2646
J. Phys. Chem. 1996, 100, 2646-2651
Natural Bond Orbital Analysis of Carbon-13 Chemical Shieldings in Acetylenes Jonathan Bohmann and Thomas C. Farrar* Department of Chemistry, UniVersity of Wisconsin, Madison, Wisconsin 53706 ReceiVed: August 28, 1995; In Final Form: NoVember 15, 1995X
Ab initio calculations of NMR chemical shieldings of alkyne carbon atoms in nine acetylene compounds computed by the gauge-including atomic orbital (GIAO) method are reported. The unusually low chemical shielding anisotropy (159 ppm) found in the terminal alkyne carbon of phenylacetylene is found to be due to the Ramsey diamagnetic component of the shielding tensor rather than the paramagnetic component, which is commonly associated with large changes in shielding. Natural bond orbital analysis of ab initio molecular orbital wave functions has been used to provide insight into the role of electronic delocalization in the chemical shielding.
1. Introduction In this study, we examine changes in the shielding for alkyne carbon nuclei in substituted acetylenes, with particular attention on phenylacetylene. Phenylacetylene is of interest to us because no satisfactory explanation for the anomalous chemical shielding anisotropy (CSA) of its terminal (β) acetylene carbon could be found in the literature, even though it has been computed1 by the IGLO2 method. Reported CSA values for acetylene carbons fall in the range of 200-240 ppm,3-5 but for phenylacetylene the CSA of the β-acetylenic carbon is 159 ppm from recent measurements in the liquid and solid states.6,7 The influence of molecular symmetry on shielding is well-known.8 Beeler and co-workers5 demonstrated that differences between experimental acetylenic 13C tensors in acetylene and methylacetylene are consistent with the effect of the C∞ molecular symmetry on the Ramsey9 paramagnetic contribution to the shielding in acetylene. By analogy, one may expect that absence of C∞ symmetry in phenylacetylene could play a role in the unusually low CSA compared to linear acetylenes. Reductions in the CSA of 31P and 15N shielding tensors in the iminophosphenium cation relative to PtN and N2 respectively have been explained on the basis of the absence of linear symmetry in the paramagnetic shielding tensor.10 In this case, the 31P CSA was reduced from 1376 (PtN) to 580 ppm, and the 15N tensor was reduced from 603 (N2) to 421 ppm. Similar reductions in the anisotropy of cyano 15N tensors have been measured in a series of 10 parasubstituted benzonitriles,11 which exhibit CSAs ranging from 369 to 384 ppm, compared to 563 ppm for HCN.12 Aside from symmetry, one might expect that the shieldings of the acetylenic carbons will also be affected by the delocalized electronic character of the phenyl ring through conjugation of the acetylenic π-bond with the ring. Spiesecke and Schneider13 and Karplus and Pople14 were able to qualitatively rationalize 13C isotropic shieldings in conjugated molecules on the basis of π-electron density.14 Although theoretical calculations15 and experimental studies11 of shieldings have found difficulty correlating shieldings with π-electron density, formal charge and electronegativity parameters, explanations of shielding trends based on measures of charge density remain popular and are somewhat useful when, for example, considering the effects of hydrogen bonding on shielding.16 In this paper, we demonstrate that the surprisingly low shielding and CSA of the β-acetylenic carbon atom in phenylacetylene is primarily due * Author to whom correspondence should be sent. X Abstract published in AdVance ACS Abstracts, January 15, 1996.
0022-3654/96/20100-2646$12.00/0
to the diamagnetic contribution to the shielding tensor and not directly related to the absence of linear symmetry and the anisotropy of the paramagnetic tensor. With the aid of natural bond orbital (NBO) analysis,17 we explore the degree of π-electron delocalization in several acetylene compounds, including phenylacetylene, and find that the unusually low CSA and low absolute shielding in phenylacetylene cannot be attributed to an anomaly in the π-electron charge distribution. 2. Representations of Shieldings NMR chemical shielding, denoted by σ, expresses a reduction in the strength of the external magnetic field (B0) at the nucleus caused by the chemical environment to give a new local field,
Blocal ) B0(1 - σ)
(1)
The most general expression for chemical shielding is of secondrank tensor form. When the shielding tensor is symmetric, diagonalization gives three independent elements, which may be written as σxx, σyy, and σzz.18 In the case of a nucleus on the axis of a symmetric top molecule, there are only two independent components, σzz and σxx ) σyy, corresponding to shielding parallel and perpendicular to the symmetry axis, respectively. The isotropic shielding, usually observed in the liquid state, is simply the mean of the components of the tensor,
σiso ) 1/3(σxx + σyy + σzz)
(2)
An important characteristic of the shielding tensor is the chemical shielding anisotropy ∆σ or CSA. When σzz g σyy g σxx, the CSA is given by18
∆σ ) σzz -
σyy + σxx 2
(3)
3. Calculation Methods Theoretical calculations of the shielding tensors presented in this paper have been reported5 and reviewed,19 but no one study has computed all the tensors by a uniform method that allows comparison among them. In order to provide a common basis for comparison, the geometry parameters of all molecules studied were determined by modern geometry optimization techniques based on ab initio molecular orbital calculations. Optimization was done with Gaussian 9220 at the 6-31G* basis set level. NBO analysis and chemical shielding calculations were done with the optimized molecular geometries. Natural © 1996 American Chemical Society
Carbon-13 Chemical Shieldings in Acetylenes
J. Phys. Chem., Vol. 100, No. 7, 1996 2647
TABLE 1: Comparison of Theoretical Shielding Tensor Anisotropies with Experimental Shielding Anisotropiesa R
σxx
σyy
σzz
σiso
∆σ
∆σ(expt)
120.3 120.9 125.0 111.8 117.6 177.4
239.0 211.4 233.9 165.4 241.7 156.4
240 ( 5c 214 ( 5d 218 ( 5e 159 ( 3f
RCtC*H(β) H 40.6 CH3 50.5 CtCH 47.0 φb 51.0 CtN 36.6 F 125.3
279.6 261.9 280.9 62.4 222.1 279.5 281.7
RC*tCH(R) CH3 CtCH φb CtN F
21.7 297.6 113.7 43.0 287.3 124.4 7.80 21.0 315.1 114.6 54.5 286.5 131.8 15.4 286.3 105.7
CH3 CtN F
32.7 57.6 79.4
RCtCR
275.9 259 ( 5d 244.3 218 ( 5e 300.7 232.0 270.9
278.9 114.7 246.2 227 ( 5d 287.4 134.2 229.8 288.1 149.0 208.7
a The first five columns give RHF/6-311G* GIAO components of d the shielding tensor σRR (R ) x, y, z), the isotropic shielding, σiso , and the shielding anisotropy, ∆σd, for terminal (β) and nonterminal (R) 13C nuclei in monosubstituted (RsC tC sH) and symmetrically R β disubstituted (RsCtCsR) acetylenes. When σxx ) σyy, only σxx is shown. The last column gives experimental values for ∆σ. b For phenylacetylene σxx is oriented perpendicular to the plane of the phenyl ring. c See ref 4. d See ref 5. e See ref 3. In the experiment, the shieldings for the R- and β-carbons could not be distinguished. f Value from refs 6 (liquid state) and 7 (solid).
population analysis and natural bond orbital analysis17 were carried out at the 6-311G* level with the Gaussian 92 program. Theoretical NMR shieldings were computed at the 6-311G* basis set level with the TEXAS93 program by Wolinski and co-workers.21 This is a very efficient implementation of the gauge-including (originally gauge-independent) atomic orbital (GIAO) concept22 first used in ab initio calculations by Ditchfield.23 4. Results Calculated components of chemical shielding tensors for 14 unique carbon sites in acetylene, monosubstituted derivatives (RsCRtCβsH), and symmetrically disubstituted derivatives (RsCtCsR) are summarized in Table 1. For the monosubstituted acetylenes, results for the β-carbon nuclei, which includes acetylene itself, are grouped at the top of the table, followed by the results for R-carbon nuclei. The results for the disubstituted acetylenes appear at the bottom of the table. The first column indicates the substituent R. The second three columns contain the Cartesian components of the diagonalized tensor. In all cases except phenylacetylene only σxx and σzz are shown, since the molecules may be classified as symmetric tops and σxx ) σyy. The fourth column gives the isotropic chemical shielding, σiso, the mean of the tensor components. Comparisons of experimental isotropic chemical shifts to calculated isotropic shieldings are not presented here; see the Appendix for this data. The fifth column gives the CSA, ∆σ. Values of the shielding are reported in units of parts per million (ppm) relative to the bare nucleus. For the sake of comparison, an isolated carbon atom would have a shielding of 260.7 ppm relative to the bare carbon nucleus C+6.24 The calculated anisotropies are in reasonable agreement with experimental values, shown in the last column. Note that the CSA is a very useful quantity for comparing theoretical shieldings to experiment. Since the CSA is a difference between tensor components, comparison of experimental to calculated CSAs is direct and does not require knowledge of the absolute
shielding of a reference compound. For phenylacetylene, acetylene, and the β-carbon of methylacetylene, agreement is excellent. In all other cases, the theoretical CSA overestimates the experimental value by about 16 ppm. The reason for this discrepancy is unknown. However, the calculations predict the correct ordering of the anisotropies for the β-carbons. 5. Interpretation of the Shielding Tensor The shielding tensor can be interpreted as a sum of the diamagnetic and paramagnetic tensors σd and σp, according to the Ramsey9 theory of shielding. When the nucleus resides at the origin of the coordinate system, a single component of the diagonalized shielding tensor for a nucleus may be written in Gaussian units as
σzz )
e2 2mc2
〈0|D ˆ (z)|0〉 -
( ) ∑{ ep
2mc
2
〈0|Pˆ 1(z)|n〉〈0|Pˆ 2(z)|n〉 En - E0
n
}
+ cc
(4)
where cc stands for the complex conjugate. The operators
D ˆ (z) ≡ ∑ i
( ) 1
-
ri
zi2
ri3
Pˆ 1(z) ≡ ∑Lˆ zi
(5)
(6)
i
Lˆ zi
Pˆ 2(z) ≡ ∑2 i
ri3
(7)
each involve a sum over the electrons in the molecule, indexed by i. The sum over n in the second term of (4) is over all the excited electronic states of the molecule, including the continuum. Similar expressions follow for σxx and σyy. The first and second terms of (4) are usually referred to as the diamagnetic, σd, and paramagnetic, σp, terms respectively. The separation of the shielding tensor into σd and σp is somewhat artificial and corresponds to the position of the nucleus as the choice of the gauge origin for the external magnetic field. However, the separation is meaningful because the paramagnetic tensor of the Ramsey formalism is directly related to the observable spin-rotation tensor.24 6. Interpretation of Shielding Trends 6.1. Diamagnetic Shielding. Relationships between shielding and molecular structure are usefully investigated by studying the diamagnetic and paramagnetic shielding terms separately. Components of the Ramsey diamagnetic tensor may be computed by the common-origin method. As in the GIAO calculation, the shielding is computed by the ab initio coupled HartreeFock (CHF) method25 but with a gauge origin of the external field common to all atoms of the molecule and centered on the carbon atom of interest. This requires the calculation to be carried out without the formation of the gauge-including atomic orbitals (GIAOs). Components of the common-origin diamagnetic tensor σdRR (R ) x, y, z), the diamagnetic contribution to d , the CSA, ∆σd, and the isotropic diamagnetic shielding, σiso are shown in Table 2. That the most important factor in the diamagnetic shielding is simply the geometry of the ground state wave function is reflected in the fact that, except for phenyld is nearly constant at about 280 ppm for the acetylene, σzz
2648 J. Phys. Chem., Vol. 100, No. 7, 1996
Bohmann and Farrar
TABLE 2: Components of the Common-Origin Diamagnetic d , the Diamagnetic Contribution to the Tensora σRR Anisotropy, ∆σd, and the Isotropic Diamagnetic Shielding, d for Mono- and Disubstituted Acetylenesb σiso R
d σxx
d σyy
d σzz
d σiso
AD d σiso
∆σ
RCtC*H(β)
d
H CH3 CtCH φd CtN F
343.5 279.6 322.2 381.1 282.9 348.4 394.6 280.9 356.5 477.7 467.1 293.1 412.8 395.2 279.5 356.5 387.2 281.7 352.0
321.4 347.2 355.9 414.1 356.7 352.0
-63.9 -98.2 -113.7 -179.3 -116.7 -105.5
CH3 CtCH φd CtN F
402.7 290.0 365.1 422.5 287.3 377.4 536.4 510.1 318.1 454.8 424.8 286.5 378.7 424.5 286.3 378.3
364.2 377.4 448.0 379.0 379.4
-112.7 -135.2 -205.2 -138.3 -138.2
CH3 CtN F
440.1 476.1 468.6
RC*tCH(R)
RCtCR
293.2 391.2 387.8 -146.9 287.4 413.2 414.5 -188.7 288.1 408.4 410.0 -180.5
a
Computed by the program TEXAS9321 with the NOGI keyword. See text for more information. b There is excellent agreement with the d isotropic shielding computed by the atom-dipole methodc (ADσiso ). d c Note the large relative magnitude of ∆σ for phenylacetylene. See ref 24. d For phenylacetylene σxx is oriented perpendicular to the plane of the phenyl ring.
β-carbons and 287 ppm for the R-carbons. The values of σdxx are within 7 ppm for fluoroacetylene, diacetylene, and methylacetylene. This feature of the diamagnetic shielding is somewhat surprising, given that these three substituents are quite different in their influence on the electronic structure of the acetylenic carbon-carbon π-bond, as shown below. The value of the isotropic diamagnetic shielding from the common-origin calculation can be checked against the value computed by using the atom-dipole method of Gierke and Flygare,24 which is known to give quite accurate results.1 In the atom-dipole calculation, σd is broken down into a local term, which depends only on the atom under consideration, and a nonlocal term, which is determined by the atomic numbers and positions of all other atoms relative to the one under consideration. Thus, the atom-dipole isotropic diamagnetic shielding is AD d σiso
d ) σatom +
e2
Zn
∑n r
3mc
(8) n
where σdatom ) 260.7 ppm for 13C. The sum is over all nuclei in the molecule excluding the one of interest. Zn and rn are the nuclear charge (atomic number) and position of each nucleus, with the origin of the coordinate system on the nucleus under consideration. The values for isotropic diamagnetic shielding d ) and the comcomputed by the atom-dipole method (ADσiso d mon origin ab initio method (σiso) are shown in Table 2. The agreement of the two methods is excellent. While they are not presented here, it is known that individual diamagnetic tensor components may be computed quite accurately by the atomdipole method.24 Note that, for most cases, the discrepancy between the results of the two methods is on the order of only 1 ppm, or about 0.3% of the approximate range of 300 ppm for carbon shielding values. The diamagnetic contribution to the anisotropy is shown in the last column of Table 2. It should be noted that for both alkyne carbon nuclei of phenylacetylene, the magnitude of the diamagnetic anisotropy (-178 ppm (β), -205 ppm (R)) is greater than for all of the other compounds
p TABLE 3: Components of the Paramagnetic Tensor σRR Found by Subtracting the Diamagnetic Tensor Elements Individually from the Total Shielding Tensora
R RCtC*H(β)
p σxx
p σyy
p σzz
p σiso
∆σp
H CH3 CtCH φb CtN F
-302.9 0 -201.9 302.9 -330.6 -21.0 -227.4 309.6 -347.6 0 -231.4 347.6 -426.7 -404.7 -71.0 -300.9 344.7 -358.9 0 -239.1 358.6 -261.9 0 -174.6 261.9
CH3 CtCH φb CtN F
-381.0 -379.5 -528.6 -489.1 -370.3 -408.1
CH3 CtN F
-407.4 -418.5 -389.2
RC*tCH(R)
RCtCR
+7.6 0 -3.0 0 0
-251.4 -253.0 -340.2 -246.9 -272.6
388.6 379.5 505.9 370.3 408.1
-14.3 -276.4 393.1 0 -279.0 418.5 0 -259.5 389.2
p a The resulting isotropic paramagnetic shielding, σiso , and anisotropy, ∆σ, are also shown. b For phenylacetylene σxx is oriented perpendicular to the plane of the phenyl ring.
(-63 to -116 ppm (β), -112 to -138 ppm (R)). Also, the alkyne carbon nuclei in phenylacetylene exhibit the greatest d d σiso values, as might be expected from the fact that ADσiso (see eq 8) only depends on the atomic number and positions of other atoms and should scale roughly as the number of atoms in a molecule. 6.2. Paramagnetic Shielding. The paramagnetic shielding tensor elements are simply found by subtracting the diamagnetic tensor elements individually from the total shielding tensor elements computed from the GIAO calculation, so that
σpRR ) σRR - σdRR, R ) x, y, z
(9)
Components of the paramagnetic tensor, σpRR, the paramagnetic contribution to the CSA, ∆σp, and the isotropic paramagnetic p , are shown in Table 3. Perhaps the most shielding, σiso important feature of the paramagnetic tensor elements is that p ) 0. As shown by Ramsey,9 when for the linear molecules σzz the molecular ground state term is 1Σ, the orbital angular momentum integrals of Pˆ 1(z) in (4) vanish by orthogonality of p to vanish. As a consequence, the eigenstates, causing the σzz σzz for the linear acetylenes is entirely diamagnetic in origin, and quite constant for the linear acetylenes in Table 2, and in a wide variety of other linear or near-linear molecules.5,26 For both alkyne carbon nuclei in phenylacetylene and methylacetylp is nonzero, as expected. For the ene, Table 3 shows that σzz p is quite large β-carbon in phenylacetylene, the value of σzz (-71.0 ppm). One might expect the lowering of the CSA in the β-carbon of phenylacetylene relative to the other compounds p . Changes in the anisotropy are to be attributable to σzz commonly associated with the paramagnetic contribution to the shielding tensor for carbon, phosphorus, and nitrogen nuclei. See, for example, ref 10. In the case of the β-carbon of phenylacetylene, the paramagnetic contribution to the anisotropy, ∆σp, for the β-carbon of phenylacetylene, 344.7 ppm lies well within the range of the other carbon nuclei (263-347 ppm). It is clear that the lowering of the total CSA for the β-carbon of phenylacetylene relative to that of the other acetylenes is not due to the paramagnetic tensor anisotropy but to the rather large diamagnetic tensor anisotropy (-178 ppm) discussed above. Similarly, the lower CSA of the β-carbon CSA for methylacetylene (211 ppm) relative to acetylene (239 ppm) cannot be
Carbon-13 Chemical Shieldings in Acetylenes
J. Phys. Chem., Vol. 100, No. 7, 1996 2649
TABLE 4: Summary of π NBO Delocalization Energies Estimated from Second Order Perturbation Theorya R b
CH3 φc
CtCHd CtN F
delocalization
no.
energy (kcal/mol)
πCC f σ* CH (A) σCH f π* CC (D) πCCx f π* ring (A) πring f π* CCx (D) πCCy f σ* CCring (A) σCCring f π* CCy (D) πCC1 f π* CC2 (A) πCC2 f π* CC1 (D) πCC f π* CN (A) πCN f π* CC (D) nF f π* CC (D)
6 6 1 1 2 2 2 2 2 2 2
