S)2 MP2 vibrational frequency shifts between the monomer and the dimer minima are listed in Table 5. Structure I exhibits some large upfield and downfield shifts in the CH2 stretching modes. Specifically, the ν3 vibrational mode shows a huge downfield shift of −42 cm−1. Structure II is characterized by large upfield shifts in the CH2 bend, rock, and wag modes, whereas structure III exhibits no significant shifts. We note, however, that these MP2/haTZ results for (CH2S)2 could change significantly at the CCSD(T) level of theory in light of the appreciable energetic deviations discussed earlier. DFT Analysis. All 17 stationary points associated with these homogeneous and heterogeneous dimers [five for (CH2O)2, seven for CH2O/CH2S, and five for (CH2S)2] have been characterized with 13 DFT methods and two different triple-ζ basis sets [6-311+G(2df,2pd) and haTZ]. The results obtained from the 6-311+G(2df,2pd) basis set are reported here as splitvalence basis sets are commonly used with DFT methods. Both basis sets, however, yield similar results, and the full set of data obtained from the haTZ basis set is included in Tables S40− S60 of the Supporting Information. The average absolute deviations (AADs) and maximum absolute deviations (MADs) from the MP2/haTZ data are reported in Table 6 for several metrics to help gauge the performance of the functionals. The Cartesian RMSD (in Å) and intermolecular separation (RCOM in Å) deviations are small, indicating that the DFT-optimized structures are very similar to those from MP2 optimizations. (CH2O)2 contains the smallest deviations, while (CH2S)2 contains the largest deviations, which is entirely consistent with the magnitudes of RCOM. The full set of RMSD and RCOM data for each dimer is included in Tables S25, S30, and S35 and Tables S26, S31, and S36, respectively, of the Supporting Information. The deviations of the DFT binding energies (EDFT bind ) are values from Table 1. Several functionals relative to the ECC‑F12 bind provide binding energies that deviate by only a few tenths of a kcal mol−1 from the CCSD(T)-F12 data on average. This includes several of the Minnesota functionals (M06-2X, M062X-D3, N12SX, and MN12SX), APF-D, and the dispersioncorrected variants of B3LYP [-D3 and -D3(BJ)]. The VSXC functional lies at the other end of the spectrum with AADs on the order of 3 kcal mol−1 for each dimer system. CCSD(T)-F12 single point energies have been used as another means of assessing the quality of the DFT-optimized structures. The CCSD(T)-F12/haTZ binding energies were computed for each optimized structure and compared to the ECC‑F12 values in Table 1 for the MP2 optimized geometries. bind The agreement is quite remarkable. For many functionals, the

Table 2. These values indicate that, when ZPVE effects are included, the lowest energy edge-to-face and edge-to-edge configurations of (CH2O)2 and CH2O/CH2S are nearly isoenergetic, whereas the latter orientation is appreciably more stable than the former for (CH2S)2. Vibrational Frequency Shift Analysis. The following evaluation of dimer vibrational frequencies closely follows the analysis of Ford and Glasser11 that was able to definitively assign the matrix isolation IR spectra of (CH2O)2 to structure I based on shifts relative to the monomer.8−10 As such, we adopt the same notation and ordering for the vibrational normal modes for each dimer system and also focus on modes with appreciable IR intensities. The complete set of IR intensities and harmonic vibrational frequencies for all MP2-optimized structures are provided in the Supporting Information. The reported monomer modes include the CH2 antisymmetric stretch [νa(CH2)], CH2 symmetric stretch [νN(CH2)], CH2 bending motion [δ(CH2)], CH2 rocking motion [ρ(CH2)], and CH2 wagging motion [ω(CH2)]. The CO stretch [ν(CO)] is reported for oxygen-containing systems, and the CS stretch [ν(CS)] is reported for sulfur-containing systems. Select (CH2O)2 MP2 vibrational frequency shifts between the monomer and the dimer minima are listed in Table 3. Table 3. Select MP2 Vibrational Frequency Shifts (in cm−1) of the (CH2O)2 Minima with the Irreducible Representations of the Dimer Modes in Parentheses I

II

monomer

dimer

this worka

ref 11b

dimer

this worka

ref 11b

νa(CH2)

ν1(a′) ν13(a″) ν2(a′) ν3(a′) ν4(a′) ν5(a′) ν6(a′) ν7(a′) ν8(a′) ν14(a″) ν9(a′) ν15(a″)

+28 +24 +20 +15 −1 −11 +1 −4 +8 0 −7 +11

+34 +29 +27 +23 +1 −9 −2 −7 +6 −4 −12 +3

ν1(ag) ν13(bu) ν2(ag) ν14(bu) ν3(ag) ν15(bu) ν4(ag) ν16(bu) ν5(ag) ν17(bu) ν8(au) ν11(bg)

+35 +34 +9 +7 −20 −6 −3 −2 +9 +9 +15 +15

+36 +34 +10 +9 −20 −7 −6 −6 +8 +7 +11 +9

νN(CH2) ν(CO) δ(CH2) ρ(CH2) ω(CH2) a

haTZ. b6-31++G**.

Excellent agreement is observed between the (CH2O)2 shifts computed in this work and those computed in ref 11 with a smaller basis set. Deviations grow no larger than 8 cm−1 for structure I and 6 cm−1 for structure II. These results demonstrate the ability of the MP2 method with the haTZ basis set to successfully facilitate the identification and interpretation of experimental vibrational frequency measurements for the simple formaldehyde dimer system. The experimental vibrational frequency shifts8−10 reported and thoroughly discussed in ref 11 are included in Table S1 of the Supporting Information. In the remainder of this section, we extend this analysis to the analogous systems of CH2O/CH2S and (CH2S)2. Select CH2O/CH2S MP2 vibrational frequency shifts between the CH2O and CH2S monomers and the dimer minima as well as corresponding IR intensities are listed in Table 4. The spectral features are sufficiently unique that it should be possible to identify specific isomers from 3380



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Table 4. Select MP2/haTZ Vibrational Frequency Shifts (in cm−1) of the CH2O/CH2S Minima and Corresponding IR Intensities (I)a with the Irreducible Representations of the Dimer Modes in Parentheses Ia monomer CH2O νa(CH2) νN(CH2) ν(CO) δ(CH2) ρ(CH2) ω(CH2) CH2S νa(CH2) νN(CH2) ν(CS) δ(CH2) ρ(CH) ω(CH2) a

Ib

II

Va

dimer

shift

I

dimer

shift

I

dimer

shift

I

dimer

shift

I

ν13(a″) ν3(a′) ν4(a′) ν5(a′) ν14(a″) ν7(a′)

+20 +16 −12 −3 −3 −21

s m s w w n

ν2(a′) ν3(a′) ν4(a′) ν5(a′) ν7(a′) ν14(a″)

+9 1 −4 −7 −1 +2

s m m w w w

ν3(a′) ν4(a′) ν5(a′) ν6(a′) ν8(a′) ν14(a″)

+23 +6 −12 −1 +8 +11

s s m w w w

ν14(b2) ν2(a1) ν3(a1) ν4(a1) ν15(b2) ν9(b1)

+12 +8 −1 0 +1 +3

s s s w w w

ν2(a′) ν1(a′) ν8(a′) ν6(a′) ν9(a′) ν15(a″)

−8 +3 +5 −4 +10 +17

w w w w w m

ν13(a″) ν1(a′) ν8(a′) ν6(a′) ν15(a″) ν9(a′)

+15 +14 +3 +1 −2 +2

w w w w w m

ν1(a′) ν2(a′) ν9(a′) ν7(a′) ν10(a′) ν15(a″)

+10 0 0 +2 +16 +24

w m w w w m

ν13(b2) ν1(a1) ν6(a1) ν5(a1) ν16(b2) ν10(b1)

+17 +14 +1 −7 −15 +16

w w w n w m

n, not IR active; w, weak (1−19 km mol−1); m, medium (20−49 km mol−1); and s, strong (≥50 km mol−1).

Table 5. Select MP2/haTZ Vibrational Frequency Shifts (in cm−1) of the (CH2S)2 Minima and Corresponding IR Intensities (I)a with the Irreducible Representations of the Dimer Modes in Parentheses I

III

dimer

shift

I

dimer

shift

I

dimer

shift

I

νa(CH2)

ν1(a′) ν13(a″) ν2(a′) ν3(a′) ν6(a′) ν7(a′) ν4(a′) ν5(a′) ν8(a′) ν15(a″) ν9(a′) ν14(a″)

−12 +10 +9 −42 +11 −8 −4 −14 −4 −3 −18 +2

w w m m w w w w w n w m

ν1(ag) ν13(bu) ν2(ag) ν14(bu) ν4(ag) ν16(bu) ν3(ag) ν15(bu) ν5(ag) ν17(bu) ν8(au) ν11(bg)

−2 −2 −9 −10 0 −3 +15 +2 +12 +12 +20 +15

n w n m n w n w n w s n

ν7(au) ν11(bg) ν1(ag) ν14(bu) ν3(ag) ν16(bu) ν2(ag) ν15(bu) ν8(au) ν12(bg) ν4(ag) ν17(bu)

+1 0 −1 −1 −1 0 +2 −2 −2 0 +3 +4

w n n m n w n w w n n s

νN(CH2) ν(CS) δ(CH2) ρ(CH2) ω(CH2) a

II

monomer

n, not IR active; w, weak (1−19 km mol−1); m, medium (20−49 km mol−1); and s, strong (≥50 km mol−1).

maximum absolute deviations do not exceed 0.20 kcal mol−1 relative to the CCSD(T)-F12 binding energies obtained with the MP2-optimized structures. These results suggest that reliable energetics for these systems can probably be obtained efficiently via DFT optimizations and subsequent CCSD(T)F12 single-point energies. A full set of binding energies for each dimer is included in Tables S27−S29, S32−S34, and S37−S39 of the Supporting Information. Although most DFT methods provide optimized structures that are very similar to the MP2 optimized geometries, harmonic vibrational frequency computations reveal some rather discouraging discrepancies in the Hessian indices for a wide range of stationary points (Table S6 of the Supporting Information). For example, the MP2/haTZ harmonic vibrational frequencies indicate that structure III of (CH2S)2 is a minimum (ni = 0) for which the smallest harmonic vibrational frequency is 25 cm−1 (ν10 belonging to the au irreducible representation). However, B3LYP, TPSS, APF, N12SX, MN12SX, and VSXC computations with the 6-311+G(2df,2pd) basis set indicate that this stationary point is a transition state (ni = 1) with an imaginary frequency of 48i, 52i, 43i, 35i, 11i, and 132i cm−1, respectively. In this case, the number of discrepancies actually increases when the haTZ basis

set is employed for the DFT computations. Similar behavior has been observed for the water dimer95 and hydrocarbon/ water96 complexes. Some of the discrepancies are less significant in a quantitative sense. Structure IV of (CH2O)2 for example, is a transition state with an imaginary frequency of 20i cm−1 according to the MP2/haTZ computations, and all but two DFT computations with the 6-311+G(2df,2pd) basis set agree with this prediction. The N12SX and VSXC functionals, however, indicate that structure IV is a minimum, but the former predicts a frequency of only 2 cm−1 for the mode in question. Such relatively minute differences could be attributed to numerical noise, even though tight convergence criteria and dense numerical integration grids have been implemented in this study. Table S6 of the Supporting Information summarizes the number of imaginary vibrational frequencies associated with each DFT-optimized structure with the 6-311+G(2df,2pd) basis set and Tables S7− S24 of the Supporting Information contain the corresponding harmonic vibrational frequencies. These sets of data from DFT methods employing the haTZ basis set are listed in Table S41 and Tables S42−S59 of the Supporting Information, respectively. 3381



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Table 6. Average (AADs) and Maximum Absolute Deviations (MADs) of the Root Mean Square Deviation (RMSD), Intermolecular Separations (RCOM), DFT/6-311+G(2df,2pd) Binding Energies (EDFT bind ), and CCSD(T)-F12/haTZ Binding Energies (ECC−F12 ) bind method

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(CH2O)2 B3LYP-D3(BJ) TPSS-D3(BJ) B3LYP-D3 TPSS-D3 M06-2X-D3 APF-D B3LYP TPSS M06-2X APF N12SX MN12SX VSXC CH2O/CH2S B3LYP-D3(BJ) TPSS-D3(BJ) B3LYP-D3 TPSS-D3 M06-2X-D3 APF-D B3LYP TPSS M06-2X APF N12SX MN12SX VSXC (CH2S)2 B3LYP-D3(BJ) TPSS-D3(BJ) B3LYP-D3 TPSS-D3 M06-2X-D3 APF-D B3LYP TPSS M06-2X APF N12SX MN12SX VSXC

EDFT bind (kcal/mol)

RCOM (Å)

RMSD (Å)

ECC‑F12 (kcal/mol) bind

AAD

MAD

AAD

MAD

AAD

MAD

AAD

MAD

0.01 0.04 0.02 0.03 0.05 0.01 0.05 0.08 0.05 0.05 0.02 0.04 0.09

0.03 0.06 0.03 0.04 0.10 0.02 0.12 0.17 0.10 0.11 0.02 0.10 0.23

0.01 0.11 0.03 0.07 0.09 0.15 0.12 0.20 0.09 0.12 0.03 0.07 0.15

0.05 0.15 0.05 0.10 0.17 0.22 0.25 0.34 0.17 0.24 0.05 0.12 0.22

0.09 0.27 0.31 0.14 0.36 0.21 1.06 1.05 0.30 1.04 0.44 0.14 2.79

0.35 0.43 0.58 0.51 0.87 0.61 1.42 1.44 0.83 1.30 0.74 0.33 4.20

0.01 0.07 0.01 0.03 0.05 0.01 0.07 0.16 0.05 0.07 0.01 0.04 0.27

0.02 0.17 0.02 0.08 0.16 0.02 0.19 0.32 0.16 0.18 0.03 0.13 0.60

0.01 0.06 0.02 0.05 0.04 0.02 0.10 0.13 0.04 0.09 0.01 0.05 0.10

0.02 0.10 0.03 0.08 0.14 0.03 0.23 0.23 0.14 0.21 0.02 0.17 0.25

0.02 0.13 0.03 0.10 0.04 0.03 0.21 0.26 0.04 0.18 0.02 0.06 0.17

0.04 0.23 0.05 0.16 0.08 0.06 0.46 0.47 0.08 0.42 0.04 0.14 0.33

0.37 0.53 0.41 0.51 0.30 0.41 1.03 0.67 0.29 0.85 0.45 0.30 3.17

1.15 1.78 0.94 1.46 0.86 1.18 1.39 1.34 0.82 1.24 0.66 0.48 5.02

0.01 0.21 0.01 0.10 0.02 0.01 0.08 0.23 0.02 0.08 0.01 0.05 0.23

0.02 0.76 0.04 0.38 0.09 0.04 0.20 0.49 0.09 0.18 0.02 0.18 0.69

0.02 0.06 0.02 0.06 0.03 0.03 0.20 0.19 0.03 0.15 0.04 0.02 0.08

0.05 0.16 0.04 0.10 0.07 0.04 0.43 0.35 0.07 0.28 0.10 0.05 0.13

0.03 0.14 0.03 0.12 0.03 0.05 0.41 0.40 0.03 0.31 0.08 0.05 0.13

0.06 0.36 0.09 0.24 0.09 0.07 0.71 0.56 0.09 0.51 0.20 0.12 0.25

0.74 1.15 0.53 0.91 0.32 0.66 1.15 0.86 0.33 0.80 0.64 0.42 3.46

2.14 4.16 1.46 3.03 0.82 1.99 1.62 1.38 0.78 1.32 1.02 0.82 5.59

0.04 0.49 0.03 0.25 0.05 0.04 0.24 0.52 0.04 0.17 0.03 0.05 0.26

0.16 2.38 0.11 1.19 0.15 0.12 0.46 1.79 0.15 0.27 0.10 0.20 0.64

CONCLUSIONS Five stationary points of the formaldehyde dimer, seven newly identified stationary points of the formaldehyde/thioformaldehyde dimer, and five newly identified stationary points of the thioformaldehyde dimer have been characterized by performing full geometry optimizations and harmonic vibrational frequency computations at the MP2/haTZ level. Explicitly correlated MP2-F12 and CCSD(T)-F12 electronic energies were computed to determine higher-order correlation effects on the binding energy of each optimized geometry. Two minima were identified for (CH2O)2, four minima were identified for CH2O/CH2S, and three minima were identified for (CH2S)2. The global minima for both (CH2O)2 and CH2O/CH2S adopt an edge-to-face configuration with a CH···O contact

(structures I and Ia, respectively). Both systems have a local minimum only 0.81 kcal mol−1 higher in energy according to CCSD(T)-F12 computations that exhibits an edge-to-edge configuration. In contrast, the (CH2S)2 global minimum adopts the edge-to-edge geometry and the edge-to-face minimum lies about 0.30 kcal mol−1 higher in energy at the CCSD(T)-F12/ haTZ level of theory. The magnitude of the binding energies for the (CH2S)2 minima are appreciably smaller than those computed for the corresponding (CH2O)2 and CH2O/CH2S structures. Interestingly, the CH2O/CH2S edge-to-face configuration containing a CH···S interaction (structure Ib) is still a minimum but is nearly 0.5 kcal mol−1 higher in energy than the edge-to-edge orientation. The vibrational frequency shifts upon dimerization to form these structures are reported to facilitate 3382



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the identification of the CH2O/CH2S and (CH2S)2 configurations in future spectroscopic studies because analogous data proved to be quite useful in the characterization of (CH2O)2.11 The MP2-F12 and CCSD(T)-F12 energetics are very similar for the (CH2O)2 and CH2O/CH2S systems but can deviate significantly for (CH2S)2. In fact, results suggest that the MP2 and CCSD(T) PESs may be qualitatively different. It could, therefore, be instructive to recharacterize the (CH 2 S) 2 structures with the CCSD(T) method. However, analytic evaluation of CCSD(T) gradients and Hessians with sufficiently large basis sets is still an arduous task for this relatively small system. Most DFT methods reproduce the MP2 geometries quite well, and some provide binding energies in reasonably good agreement with the CCSD(T)-F12 values. CCSD(T)-F12 binding energies computed with the DFT-optimized structures are virtually identical to those computed using the MP2 optimized geometries. The VSXC functional performed poorly for all three dimer systems, whereas TPSS (and its dispersion corrected variants) struggled with the sulfur-containing systems. Despite the similarity of the MP2 and DFT optimized structures, the methods did not always predict the same number of imaginary frequencies (or Hessian index) for each stationary point, raising more concerns95,96 about DFT frequencies for noncovalent complexes.

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ASSOCIATED CONTENT

* Supporting Information S

Counterpoise corrected binding energies, IR intensities, and Cartesian coordinates of the MP2 optimized structures. Number of imaginary vibrational frequencies, harmonic vibrational frequencies, RMSD values, intermolecular parameters, and binding energies for every optimized structure. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +1 (662) 915-7301. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the Mississippi Center for Supercomputing Research for access to their computational resources. This work was funded in part by the National Science Foundation (Grants CHE-0957317, EPS-0903787, and CHE-1338056).

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