Article pubs.acs.org/JPCA
Structural and Energetic Characterization of Prebiotic Molecules: The Case Study of Formamide and Its Dimer Silvia Alessandrini and Cristina Puzzarini* Dipartimento di Chimica “Giacomo Ciamician”, Università di Bologna, Via Selmi 2, I-40126 Bologna, Italy ABSTRACT: State-of-the-art quantum-chemical computations have been employed to determine the accurate equilibrium structure of formamide and its symmetric dimer as well as the interaction energy of the latter, thus extending available reference data for the peptide (also denoted as amide) bond and the hydrogen-bond interaction that characterizes peptides and proteins. Equilibrium geometries and electronic energies have been evaluated by means of a composite scheme based on coupled-cluster calculations, including up to triple excitations, which also accounts for extrapolation to the complete basis set limit and core-correlation effects. This approach provides molecular structures with an accuracy of 0.001−0.002 Å and 0.05−0.1° for bond lengths and angles, respectively, and relative energies with an accuracy of about 1−2 kJ/mol.
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INTRODUCTION Formamide is well recognized to be of biochemical relevance because it is the smallest system containing the peptide (also denoted as amide, −CO−NH−) bond. As a consequence, it has been investigated from (physico-)chemical, spectroscopic, and astrophysical points of view. In the context of the present study, previous efforts to characterize its molecular structure and to investigate its planarity should be pointed out.1,2 One point of interest from such investigations is that an important and controversial aspect of protein structures is the possible deviation of the peptide bond from planarity.3 Because the structure adopted by a protein results from a complex balance of different interactions (both intrinsic and environmental)4 and because the planarity of the peptide bond is usually constrained in describing the configuration of the polypeptide chain,5,6 a deep and accurate characterization of the single peptide bond can be seen as an important step toward understanding the factors that determine the stability of proteins. The planarity of formamide, and in general of the amide structural unit, is usually explained by means of the following resonance model where the partial double-bond character of
equilibrium structure would lie well below the vibrational zeropoint level. From a theoretical point of view, as will be further demonstrated in the present work, the results are sensitive to both basis set effects and electron correlation.1 More precisely, accurate description of electron correlation and large basis sets are required to correctly describe the equilibrium geometry of formamide. Despite the number of studies carried out, a systematic investigation aiming at addressing the magnitude and importance of the various contributions and corrections is still lacking. The importance of formamide in the field of astrophysics and astrochemistry is related to its role as potential prebiotic molecule (see, for example, ref 12). Formamide has been detected in a large variety of star-forming environments, and it has been found in solar system comets (the reader is referred to ref 13 for an exhaustive account). These observations might support the exogenous theory for the origin of life, i.e., the hypothesis that prebiotic molecules were delivered to Earth from space by means of comets, asteroids, and meteorites instead of being synthesized directly on our planet (see, for example, ref 14). Despite the astrochemical importance of formamide, its gas-phase formation routes have been only marginally investigated prior to a very recent computational study that demonstrated the reliability of a barrierless reaction mechanism.13 In the frame of the biological importance of formamide, its dimer can be considered the simplest model to investigate the intermolecular interactions that characterize, for example,
C−N is thought to enforce a planar amide nitrogen. Nevertheless, the magnitude of the barrier to internal rotation around the C−N bond should be considered, especially in sterically constrained situations.1 As reported in ref 1, experimental spectroscopic investigations7−11 were not able to resolve the planarity issue because the possible nonplanar © XXXX American Chemical Society
Special Issue: Piergiorgio Casavecchia and Antonio Lagana Festschrift Received: February 2, 2016 Revised: March 13, 2016
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DOI: 10.1021/acs.jpca.6b01130 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A
tion theory (MP2)25 calculations were also carried out. All computations employed the correlation-consistent, cc-p(C)VnZ (n = T, Q, 5), basis sets.26,27 The quantum-chemical CFOUR program package was used throughout.28 Preliminary calculations employing triple-ζ quality basis sets in conjunction with CCSD(T) and triple- and quadruple-ζ quality sets with MP2 (all within the frozen-core approximation), were carried out without constraining the planarity of formamide and of its FA1 dimer. Additional calculations at the CCSD(T)/cc-p(C)VnZ, with n = T, Q, levels of theory were also performed. Subsequently, best estimates for the molecular structure and electronic energy of formamide and its FA1 dimer were obtained by means of the composite scheme introduced by Gauss and co-workers.29,30 The contributions considered are the Hartree−Fock self-consistent-field (HF-SCF) part extrapolated to the complete basis-set (CBS) limit, the valence CCSD(T) correlation energy extrapolated to the CBS limit as well, and the core−valence correlation correction (at the CCSD(T) level). The overall gradient employed in the geometry optimizations was therefore given by
nucleic acids and proteins. Amide groups are, in fact, responsible for donor−acceptor hydrogen bonds in peptides and proteins and play a crucial role in engineering their threedimensional structures.15,16 The accurate description of the N− H···OC and C−H···OC hydrogen bonds is therefore important for understanding their biological roles. The formamide dimer has been previously investigated by means of different computational approaches involving either density functional theory or post-Hartree−Fock methods, also considering extrapolation to the complete basis set limit. The reader is referred to, for example, refs 17−23 for an overview of previous works. Nevertheless, the focus in all previous studies was on the binding energy, rather than on an accurate and systematic investigation of the molecular structure. As reported in refs 17, 18, 20, 21, and 23, five singly and doubly hydrogenbonded dimers of formamide, showing either N−H···OC or C−H···OC interactions, have been identified on the potential energy surface as local minima. Among them, the symmetric one, which has two N−H···OC hydrogen bonds and is depicted in Figure 1, was found to be the most stable. In
dECBS + CV dE CBS(HF‐SCF) dΔE CBS(CCSD(T)) = + dx dx dx dΔE(CV) + (1) dx
where dECBS(HF-SCF)/dx and dΔECBS(CCSD(T))/dx are the energy gradients corresponding to the three-point exponential scheme for the HF-SCF energy31 and to the n−3 extrapolation formula for the CCSD(T) correlation contribution,32 respectively. In the expression given above, basis sets with n = T, Q, and 5 were chosen for the HF-SCF extrapolation, and n = T and Q were used for CCSD(T). The core-correlation energy correction, ΔE(CV), was obtained as the difference of allelectron (all) and frozen-core (fc) CCSD(T) calculations using the core−valence cc-pCVTZ basis set. As for the dimer binding energy, the energies obtained from the composite scheme were used to obtain the best estimate. To monitor the basis set and correlation effects, the binding energy was also evaluated at different levels of theory. When the extrapolation to the CBS limit is not considered, the basis-set superposition error (BSSE) was taken into account [In the case of CBS energies, by definition, the basis-set superposition error vanishes.33]. While at the CCSD(T)/CBS and CCSD(T)/CBS +CV levels the binding energy was evaluated as the electronic energy difference between the dimer and two times the isolated monomer (i.e., the first term within squared brackets of eq 2); in all other cases, the BSSE was recovered via counterpoise correction (CP),34 according to the following expression:
Figure 1. Molecular structures and atom labeling of formamide and its symmetric (FA1) dimer.
the present work, in the frame of a larger project aiming at the accurate characterization of the intra- and intermolecular interactions in model systems for biological molecules, we focus on the most stable formamide dimer, denoted as FA1 in the following. The investigation of FA1 and formamide at the same levels of theory, i.e., by means of state-of-the-art quantumchemical composite approaches, allowed us to study in great detail the hydrogen bonding and provides a foundation for future work. This paper is organized as follows. In the next section, the methodology and computational details are introduced, thus describing the theoretical and computational requirements for structural and energetic determinations. This is then followed by an extensive discussion of our results with a particular focus on molecular structure determinations and the binding energy of the FA1 formamide dimer.
ΔECP = [E DD − 2E FF] − 2[E FD − E FF] = E DD − 2E FD
(2)
where EYX is the energy of the subsystem X computed with the Y basis set; D and F denote the formamide dimer and the monomer, respectively. Subsequently, the interaction energies were corrected for the zero-point vibrational (ZPV) contribution at the harmonic level. For each species, the ZPV correction is thus given by
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METHODOLOGY AND COMPUTATIONAL DETAILS The coupled-cluster (CC) level of theory employing the CC singles and doubles (CCSD) approximation augmented by a perturbative treatment of triple excitations (CCSD(T))24 was mainly employed, but second-order Møller−Plesset perturba-
ΔEZPV = B
1 2
∑ ωr r
(3) DOI: 10.1021/acs.jpca.6b01130 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A where the harmonic frequencies ωr , with r denoting the rth vibrational normal mode, were computed at the fc-CCSD(T)/ cc-pVTZ and MP2/cc-pVQZ levels, within the frozen-core approximation. As implemented in CFOUR, they were obtained using analytic second derivatives of the energy.35 Taking advantage of the availability of the experimental ground-state rotational constants for all singly and one multiply substituted isotopic species of formamide,9,11 the so-called semiexperimental equilibrium structure,36 rSE e , was also obtained in the present study. The procedure is based on a determination of approximate equilibrium moments of inertia, Iie, that depend on only the equilibrium geometry (and isotopic masses) and then doing a least-squares fit of the geometry to best approximate the Iie’s. The latter are straightforwardly derived from the corresponding semiexperimental equilibrium 37 rotational constants, Bi,SE These are in turn obtained by e . correcting the experimental vibrational ground-state constants, Bi,exp 0 , for the vibrational effects: i ,calc Bei ,SE = B0i ,exp − ΔBvib
Figure 2. Potential energy profile of formamide as a function of the OCNHcis torsional angle at the CCSD(T)/cc-pVTZ level.
(4)
be accurate within 0.001−0.002 Å for bond distances and about 0.05−0.1° for angles. In Table 1, the best structural determination prior to this work is also reported. It was obtained in ref 2 by means of a composite scheme: starting from the geometry optimization at the fc-CCSD(T)/cc-pVQZ level, corrections due to basis set enlargement (from quadrupleto quintuple-ζ) and core correlation (using a quadruple-ζ set) were evaluated with the MP2 method. When this structure is compared to the CCSD(T)/CBS+CV one, a very good agreement is observed, with the largest deviation for distances being 0.0004 Å. The only noticeable discrepancy is a difference of about 0.2° for the ∠(HCN) angle. As mentioned in Methodology and Computational Details, the semiexperimental equilibrium structure was also determined by making use of the vibrational ground-state rotational constants for 14 isotopic species9,11 and is reported in Table 1 as well. A good agreement with the CCSD(T)/CBS+CV structure is noted except for the parameters involving the −NH2 group. While for angles (i.e., ∠(CNHtrans) and ∠(CNHcis)) the deviations are small (i.e., less than 1°, ∼ 0.5% in relative terms), for distances the discrepancy is more significant; in particular, for r(NHtrans) it is as large as 0.016 Å, which means a deviation of about 2%. This can be ascribed to the failure of perturbation theory in properly describing the large-amplitude motion. This inability affects both the α constants and the model itself. A deeper investigation of the problem is warranted but is beyond the scope of the present work. The last comment concerns the comparison with the pure experimental geometries reported in Table 1. In ref 2, the so-called r(2) m mass-dependent structure of Watson et al.45 was determined by exploiting the availability of the rotational constants for several isotopologues. Despite the fact that the authors of ref 2 considered this type of geometry suitable for nonrigid molecules like formamide, it presents limitations in accurately describing the equilibrium geometry. The C−N, C−H, and N−Htrans distances deviate from our bestestimated values by +0.007, + 0.012, and −0.017 Å, respectively, while the other bond lengths agree within the given uncertainties. Large deviations are also noted for the ∠(CNHtrans) and ∠(CNHcis) angles, which are overestimated and underestimated by 1.3° and 1.5°, respectively. In Table 1 the so-called substitution structure, rs, is also given. In ref 9, by using the Kraitchman equations,46 the substitution coordinates of all nuclei and the corresponding structure were determined. Contrary to what is usually observed (i.e., severe limitations in
ΔBi,calc vib
where is the computed vibrational correction. Within vibrational second-order perturbation theory (VPT2), it is given by the following expression:38,39 i ,calc ΔBvib =−
1 2
∑ αri r
(5)
where the αis values are the vibration−rotation interaction constants, with r and i denoting the normal mode and the inertial axis, respectively. The computation of the αis values requires the cubic force field, with the latter being computed at the MP2/cc-pVQZ level of theory.
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RESULTS AND DISCUSSION As mentioned in the Introduction, the planarity of formamide has been the subject of many studies. According to our preliminary calculations, we can conclude that the molecule is beyond any doubt planar. The geometries optimized constraining planarity and employing quadruple-ζ basis sets irrespective of the theoretical method employed are real minima on the potential energy surface (PES), as demonstrated by the corresponding Hessian matrix. The equilibrium structures obtained from calculations with triple-ζ quality basis sets are found to be not entirely planar, with the corresponding torsional angle deviating a few degrees from planarity constraints and the corresponding barrier being extremely small. Figure 2 shows the behavior of the potential energy as a function of the torsional angle OCNHcis at the CCSD(T)/cc-pVTZ level (for the atom labeling, see Figure 1). It is seen that the barrier is only ∼0.55 cm−1. The structural parameters evaluated at different levels of theory are collected in Table 1. From these results, one sees that the valence correlation limit is already reached at the CCSD(T)/cc-pVQZ level, as the largest change observed when going to the CBS limit is about 0.001 Å for the C−N bond length. Core−valence corrections are known to be important for improving the molecular structure accuracy,40,41 thus lowering the bond distances by 0.001−0.002 Å. The angles seem to be well-converged at the CCSD(T)/cc-pVQZ level and, for these geometrical parameters, core-correlation effects seem to be negligible. According to the literature on this topic (see, for example, refs 30 and 42−44 and references therein), the CCSD(T)/CBS+CV equilibrium structure is expected to C
DOI: 10.1021/acs.jpca.6b01130 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A Table 1. Equilibrium Structurea (Distances in Angstroms, Angles in Degrees) of Formamide this work
ref 2
ref 9
parameter
CCSD(T)/ cc-pVTZ
CCSD(T)/ cc-pVQZ
CCSD(T)/ CBSb
CCSD(T)/ CBS+CVc
d rSE e
rBOe
f r(2) m
rsg
r(CO) r(CN) r(CH) r(NHtrans) r(NHcis) ∠(OCN) ∠(HCN) ∠(CNHtrans) ∠(CNHcis)
1.2140 1.3608 1.1025 1.0023 1.0049 124.90 112.21 121.08 119.23
1.2117 1.3577 1.1015 1.0016 1.0043 124.71 112.48 121.08 119.20
1.2112 1.3563 1.1008 1.0016 1.0042 124.58 112.69 121.08 119.19
1.2097 1.3543 1.0997 1.0007 1.0034 124.58 112.72 121.08 119.18
1.212(2) 1.354(2) 1.097(3) 1.017(2) 1.008(2) 124.2(5) 112.4(13) 120.5(2) 119.9(1)
1.2097 1.3547 1.1001 1.0006 1.0033 124.63 112.53 121.09 119.18
1.210(4) 1.361(4) 1.112(3) 0.984(4) 1.005(2) 124.8(4) 112.3(20) 121.8(5) 117.8(3)
1.219(12) 1.352(12) 1.098(10) 1.0015(30) 1.0016(30) 124.7(3) 112.7(20) 120.0(5) 121.6(3)
For atom labeling, see Figure 1. bEquilibrium structure accounting only for extrapolation to the CBS limit (i.e., first two terms of eq 1). cBestestimated equilibrium structure accounting for extrapolation to the CBS limit and core−valence correlation effects (eq 1). dSemiexperimental equilibrium structure; see text. eEquilibrium structure obtained from the following composite scheme: fc-CCSD(T)/cc-pVQZ + [(fc-MP2/ V(5,Q)Z)-(fc-MP2/VQZ)] + [(all-MP2/wCVQZ)-(fc-MP2/wCVQZ)]. See ref 2 for all details. fTwo-parameter mass-dependent r(2) m structure. See ref 2 for all details. gSubstitution rs structure. See ref 9 for all details. a
Table 2. Equilibrium Structurea (Distances in Angstroms, Angles in Degrees) of Formamide Dimer this work
ref 20
parameter
MP2/cc-pVQZ
CCSD(T)/cc-pVTZ
CCSD(T)/cc-pVQZ
CCSD(T)/CBS
r(CO) r(CN) r(CH) r(NHtrans) r(NHcis) ∠(OCN) ∠(HCN) ∠(CNHtrans) ∠(CNHcis) R(O···Hcis) ∠(O···HcisN)
1.2276 1.3370 1.0971 1.0016 1.0224 125.22 122.61 119.29 120.53 1.8344 173.88
1.2290 1.3424 1.1004 1.0032 1.0226 125.49 123.55 119.21 120.73 1.8407 174.34
1.2265 1.3398 1.0995 1.0025 1.0218 125.24 122.52 119.32 120.55 1.8448 173.65
1.2256 1.3383 1.0987 1.0023 1.0216 125.06 121.58 119.43 120.41 1.8375 172.97
b
CCSD(T)/CBS+CV 1.2240 1.3363 1.0976 1.0014 1.0208 125.07 121.48 119.45 120.40 1.8364 172.91
c
RI-MP2/aug-cc-pVQZ 1.229 1.338 1.097 1.002 1.023 125.1 114.0 119.4 120.5 1.837 173.5
For atom labeling, see Figure 1. bEquilibrium structure accounting only for extrapolation to the CBS limit (i.e., first two terms of eq 1). cBestestimated equilibrium structure accounting for extrapolation to the CBS limit and core−valence correlation effects (eq 1).
a
an accuracy comparable to that which we have presented for formamide. In Table 2 the geometry optimized at the RI-MP2/ aug-cc-pVQZ level from ref 20 is also reported. A reasonable agreement with the CCSD(T)/CBS+CV structure is noted, with the largest discrepancies noted for r(CO) and ∠(HCN): the distance is overestimated by ∼0.005 Å, and the angle underestimated by more than 6°. Such a large deviation for the angle is suspicious and perhaps results from a typographic mistake. The last comment concerns the ∠(O···HcisN) angle involved in the hydrogen bond. At all levels of theory this angle is about 173−174°, with very small changes when going from CCSD(T)/cc-pVTZ to CCSD(T)/CBS and then to CCSD(T)/CBS+CV. From the less accurate to the best level of theory the overall lowering is about 1.4°. Because the ∠(O··· HcisN) angle is very close to 180°, the CO···HcisN frame is very close to linearity. The comparison of the results of Tables 1 and 2 allows us to point out how the formamide structural parameters change when moving to the dimer. In Table 1 we note that the CN bond (r(CN) = 1.354 Å) has a partial double-bond character, which is explained with the resonance structures shown in the Introduction. Moving to FA1, a shortening of the CN bond by about 0.018 Å is observed, while r(CO) experiences a lengthening of about 0.014 Å. This means that the formation of the hydrogen bond increases the partial double-bond
properly describing the equilibrium geometry; see, for instance, ref 42), the structural parameters agree well with our bestestimated equilibrium structure. Only for the ∠(CNHtrans) and ∠(CNHcis) angles are discrepancies of about 1 and 2°, respectively, found. However, the uncertainties affecting the rs parameters are rather large, being about 1 order of magnitude larger than those associated with the CCSD(T)/CBS+CV geometry. As mentioned in the Introduction, this is the first systematic study of the equilibrium structure of the FA1 dimer of formamide. The results obtained are summarized in Table 2; for the atom labeling, the reader is referred to Figure 1. First, as already noted for formamide, quadruple-ζ quality basis sets are required to accurately describe the molecular structure. When MP2/cc-pVQZ and CCSD(T)/cc-pVTZ results are compared to the CCSD(T)/cc-pVQZ results, it is observed that the former level of theory provides structural parameters in better agreement with CCSD(T)/cc-pVQZ. This seems to suggest that the improvement in the basis set is more important than the improvement in the correlation treatment. When we move from considering the CCSD(T)/cc-pVQZ level to CCSD(T)/ CBS, bond distances shorten by about 0.001 Å. A further shortening of about 0.001−0.002 Å is then obtained by including the core-correlation correction. The resulting CCSD(T)/CBS+CV molecular structure is expected to have D
DOI: 10.1021/acs.jpca.6b01130 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A Table 3. Binding Energy (kJ/mol) of Formamide Dimer this work
ΔE ΔECPg ΔECP+ZPVh
ref 21a
ref 19b
ref 20c
ref 23d
MP2/ cc-pVQZ
CCSD(T)/ cc-pVTZ
CCSD(T)/ cc-pVQZ
CCSD(T)/ CBSe
CCSD(T)/ CBS+CV f
MP2/ cc-pVTZ
MP2/ CBS
RI-MP2/ CBS+ΔCC/aVTZ
CCSD(T)/ 6-31++g(d.p)
−63.23 −57.22 −48.18
−41.01 −28.69 −18.60i
−61.02 −55.70 −45.61i
−61.64 −61.64 −51.56i
−61.65 −61.65 −51.57i
−65.23 −54.68 −43.56
−62.34 − −
−62.68 −62.34 −
− − −54.06
a
Energies evaluated at the MP2/cc-pVTZ optimized geometries. bEnergies evaluated at the MP2/aug-cc-pVTZ optimized geometries. CBS limit obtained from all-electron MP2/aug-cc-pwCVnZ (n = D, T, Q) calculations. cEnergies evaluated at the RIMP2/aug-cc-pVTZ optimized geometries. ΔCC stands for a correction at the CCSD(T) level, and aVTZ stands for aug-cc-pVTZ. See text. dEnergies evaluated at the CCSD/6-31++g(d, p) optimized geometries. eFrom extrapolated energies to the CBS limit, as obtained at the corresponding equilibrium structure. fFrom CCSD(T)/CBS +CV energies, as obtained at the corresponding equilibrium structure (eq 1). gCounterpoise-corrected interaction energy according to eq 2. hZPV correction (10.08 kJ/mol) computed at the CCSD(T)/cc-pVTZ level. For the MP2/cc-pVQZ determination, ZPV correction (9.04 kJ/mol) at the corresponding level of theory has been used. iWhen ZPV MP2/cc-pVQZ corrections are applied, the results are CCSD(T)/cc-pVTZ, −19.65 kJ/ mol; CCSD(T)/cc-pVQZ, −46.65 kJ/mol; CCSD(T)/CBS, −52.60 kJ/mol; CCSD(T)/CBS+CV, −52.61 kJ/mol.
character of r(CN), whereas the double-bond character of r(CO) decreases. The r(NHcis) bond length is also affected and experiences a significant lengthening of about 0.018 Å that goes with an increase of the corresponding angle by about 1°. All the other structural parameters remain essentially unaffected by the hydrogen bond formation. Table 3 collects the binding energy values of the FA1 dimer evaluated at different levels of theory. This table reports the electronic energy differences ΔE corresponding to the first term within squared parentheses in eq 2 as well as the counterpoisecorrected ΔECP values, obtained as explained in Methodology and Computational Details (see eq 2). As already noted for the molecular structure, the MP2/cc-pVQZ level performs better than the CCSD(T)/cc-pVTZ level, thus providing a binding energy in good agreement with the CCSD(T)/CBS result. Inclusion of the core-correlation correction lowers the binding energy by only 0.01 kJ/mol, thus providing a negligible contribution. The binding energy increases with basis set size; in particular, the relative increase of ΔE and ΔECP going from the CCSD(T)/cc-pVTZ level to CCSD(T)/cc-pVQZ is on the order of 50% and ∼100%, respectively. The BSSE error (about 12 kJ/mol) is particularly large at the CCSD(T)/cc-pVTZ level (about 30% of ΔE), and is reduced to about 5 kJ/mol when the cc-pVQZ basis is employed. The large value for the BSSE error when the cc-pVTZ basis set is used might be, at least partially, an artifact due to limitations of the counterpoise correction approach when applied to post-Hartree−Fock methods. Inclusion of the ZPV correction, evaluated at both the CCSD(T)/cc-pVTZ and MP2/cc-pVQZ levels within the harmonic approximation (see Methodology and Computational Details), lowers the binding energy by about 10 kJ/mol. Our best-estimated zero-point corrected value, ΔCP+ZPV, is −51.6 kJ/ mol, and it is expected to have an accuracy of a few kilojoules per mole (see, for example, refs 43 and 44). Because the dimer contains two equivalent hydrogen bonds, each of them contributes roughly half of the binding energy and their strength can be considered moderate. In Table 3, previous results are also given. In particular, it is noted that in ref 20 the RI-MP2 method was employed to derive the CBS limit, subsequently corrected for the contribution of triple excitations using the CCSD(T)/aug-cc-pVTZ level of theory, thus obtaining an equilibrium binding energy of about −62.7 kJ/ mol, which is only 1 kJ/mol larger than our best value. A similar agreement is found for the MP2/CBS value determined by Vargas et al.19 Interestingly, the MP2/cc-pVTZ level of theory obtained in ref 21 provides fortuitously better results than the CCSD(T) method in conjunction with the same basis set. For
the ZPV- and CP-corrected binding energy, the CCSD(T)/631++g(d,p) value obtained by Cato et al.23 deviates from our best determination by only ∼2 kJ/mol.
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CONCLUDING REMARKS
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AUTHOR INFORMATION
A state-of-the-art quantum-chemical composite scheme has been applied to the structural and energetic characterization of formamide and its symmetric dimer, thus providing benchmark results for the peptide bond and the hydrogen-bond interaction. It has been reported that quadruple-ζ quality basis sets are needed to correctly describe both systems. We furthermore note that computation of accurate structures and hydrogen-bonding energies is a fundamental step for the development of accurate molecular mechanics force fields. For both formamide and FA1, structural parameters have been determined with an estimated accuracy of about 0.001− 0.002 Å for bond distances and of about 0.05−0.1° for angles. Concerning the binding energy, our best-estimated, zero-pointcorrected value is −51.6 kJ/mol and can be considered a reliable reference value, well within the range of chemical accuracy. In our opinion, in addition to the intrinsic interest of the results herein obtained, an interesting outcome of this work is the promise that high-level quantum-chemical composite approaches can be successfully employed to characterize the peptide bond and the hydrogen-bond interaction in model systems with an accuracy reached so far only for small rigid molecules.
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
This work was supported by Italian MIUR (PRIN 2012 “STAR: Spectroscopic and computational Techniques for Astrophysical and atmospheric Research”) and by the University of Bologna (RFO funds). The support of the COST CMTS-Actions CM1405 (MOLIM: MOLecules In Motion) and CM1401 (Our Astro-Chemical History) is acknowledged. E
DOI: 10.1021/acs.jpca.6b01130 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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