Article pubs.acs.org/JPCA
Molecular Structure of Thiourea Cristina Puzzarini* Dipartimento di Chimica “G. Ciamician”, Università di Bologna, Via F. Selmi 2, 40126 Bologna, Italy ABSTRACT: The molecular structure of thiourea has been investigated under Cs, C2, and C2v symmetry constraints. At the coupled-cluster level in conjunction with a triple-ζ basis set, only the C2 conformer has been found to be a real minimum on the potential energy surface. Its equilibrium structure has therefore been accurately evaluated using both theoretical and experimental data. With respect to the former, high-level quantum-chemical calculations at the coupled-cluster level in conjunction with correlationconsistent basis sets ranging in size from triple- to quintuple-zeta have been carried out. Extrapolation to the complete basis-set limit as well as corecorrelation effects and inclusion of full treatment of triple excitations in the cluster operator have been considered. On the basis of the vibrational groundstate rotational constants available for five isotopic species and the corresponding computed vibrational corrections, the semiexperimental equilibrium geometry of thiourea has also been determined for the first time.
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actually a transition state.9 In order to further clarify this point, in the present work, a preliminary investigation at the coupledcluster (CC) and MP2 levels with basis sets of triple- and quadruple-ζ quality has been carried out for structures of Cs, C2, and C2v (planar) symmetry. As it has been confirmed that only the C2 conformer is a minimum on the PES and an accurate investigation of the molecular structure of thiourea is still missing, its equilibrium geometry has been determined by means of a state-of-the-art computational approach. The latter is based on the coupled-cluster theory in conjunction of hierarchical series of correlation-consistent basis sets, extrapolation to the complete basis-set limit, and consideration of core-correlation effects. Furthermore, the availability of the rotational constants for five isotopic species (namely, CS(NH2)2, C34S(NH2)2, 13CS(NH2)2, CS(15NH2)(NH2), and CS(ND2)2)6 enables the determination of a semiexperimental equilibrium structure. The latter is based on the combination of experimental ground-state rotational constants with calculated vibrational corrections and, nowadays, it is considered the best approach to determine reliable equilibrium geometries for polyatomic molecules.10−12 Finally, following the rotational study of laser ablated thiourea of ref. 6, some spectroscopic properties have been theoretically investigated. As pointed out by Lesarri et al.,6 since sulfur-containing molecules have been detected in the interstellar medium and related compounds, such as thioformaldehyde and formamide, have also been identified (see, for instance, ref. 13), a deeper knowledge of spectroscopic parameters might turn out to be useful for future radioastronomical investigations.
INTRODUCTION Thiourea (SC(NH2)2) is the sulfur analogue of urea and one of the simplest thioamides. It has been known for more than one century and has a wide range of uses; for example, it is widely employed in the production of pharmaceuticals (sulfothiazoles, thiobarbiturates) and pesticides (see refs 1−3 and references therein) and as an additive to some plastic materials.3 Some thioureas are also well-known toxins.1 Due to nonlinear optical properties, single crystals of thiourea are being extensively employed in the electronic industry, for example, as polarization filters, electronic light shutters, electronic modulators, and as components in electro-optic and electro-acoustic devices (see ref 3 and references therein). Thiourea and substituted thioureas are furthermore widely used as additives in various electrochemical processes.4 As a consequence, thiourea has received considerable attention over the past decades, but, despite its importance and use in various fields, investigation of its molecular structure is rather limited. After its first structure determination by X-ray diffraction,5 only recently (in 2004) has a microwave spectroscopy study provided a partial gas-phase substitution structure.6 On the contrary, the vibrational spectrum of thiourea has been widely investigated and characterized (see refs 7−9 and references therein). While in most vibrational studies bands were assigned assuming for thiourea a C2v planar symmetry, ab initio calculations ranging from second-order Møller−Plesset perturbation theory (MP2) to density functional theory (DFT) have shown that only the heavy atom skeleton, NCSN, is planar, and the C2 conformer, with nonplanar amino groups, is the lowest in energy. While at the MP2 level of theory, with basis sets of double-ζ quality, both Cs and C2 symmetry structures have been found to be minima on the potential energy surface (PES), 7 computations at different levels of theory in conjunction with basis sets of triple-ζ quality showed that the Cs conformer is © 2012 American Chemical Society
Received: February 14, 2012 Revised: April 3, 2012 Published: April 3, 2012 4381
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Article
formula for the CCSD(T) correlation contribution,29 respectively. In the expression given above, n = T, Q, and 5 have been chosen for the HF-SCF extrapolation, and n = Q and 5 have been used for CCSD(T). To monitor the convergence to the CBS limit, geometry optimizations at the CCSD(T) level in conjunction with the cc-pVnZ (n = T,Q,5) basis sets have also been performed. Core-correlation (CV) effects have been included by adding the corresponding correction, dΔE(core)/dx, to eq 1:
METHODOLOGY The CC level of theory employing the CC singles and doubles (CCSD) approximation augmented by a perturbative treatment of triple excitations (CCSD(T))14 has been mainly used in the present work in conjunction with the correlation-consistent Dunning and co-workers basis sets, cc-p(C)VnZ (n = D,T,Q,5).15−18 All the calculations reported have been carried out with the quantum-chemical CFOUR program package.19 Conformers Investigation. A preliminary investigation of the C2, Cs, and C2v (planar) conformers has been carried out at the MP220 and CCSD(T) levels of theory in conjunction with the cc-pVTZ basis set, within the frozen core (fc) approximation. Geometry optimizations have been performed using analytic-gradient techniques21 as implemented in CFOUR. Analogously, the harmonic force constants have been determined using analytic second-derivative techniques.22 For the Cs conformer, further geometry optimizations and harmonic force field calculations have also been carried out at the MP2/cc-pCVTZ (all electrons correlated) and (fc)MP2/ccpVQZ levels. Theoretical Equilibrium Structure. For the C2 conformer (see Figure 1), the geometry optimizations described in the
dECBS + core dE∞(HF‐SCF) dΔE∞(CCSD(T)) = + dx dx dx dΔE(core) + dx
(2)
The core-correlation energy correction, ΔE(core), is obtained as the difference of the all-electron and fc CCSD(T) calculations using the core−valence cc-pCVQZ basis set.17,18 Due to the high computational cost, the additivity of the full treatment of triples (full-T) directly applied to the geometrical parameters has been assumed. Therefore, full triples corrections have been obtained as Δr(full‐T) ≃ r(CCSDT) − r(CCSD(T))
(3)
in conjunction with the cc-pVDZ basis set. Semiexperimental Equilibrium Structure. The so-called semiexperimental structure has also been considered and obtained by a least-squares fit of the molecular structural parameters to the equilibrium moments of inertia, Iie. The latter are straightforwardly obtained from the corresponding equilibrium rotational constants, Bie, which are derived from the experimental ground-state constants, Bi0, by correcting them for vibrational and electronic effects: Bei = B0i +
present section mainly involve the CCSD(T) method mentioned above. The full CC singles, doubles and triples (CCSDT)23−25 model has also been considered in order to include the full account of triple excitations. Basis-set effects as well as core-correlation contributions have been accounted for simultaneously at an energy-gradient level. In detail, the equilibrium structure has been obtained by making use of the composite quantum-chemical scheme presented in refs 26 and 27. The contributions considered are the Hartree−Fock self-consistent-field (HF-SCF) part extrapolated to the basis-set limit, the valence correlation energy at the CCSD(T) level extrapolated to the basis-set limit, and the core-correlation correction. The extrapolation to the complete basis set (CBS) limit has been performed as described in ref 26. The CBS gradient is given by
∞
∑ αri − ΔBeli r
(4)
In the fitting procedure, the weighting scheme has been chosen in order to have the moments of inertia equally weighted. As mentioned in the Introduction, experimental ground-state rotational constants for five isotopic species are available, namely, CS(NH2)2, C34S(NH2)2, 13CS(NH2)2, CS(15NH2)(NH2), and CS(ND2)2.6 This means that, in addition to the main isotopologue, data for the isotopic substitution at sulfur, carbon, nitrogen, and hydrogen are available. In eq 4, αir are the computed vibration−rotation interaction constants, with r and i denoting the normal mode and the inertial axis, respectively. These constants have been obtained by means of vibrational second-order perturbation theory (VPT2),30 following the approach described in ref 31. The required cubic force fields have been computed at the MP2 level in conjunction with different correlation-consistent basis sets of triple-ζ quality, the cc-pVTZ,15,16 the aug-cc-pVTZ,16,32 and the core−valence cc-pCVTZ.17,18 All electrons have been correlated in conjunction with the latter, whereas the fc approximation has been used with the other basis sets. As already mentioned, the harmonic part has been obtained using analytic second derivatives of the energy,22 while the corresponding cubic force field has been determined in a normal-coordinate representation via numerical differentiation of the analytically evaluated force constants, as described in refs 31 and 33−35. The cubic force fields have been initially obtained for the main isotopic species and then transformed to the normal-coordinate representations of all the other isotopic
Figure 1. Molecular structure of thiourea: atoms labeling. Top right: the tridimensional picture of the C2 conformer.
dECBS dE∞(HF‐SCF) dΔE∞(CCSD(T)) = + dx dx dx
1 2
(1)
∞
where dE (HF-SCF)/dx and dΔE (CCSD(T))/dx are the energy gradients corresponding to the exp(−Cn) extrapolation scheme for the HF-SCF energy28 and to the n−3 extrapolation 4382
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species for which experimental ground-state rotational constants are available. The electronic corrections to rotational constants, ΔBiel, are due to the electronic-distribution contribution to the moments of inertia and are thus connected to the rotational g-factor (see, for example refs 36−38): m ΔBeli = e g i Bei mp (5)
Table 1. Equilibrium Structure, Rotational Constants, Energy, and Harmonic Frequencies of Thiourea Conformers at the CCSD(T)/cc-pVTZ level C−S C−N ∠NCS N−H1 ∠CNH1 N−H2 ∠CNH2 ∠SCNH1 ∠SCNH2 ∠NCSN Ae Be Ce ΔEe ΔE0b ω1 ω2 ω3 ω4 ω5 ω6 ω7 ω8 ω9 ω10 ω11 ω12 ω13 ω14 ω15 ω16 ω17 ω18
where me and mp are the masses of the electron and proton, respectively. Since there are not experimental values available for the rotational g-tensor of any isotopic species of thiourea, the rotational g-tensor and the corresponding electronic corrections to rotational constants for the various isotopic species have been computed at the CCSD(T)/aug-cc-pVTZ level (using the CBS+CV+fT geometry). The quantumchemical calculation of the rotational g tensor is performed as a second derivative of the energy with respect to the components of an external magnetic field as well as of the total angular momentum of the molecule.39 The calculations are performed using analytic derivative techniques40 together with perturbation-dependent basis functions39 in order to speed up the basis-set convergence. Electronic contributions are usually small and negligible.
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RESULTS AND DISCUSSION As mentioned above, stable conformers of Cs, C2, and C2v (planar) symmetry have been investigated at the MP2/ccpVTZ and CCSD(T)/cc-pVTZ levels of theory. The results for the latter level are collected in Table 1. We first note that, as already pointed out in the literature,6,9 the conformer of C2 symmetry results to be the more stable by less than 1 kcal/mol. The energy difference further decreases once the zero-point vibrational (ZPV) corrections, obtained within the harmonic approximation, are included. ZPV energies (within the harmonic approximation) are obtained as: harm EZPV =
1 2
∑ diωi
(Å) (Å) (deg.) (Å) (deg.) (Å) (deg.) (deg.) (deg.) (deg.) (MHz) (MHz) (MHz) kcal/mol kcal/mol cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1
C2 conformer
Cs conformer
C2v conformer
1.6637 1.3693 123.09 1.0059 114.12 1.0081 117.56 12.39 152.44 180.0 10604.9 5076.4 3450.0 0.0a 0.0a 383.7 395.0 407.1 453.1 547.8 586.1 643.7 771.8 1075.9 1089.4 1427.7 1430.5 1635.6 1655.0 3572.9 3577.7 3703.1 3703.6
1.6712 1.3596 122.45 1.0034 116.22 1.0050 121.42 8.49 165.51 180.0 10602.7 5096.4 3447.1 0.89 0.35 i223.9 229.8 391.2 422.5 454.3 586.2 639.4 770.8 1046.2 1066.3 1421.5 1447.3 1628.4 1655.6 3601.2 3609.4 3743.5 3744.9
1.6737 1.3555 122.35 1.0023 117.41 1.0038 122.89 0.0 180.0 180.0 10627.0 5097.1 3444.8 0.96 0.69 i241.6 i362.8 392.0 412.9 452.2 595.8 642.1 766.0 1031.4 1061.6 1413.9 1455.0 1627.6 1650.7 3613.9 3622.0 3761.3 3762.5
(6)
Arbitrarily fixed. bZPV correction added to the equilibrium value, ΔEe.
where di and ωi are the degeneracy and the harmonic frequency of the ith vibrational mode, respectively. Inspection of the harmonic frequencies reveals that only the C2 conformer is a real minimum on the PES, the Cs and C2v conformers having one and two imaginary frequencies, respectively. The former is thus a transition state, and it might be seen as the transition state for either the internal rotation of one amino group, corresponding to a rotation of 180 degrees, or for the inversion of one amino group. Therefore, the C2 and Cs conformers are connected via either the C−N torsion or the NH2 inversion. On the other hand, the C2v planar structure can be viewed as the “transition state” for the amino groups inversion, for both of them at the same time. In other words, the C2v planar structure turns to be a second-order saddle point connecting two equivalent C2 minima as well as two equivalent Cs transition states, that in turn connect two equivalent C2 minima. The transition state nature of the Cs conformer has also been confirmed by harmonic force field evaluation at the MP2/ccpCVTZ (with all electrons correlated) and MP2/cc-pVQZ (within frozen core approximation) levels of theory. Being the only minimum on the PES, the C2 conformer has therefore been investigated in more details. The corresponding optimized geometries, as obtained at the CCSD(T) level
employing different basis sets, are summarized in Table 2 together with the extrapolated structure (eq 1), that including the core-correlation correction (eq 2) and the best estimate derived by inclusion of full-T contribution (eq 3). From these results, it is first observed that the valence correlation limit is not entirely reached at the CCSD(T)/cc-pV5Z level, as changes as large as 0.002 Å for bond lengths and 1° for angles can been observed. Core−valence corrections are important for improving the molecular structure accuracy, as they can be as large as 0.003 Å for distances and 0.9° for angles. Full-T contributions are small and almost negligible, as the largest corrections are smaller than 0.001 Å for bonds and 0.03° for angles. On the whole, according to the literature on this topic (see, for example, refs 12, 26, 27, 38, 41, and 42), the best estimated structural parameters (denoted as CBS+CV+fT in the following) are expected to have an accuracy of 0.001−0.002 Å for bond distances and about 0.03−0.05 degrees for angles. Comparison to previous theoretical results is not reported in the table, as, to the best of our knowledge, only geometry optimizations at lower levels of theory have been previously carried out.6,7,9 We limit our discussion to briefly note an
i
a
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Table 2. Semiexperimental and Computed Equilibrium Geometries of the C2 Conformer of Thioureaa semiexp.: ABe C−S C−N ∠NCS N−H1 ∠CNH1 N−H2 ∠CNH2 ∠SCNH1 ∠SCNH2 ∠NCSN
b
c
VQZ
V5Z
CBS
CBS+CV
1.6603 1.3641 122.90 1.0048 114.68 1.0066 118.40 11.28 154.40 180.0
1.6574 1.3633 122.87 1.0045 114.93 1.0063 118.76 10.85 155.42 180.0
1.6550 1.3626 122.84 1.0045 115.14 1.0062 119.08 10.48 156.42 180.0
1.6518 1.3594 122.78 1.0033 115.35 1.0049 119.37 10.01 157.27 180.0
CBS+CV+fT
fit 1
fit 2
fit 3
fit 4
1.65395(23) 1.35975(15) 122.760(10) 0.99874(3) 115.36f 1.00376(11) 119.40f 9.99f 157.31f 180.0
1.65455(18) 1.35940(11) 122.737(7) 1.00308(90) 114.934(85) 1.00598(46) 119.40f 9.99f 157.31f 180.0
1.65455(18) 1.35940(11) 122.737(7) 1.0125(28) 115.36f 1.00727(78) 118.05(27) 9.99f 157.31f 180.0
1.65455(18) 1.35940(11) 122.737(7) 1.0033f 114.94(12) 1.00601(36) 119.34(13) 9.99f 157.31f 180.0
d
1.6526 1.3595 122.77 1.0033 115.36 1.0049 119.40 9.99 157.31 180.0
For atoms labeling see Figure 1. Distances in Å, angles in degrees. bCBS geometries evaluated using the n−3 extrapolation technique with n = Q,5. See text. cCV corrections, obtained with the cc-pCVQZ basis set, added to CBS values. See text. dfT corrections added to the CBS+CV results. See text. eSemiexperimental equilibrium structure obtained employing vibrational corrections at the MP2/aug-cc-pVTZ level and the A and B rotational constants (see text). One time the standard deviation is given as uncertainty. fFixed at the CBS+CV+fT value. a
Table 3. Partial Semiexperimental and Experimental Structures of the C2 Conformer of Thioureaa semiexp.: fit 2/CVTZab AB C−S C−N ∠NCS N−H1 ∠CNH1 N−H2
d
1.65468(17) 1.35893(10) 122.710(7) 1.00050(82) 115.128(78) 1.00800(43)
AC
e
1.65155(50) 1.36009(30) 122.786(20) 0.9960(26) 115.48(25) 1.0220(15)
semiexp.: fit 2/ABc BC
f
1.65319(69) 1.35872(41) 122.801(28) 1.0151(34) 115.52(31) 1.0076(17)
augVTZ
g
1.65455(18) 1.35940(11) 122.737(7) 1.00308(90) 114.934(85) 1.00598(46)
VTZh
CVTZi
r0j
r0k
1.65465(17) 1.35891(10) 122.705(7) 0.99959(81) 115.186(77) 1.00844(42)
1.65468(17) 1.35893(10) 122.710(7) 1.00050(82) 115.128(78) 1.00800(43)
1.6493(21) 1.3680(13) 122.84(82) 0.9511(92) 119.5(11) 0.9992(65)
1.645(4) 1.368(3) 123.0(2)
a
Distances in Å, angles in degrees. bSemiexperimental equilibrium structure obtained employing vibrational corrections at the MP2/cc-pCVTZ level (see text). One time the standard deviation is given as uncertainty. cSemiexperimental equilibrium structure obtained employing the A and B rotational constants (see text). One time the standard deviation is given as uncertainty. dThe A and B rotational constants have been used. eThe A and C rotational constants have been used. fThe B and C rotational constants have been used. gVibrational corrections at the (fc)MP2/aug-cc-pVTZ level have been used. hVibrational corrections at the (fc)MP2/cc-pVTZ level have been used. iVibrational corrections at the (all)MP2/cc-pCVTZ level have been used. jEffective structure. This work. kSubstitution structure.6
overall good agreement and we refer interested readers to refs 6, 7, and 9. The semiexperimental equilibrium structure of thiourea has been obtained as explained in the Methodology section, and the results are collected in Tables 2 and 3 (for atoms labeling, we refer the reader to Figure 1). In all fitting procedures, the nondeterminable geometrical parameters have been kept fixed at the corresponding CBS+CV+fT values. First of all, it is observed (Table 2) that the available rotational constants only allow one to accurately determine the structure of the heavy atom skeleton. The determination of the geometrical parameters involving hydrogens is limited in number and accuracy. At most, the two N−H distances and one ∠CNH angle or one N−H bond length and the two ∠CNH angles can be obtained from the fit. In all cases, the derived parameters turn out to be less accurate. The fits reported in Table 2 only make use of the moments of inertia corresponding to the A and B rotational constants (the reason will be clear from the discussion given below). In more detail, the fit involving only the parameters of the heavy atom skeleton and the two N−H distances is denoted as “fit 1”; “fit 2” and “fit 3” in addition fit one ∠CNH angle (∠CNH1 and ∠CNH2, respectively), while “fit 4” considers the N−H2 bond length and the two ∠CNH angles. From Table 2, the fit denoted as “fit 2” seems to be the one that provides the most reliable results. The comparison of this empirical structure with the CBS+CV+fT geometry shows an
agreement within 0.001−0.002 Å for bond lengths and within 0.03−0.4° for angles. Such discrepancies are on the order of the estimated uncertainties affecting our best estimated structure, and only slightly larger for one angle. On the contrary, the errors reported for the semiexperimental structures, based on the standard deviation of the fit, are clearly underestimated. According to ref.,10 0.001 Å is the typical error in the determined bond distances when only first-row elements are involved; such error then increases whenever heavier atoms are considered and/or fits are ill-conditioned.11,12,43 The issue of the determinable parameters and their accuracy deserves a deeper investigation, and the corresponding results are collected in Table 3. In particular, as “fit 2” seems to provide the best results, in this context it was the only one considered. It should be pointed out that we use the rotational constants for labeling and discussing the fits, but in all cases the moments of inertia have been actually fitted. We first note that the results corresponding to the fit in which all the three moments of inertia (IA, IB, and IC) are used, are not reported as such fit provides unreliable and inaccurate results, even for the heavy atom skeleton. This might be ascribed to the molecular structure that, being close to the planarity, renders independent only two rotational constants over three.37 On the contrary, any combination of two rotational constants, A and B, or A and C, or B and C, leads to similar results for the NCSN planar frame of the molecule, but the results obtained for the geometrical parameters involving hydrogens are different. In particular, we 4384
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4385
10669.1 5161.5 3490.1 89.2 14.3 24.3 −0.227 −0.084 −0.003 10579.9 5147.2 3465.8 1.08 4.60 4.89 0.37 4.56 1.96 2.12 −4.08 −0.135
exp
c
10581.8159(169) 5143.31525(178) 3463.78724(184) 1.305(195) 4.55(43) 4.27(126) 0.3938(88) 4.34(61) 1.9958(23) 2.0726(28) −4.0684(28) −0.1150(2)
Main-iso 10669.1 4999.1 3415.0 89.2 13.8 23.4 −0.227 −0.077 −0.002 10579.9 4985.3 3391.6 1.02 4.47 5.08 0.34 4.43 1.96 2.12 −4.08 −0.134
theo
b
exp
c
10581.797(70) 4981.48027(315) 3389.59742(125) 1.305d 4.55d 4.27d 0.3938d 4.34d 1.9950(30) 2.0711(55) −4.0661(55) −0.1138(4)
S-iso
34
10669.1 5154.3 3486.8 88.3 13.9 23.9 −0.227 −0.084 −0.003 10580.8 5140.4 3462.9 1.07 4.65 4.84 0.37 4.57 1.96 2.12 −4.08 −0.135
theo
b
exp
c
10582.801(69) 5136.4700(36) 3460.78147(142) 1.305d 4.55d 4.27d 0.3938d 4.34d 1.9922(41) 2.0659(81) −4.0581(81) −0.1148(4)
C-iso
13
10393.7 5096.8 3430.9 86.4 13.8 23.6 −0.215 −0.083 −0.003 10307.3 5083.0 3407.3 1.06 4.40 4.63 0.36 4.38 1.98 2.14 −4.12 −0.134
theo
b
15
exp
c
10308.983(77) 5079.1886(45) 3405.29515(184) 1.305d 4.55d 4.27d 0.3938d 4.34d 1.9739(53) 2.096(11) −4.070(11) −0.1134(5)
N-iso 8694.5 4725.3 3077.2 61.9 17.8 22.2 −0.150 −0.075 −0.003 8632.6 4707.5 3055.0 0.87 3.26 2.40 0.31 3.25 1.96 2.12 −4.08 −0.469
theo
b
expc 8638.51(33) 4703.5156(50) 3051.5683(37) 1.305d 4.55d 4.27d 0.3938d 4.34d 1.9958c 2.0726c −4.0684d −0.337(3)
D4-iso
Rotational and nitrogen quadrupole-coupling constants in MHz, quartic centrifugal-distortion constants in kHz, and inertial defects in uÅ2. bCBS-CV-fT equilibrium rotational constants (Ae, Be, and Ce) augmented by vibrational corrections (ΔA0, ΔB0 and ΔC0) at the (all)MP2/cc-pCVTZ level and electronic corrections (ΔAel, ΔBel, and ΔCel) at the (fc)CCSD(T)/aug-cc-pVTZ level, quartic centrifugaldistortion constants at the (fc)CCSD(T)/cc-pVTZ level, nuclear quadrupole-coupling constants at the (all)CCSD(T)/cc-pCVQZ level (CBS+CV+fT geometry). cReference 6. dFixed at the corresponding main isotopologue value. See ref 6. eInertia defect: Δ0 = I0c − I0a − I0b (I’s are the moments of inertia).
a
Ae Be Ce ΔA0 ΔB0 ΔC0 ΔAel ΔBel ΔCel A0 B0 C0 ΔJ ΔJK ΔK δJ δK χaa(14N) χbb(14N) χcc(14N) Δ0e
theo
b
Table 4. Rotational Parameters of Isotopic Species of Thiourea (C2 Conformer)a
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centrifugal-distortion constants, we note that the experimental determination was limited to the main isotopic species and, with the exception of δJ, the values are affected by large uncertainties. As computations show that in some cases large changes occur when moving from one isotopologue to another, a better option would have been to fix in the fit the centrifugaldistortion constants to the computed values rather than to the experimental values of the main isotopic species. With respect to the nitrogen quadrupole-coupling constants, a good agreement between theory and experiment is observed, with discrepancies ranging from 0.3% to 2%. Predictions for isotopologues and parameters here not considered can be obtained by the author. The last comment concerns the issue of which conformer was actually observed. As mentioned in ref 6, the available rotational data did not allow the determination of the position of the hydrogen atoms (i.e., dihedral angles) and thus did not enable one to discriminate between C2 and Cs structures. At the CCSD(T)/cc-pVTZ level of theory, a difference of about 20 MHz in their equilibrium B rotational constants is observed. Furthermore, even if the inclusion of zero-point vibrational corrections reduces the energy difference between the two conformers to 0.35 kcal/mol (∼122 cm−1), such a difference still prevents the detection of the Cs conformer with the technique employed in ref 6. Therefore, inspection of our results in Tables 1 and 4 confirms the conclusions drawn in ref 6, based on computations at the MP2/ 6-311++G(3df,2pd) level (MP4(SDTQ)/6-311++G(3df,2pd) for energy evaluations), that the C 2 conformer was experimentally observed.
note that the N−H1 distance results to be too short when A and C are employed and too long when B and C are used. On the whole, a lower accuracy is observed for the fits involving either the A and C rotational constants or the B and C ones. To clarify this point, we decided to analyze the derivatives of the rotational constants with respect to the structural parameters. From their inspection we note that, while A strongly depends on the C−N distance, it does not depend on the C−S bond length at all. The dependence of all rotational constants on both N−H distances is also small. As concerns angles, while the dependence of all rotational constants on ∠NCS is evident, the dependence of B and C on the two ∠CNH angles is nearly negligible. In view of these considerations, it is clear that it is not possible to find any combination of two rotational constants that is able to properly determine all geometrical parameters. As a consequence, only the partial structure already discussed above can be obtained. Furthermore, the determination of the semiexperimental equilibrium structure is hampered by correlation between parameters. The correlation matrix in fact indicates a strong correlation between C−N, C−S and ∠NCS and between the two N−H distances and the corresponding angles. In Table 3, the results obtained from the use of different force fields, i.e., (all)MP2/cc-pCVTZ, (fc)MP2/aug-cc-pVTZ, and (fc)MP2/cc-pVTZ, are also collected. We first note that all levels of theory provide fits of good quality, with remaining maximum residuals for rotational constants ranging from 20 kHz to 1.5 MHz, where the largest residuals apply to the rotational constants not involved in the fit. Concerning the geometrical parameters, the different force fields lead to very similar results, with the largest differences observed for the two N−H distances (discrepancies as large as 0.003 Å). By comparing the semiexperimental structural parameters to the CBS+CV+fT ones, the (fc)MP2/aug-cc-pVTZ level of theory provides the best agreement. In Table 3, for comparison purposes, pure experimental geometries are also reported. These are the partial effective r0 structure,37 obtained by a leastsquares fit of the molecular parameters to the vibrational ground-state moments of inertia (derived from the experimental ground-state rotational constants6), and the partial substitution rs structure.6,37 As well-known (see, for instance, ref 12), both types of structure present severe limitations in properly describing the equilibrium geometry. In the present case, the C−S and C−N distances result to be overestimated and underestimated, respectively, by about 0.01 Å. For r0, it is also evident that the parameters involving hydrogens are far from the corresponding equilibrium values. In Table 4, the computed vibrational and electronic contributions to rotational constants for all the isotopic species considered are collected. From these results it is evident that the vibrational contributions are smaller than 1%, while the electronic are largely smaller than 1 MHz (0.003−0.23 MHz). While the former are of fundamental importance for properly deriving the equilibrium structure from the experimental ground-state rotational constants, the latter turned out to be unimportant. The last point touched in the present work concerns the predictive capability of the chosen computational approach. In Table 4, theoretical and experimental ground-state rotational, quartic centrifugal-distortion, and nitrogen quadrupole-coupling constants of the five isotopologues considered so far are collected. For rotational constants, the good agreement is evident, with deviations largely smaller than 0.1%. As concerns
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CONCLUSIONS In the present paper, a thorough investigation of the equilibrium structure of thiourea is reported. For the first time, the molecular geometry has been determined by means of high-level quantum-chemical calculations at the coupled-cluster level, thus providing structural parameters with an estimated accuracy of about 0.001−0.002 Å for bond distances and of about 0.03−0.05 degrees for angles. The pure computational equilibrium structure determination has also been complemented by a semiexperimental approach, which is based on the combination of experimental ground-state rotational constants with calculated vibrational corrections. This is nowadays considered the best approach to determine reliable equilibrium geometries for polyatomic molecules (see, for instance, refs 10−12). Ground-state rotational constants, which are the most important parameters in the field of rotational spectroscopy, have been determined with discrepancies from experimental values well within 0.1%. In conclusion, the present study further confirms that highlevel quantum-chemical computations with an adequate treatment of electron correlation effects, extrapolation to the basis-set limit, and inclusion of core correlation are able to quantitatively predict molecular structures and spectroscopic parameters, and thus provide important benchmark data in order to either validate or predict experimental information.
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AUTHOR INFORMATION
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[email protected]. Notes
The authors declare no competing financial interest. 4386
dx.doi.org/10.1021/jp301493b | J. Phys. Chem. A 2012, 116, 4381−4387
The Journal of Physical Chemistry A
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ACKNOWLEDGMENTS
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REFERENCES
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This work has been supported by “PRIN 2009” funds and by the University of Bologna (RFO funds).
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dx.doi.org/10.1021/jp301493b | J. Phys. Chem. A 2012, 116, 4381−4387
