(HCNH)+:Z with X, Z = NCH, CNH, FH, ClH, and FCl - American

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Ab Initio Study of Ternary Complexes X:(HCNH)þ:Z with X, Z = NCH, CNH, FH, ClH, and FCl: Diminutive Cooperative Effects on Structures, Binding Energies, and SpinSpin Coupling Constants Across Hydrogen Bonds Janet E. Del Bene,*,† Ibon Alkorta,*,‡ and Jose Elguero‡ † ‡

Department of Chemistry, Youngstown State University, Youngstown, Ohio 44555, United States Instituto de Química Medica, CSIC, Juan de la Cierva, 3, E-28006 Madrid, Spain

bS Supporting Information ABSTRACT: Ab initio calculations have been performed on a series of complexes in which (HCNH)þ is the proton donor and CNH, NCH, FH, ClH, and FCl (molecules X and Z) are the proton acceptors in binary complexes X:HCNHþ and HCNHþ:Z, and ternary complexes X:HCNHþ: Z. These complexes are stabilized by CHþ 3 3 3 A and NHþ 3 3 3 A hydrogen bonds, where A is the electron-pair donor atom of molecules X and Z. Binding energies of the ternary complexes are less than the sum of the binding energies of the corresponding binary complexes. In general, as the binding energy of the binary complex increases, the diminutive cooperative effect increases. The structures of these complexes, data from the AIM analyses, and coupling constants 1J(NH), 1hJ(HA), and 2hJ(NA) for the NHþ 3 3 3 A hydrogen bonds, and 1J(CH), 1hJ(HA), and 2hJ(CA) for the CHþ 3 3 3 A hydrogen bonds provide convincing evidence of diminutive cooperative effects in these ternary complexes. In particular, the symmetric N 3 3 3 Hþ 3 3 3 N hydrogen bond in HCNHþ: NCH looses proton-shared character in the ternary complexes X:HCNHþ:NCH, while the proton-shared character of the C 3 3 3 Hþ 3 3 3 C hydrogen bond in HNC:HCNHþ decreases in the ternary complexes HNC:HCNHþ:Z and eventually becomes a traditional hydrogen bond as the strength of the HCNHþ 3 3 3 Z interaction increases.

’ INTRODUCTION Among the many small molecules that are suitable choices for the central molecule in ternary complexes are hydrogen cyanide (HCN) and hydrogen isocyanide (HNC). These linear molecules may act as bases on one end and acids on the other and are capable of forming intermolecular bonds of various types. For this reason, studies of linear and cyclic clusters of HCN and HNC have been of continuing interest.18 Recently, we investigated cooperativity, also called nonadditivity effects, in complexes represented as X:NCH:Z9 and X:CNH:Z,10 for a series of molecules X and Z, which could serve as both Lewis acids and Lewis bases in these complexes. We observed an enhancement (a synergistic effect) of the binding energies of ternary complexes relative to the corresponding binary complexes. That is, HCN and HNC are stronger proton donors when they also act as electron pair donors, and stronger electron pair donors when they act as proton donors. Synergistic effects were also evident from the structures of these complexes and spinspin coupling constants across intermolecular bonds. As an extension of these two studies, we have now investigated complexes in which HCN and HNC have been replaced by the protonated ion (HCNH)þ in complexes X:(HCNH)þ:Z. It has r 2011 American Chemical Society

been observed previously that in complexes in which a single molecule acts as a double proton donor, binding energies are nonadditive in an antagonistic sense (diminutive), that is, the binding energies of ternary complexes are less than the sum of the binding energies of the corresponding binary complexes.11 We anticipate that diminutive relationships will not be limited to the binding energies of complexes X:(HCNH)þ:Z but will also extend to other properties as well. In this paper we examine the extent to which diminutive cooperative effects influence the structures, binding energies, and spinspin coupling constants across hydrogen bonds of ternary complexes X:(HCNH)þ:Z.

’ METHODS (HCNH)þ and 5 neutral monomers CNH, NCH, FH, ClH, and FCl (molecules X and Z), 5 binary complexes X:(HCNH)þ, 4 binary complexes (HCNH)þ:Z, and 20 ternary complexes Special Issue: Richard F. W. Bader Festschrift Received: April 17, 2011 Revised: May 12, 2011 Published: June 03, 2011 12677

dx.doi.org/10.1021/jp203576j | J. Phys. Chem. A 2011, 115, 12677–12687

The Journal of Physical Chemistry A

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Table 1. MP2/aug-cc-pVTZ Binding Energies of Ternary Complexes, Binary Complexes Isolated and in Ternary Complexes, And Reduced Binding Energies of Ternary Complexes X:(HCNH)þ:Z (kJ/mol) for Fixed X as a Function of Z ternary complexes X:(HCNH)þ:Z

δE(X:HCNHþ:Z)a

δE(ternary X:HCNHþ)b

δE(ternary HCNHþ:Z)c

δE(binary X:HCNHþ)d

δE(binary HCNHþ:Z)e

δ(δE)f

HNC:HCNH:NCH HNC:HCNH:FH

205.55 155.33

73.99 87.49

106.83 56.62

98.71 98.71

131.56 67.84

24.73 11.22 11.14

HNC:HCNH:ClH

142.55

87.57

43.84

98.71

54.98

HNC:HCNH:FCl

136.96

88.97

38.25

98.71

47.99

9.74

HCN:HCNH:NCH

202.74

71.18

108.98

93.76

131.56

22.58

HCN:HCNH:FH

151.52

83.68

57.76

93.76

67.84

10.08

HCN:HCNH:ClH

138.67

83.69

44.91

93.76

54.98

10.07

HCN:HCNH:FCl

133.00

85.00

39.24

93.76

47.99

8.75

HF:HCNH:NCH HF:HCNH:FH

170.71 114.25

39.14 46.41

119.16 62.71

51.54 51.54

131.56 67.84

12.40 5.13

HF:HCNH:ClH

101.28

46.30

49.74

51.54

54.98

5.24

HF:HCNH:FCl

95.01

47.02

43.47

51.54

47.99

4.53 11.22

HCl:HCNH:NCH

157.85

26.29

120.34

37.51

131.56

HCl:HCNH:FH

100.61

32.77

63.10

37.51

67.84

4.74

HCl:HCNH:ClH

87.68

32.70

50.17

37.51

54.98

4.81

HCl:HCNH:FCl

81.35

33.35

43.84

37.51

47.99

4.15

ClF:HCNH:NCH ClF:HCNH:FH

154.95 96.84

23.39 29.00

121.91 63.80

33.04 33.04

131.56 67.84

9.65 4.04

ClF:HCNH:ClH

83.90

28.92

50.86

33.04

54.98

4.13

ClF:HCNH:FCl

77.48

29.49

44.44

33.04

47.99

3.56

Equation 1a. b Equation 2. c Equation 5. d Equation 6. e Equation 3. f δ(δE) = δE(ternary X:HCNHþ) δE(binary X:HCNHþ) = δE(ternary HCNHþ:Z) δE (binary HCNHþ:Z). a

X:(HCNH)þ:Z have been optimized at second-order Møller Plesset perturbation theory (MP2)1215 with the 6-31þG(d,p) basis set.1619 The missing binary complex is (HCNH)þ:CNH, which spontaneously converts to HCN:(HCNH)þ through proton transfer. A similar reaction occurs in ternary complexes, in which case X:(HCNH)þ:CNH becomes X:HCN:(HCNH)þ. Thus, there are no ternary complexes with CNH as Z. Vibrational frequencies were computed to establish that each of the optimized structures is a local minimum on its potential surface. These structures have essentially linear CHþ 3 3 3 A and NHþ 3 3 3 A hydrogen bonds, with no more that a 5 deviation from linearity. Atom A is the electron pair donor atom (C, N, F, or Cl) of X and Z. The structures of monomers and complexes were subsequently fully reoptimized at MP2 using the Dunning aug-cc-pVTZ basis set.20,21 Binding energies and spinspin coupling constants are reported for these geometries. Geometry optimization and frequency calculations were carried out with the Gaussian 03 suite of programs.22 Nonadditivities of hydrogen bond energies in ternary complexes are traditionally evaluated according to eqs 1a and 1b. δEðX:HCNHþ :ZÞ ¼ EðX : HCNHþ :ZÞ ½EðXÞ þ EðHCNHþ Þ þ EðZÞ

ð1aÞ

δEðnonaddÞ ¼ δEðX:HCNHþ :ZÞ ½δEðX:HCNHþ Þ þ δEðHCNHþ :ZÞ ð1bÞ with δE(X:HCNHþ:Z) the binding energy of the ternary complex. That cooperative effects decrease the binding energies of ternary complexes can be seen in Table 1, which shows that the binding energy of the ternary complex X:HCNHþ:Z is less than the sum of the binding energies of the corresponding binary

complexes X:HCNHþ and HCNHþ:Z. However, we may still evaluate the binding energy of a ternary complex using an approach similar to that which will be used to examine spinspin coupling constants. δEðternary X:HCNHþ Þ ¼ EðX:HCNHþ :ZÞ EðHCNHþ :ZÞ EðXÞ

ð2Þ

δEðbinary X:HCNHþ Þ ¼ EðX:HCNHþ Þ EðXÞ EðHCNHþÞ

ð3Þ

δðδE ternary X:HCNHþ :ZÞ ¼ δEðternary X:HCNHþ Þ δEðbinary X:HCNHþ Þ ð4Þ For ease of discussion, δ(δE ternary X:HCNHþ:Z) will be referred to as the reduced binding energy of the ternary complex X:HCNHþ:Z (the diminutive effect) arising from the reduced binding energy of X:HCNHþ due to the presence of Z [δE(ternary X:HCNHþ)], with δE(binary X:HCNHþ) the binding energy of the binary complex. Similarly, the reduced binding energy of the ternary complex X:HCNHþ:Z arising from the reduced binding energy of HCNHþ:Z due to the presence of X is δEðternary HCNHþ:ZÞ ¼ EðX:HCNHþ:ZÞ EðX:HCNHþ Þ EðZÞ

ð5Þ

δEðbinary HCNHþ:ZÞ ¼ EðHCNHþ :ZÞ EðZÞ EðHCNHþ Þ 12678

ð6Þ

dx.doi.org/10.1021/jp203576j |J. Phys. Chem. A 2011, 115, 12677–12687


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Figure 1. Schematic representation of binding energies for complexes HCN:(HCNH)þ:FH and FH:(HCNH)þ:NCH. In each diagram, energies to the left on the upper half are δE[binary X:(HCNH)þ] and those on the lower half are δE[ternary HCNH)þ:Z]. Energies to the right on the upper half are δE[binary (HCNH)þ:Z] and those on the lower half are δE[ternary X:(HCNH)þ]. The sum of these for each pair is equal to the binding energy of the ternary complex δE[X:(HCNH)þ:Z]. The value of δ(δE) is given in the center of the diagram and is connected by dashed lines to the energies of corresponding complexes. The zero of energy on this diagram is E(HCNH)þ.

δðδE ternary X:HCNHþ :ZÞ ¼ δEðternary HCNHþ :ZÞ δEðbinary HCNHþ :ZÞ ð7Þ However, as demonstrated in refs 9 and 10, both eqs 4 and 7 lead to the same δ(δE). δðδE ternary X:HCNHþ :ZÞ ¼ δEðternary X:HCNHþ Þ δEðbinary X:HCNHþ Þ ð8aÞ ¼ δEðternary HCNHþ :ZÞ δEðbinary HCNHþ :ZÞ ð8bÞ where δ(δE ternary X:HCNHþ:Z) is also equal to the nonadditivity computed traditionally from eqs 1a and 1b. The inherent assumption in eq 4 is that the decreased stability of the ternary complex relative to the corresponding binary complexes arises from the weakening of only the X 3 3 3 HCNHþ interaction, while eq 7 attributes it solely to the weakening of the HCNHþ 3 3 3 Z interaction. In refs 9 and 10, it was demonstrated that these assumptions lead to useful structural and energetic correlations and may be related to changes in spinspin coupling constants in ternary complexes X:CNH:Z and X:NCH:Z relative to the corresponding binary complexes. To what extent similar

relationships hold for X:HCNHþ:Z complexes in which cooperative effects are diminutive will be examined below. MP2/aug-cc-pVTZ electron densities in binary and ternary complexes have been analyzed using the Atom in Molecules (AIM) methodology23 with the AIMAll program.24 A topological analysis has been carried out and atomic charges have been evaluated by numerical integration of the electron densities in the atomic basins. A value of 1 103 for the integrated Laplacian has been used as a cutoff, because smaller values of this parameter have been shown to provide small average errors in the total charge of the system.25 Spinspin coupling constants for monomers and complexes were computed using the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) method in the CI(configuration interaction)-like approximation,26,27 with all electrons correlated. For these calculations, the Ahlrichs28 qzp basis set was placed on 13C, 15N, and 19F atoms, and the qz2p basis set on 35Cl and the hydrogen-bonded 1H atoms of (HCNH)þ. The Dunning cc-pVDZ basis set20,21 was placed on the remaining H atoms. Coupling constants were evaluated as a sum of four terms, namely, the paramagnetic spinorbit (PSO), diamagnetic spinorbit (DSO), Fermi-contact (FC), and spin-dipole (SD).29 The coupling constant calculations were carried out 12679



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using ACES II30 on the IBM 1350 cluster (Glenn) at the Ohio Supercomputer Center.

’ RESULTS AND DISCUSSION Table S1 of the Supporting Information reports the structures of monomers and of binary and ternary complexes, and Figure S1 illustrates ternary complexes with X = Z. Table S2 provides the total energies of monomers and binary and ternary complexes. Structures and Binding Energies. The structures of binary complexes HCN:(HCNH)þ and HNC:(HCNH)þ, and ternary complexes HNC:(HCNH)þ:NCH and HCN:(HCNH)þ:NCH have C¥v symmetry; (HCNH)þ:NCH has D¥h symmetry. The remaining binary and ternary complexes have Cs symmetry with an essentially linear CH 3 3 3 A or NH 3 3 3 A arrangement, where A is the electron-pair donor atom of molecule X or Z. In ternary complexes X:(HCNH)þ:Z, the orientations of X and Z are similar to the orientations found in the corresponding binary complexes. A discussion of selected inter- and intramolecular distances in these complexes will be given below in the section on coupling constants. Table 1 reports the binding energies of ternary complexes [δE(X:HCNHþ:Z)], reduced binding energies of binary complexes in the ternary complexes [δE(ternary X:HCNHþ)] and δE(ternary HCNHþ:Z)], binding energies of binary complexes [δE(binary X:HCNHþ) and δE(binary HCNHþ:Z)], and the nonadditivity of binding energies of ternary complexes [δ(δE), the diminutive effect]. The complexes are arranged for fixed X as a function of Z. For ease of analysis, Table S3 of the Supporting Information reports corresponding data for these same complexes arranged for fixed Z as a function of X. Figure 1 graphically depicts the energetic relationships from eqs 4 and 7, and also illustrates that computing the diminutive effect on binding energies for the complexes HCN:(HCNH)þ:FH and HF:(HCNH)þ:NCH as described by these equations gives the same δ(δE). It also illustrates that evaluation of the binding energies of the ternary complexes gives the same result as eq 1a. For all complexes in Table 1, δ(δE) is positive, indicating that the X 3 3 3 (HCNH)þ interaction is weakened by the presence of Z, that is, the cooperative effect is diminutive. The weakening of the X 3 3 3 (HCNH)þ interaction decreases for fixed X with respect to Z in the order NCH . FH ClH > FCl which reflects the order of decreasing binding energies of the binary complexes (HCNH)þ:Z, although complexes with FH and ClH as Z may be interchanged. The largest effect is found for ternary complexes X:(HCNH)þ:NCH formed from the binary complex (HCNH)þ:NCH. This complex has a significantly greater binding energy than any other binary complex due to the presence of a symmetric HCN 3 3 3 Hþ 3 3 3 NCH hydrogen bond. However, in the ternary complexes X:(HCNH)þ:NCH, this bond loses proton-shared character. Thus, the NHþ 3 3 3 N hydrogen bond is significantly weakened due to the presence of X. Similarly, Table S3 indicates that the order of decreasing diminutive cooperative effects on binding energies of ternary complexes X:(HCNHþ):Z for fixed Z as a function of X is HNC > HCN . HF > HCl > ClF which is also the order of decreasing binding energies of the binary complexes X:(HCNH)þ.

Figure 2. Diminutive effects on the binding energies of ternary complexes X:(HCNH)þ:Z for fixed X as a function of the binding energies of binary complexes (HCNH)þ:Z.

Figure 3. Diminutive effects on the binding energies of ternary complexes X:(HCNH)þ:Z for fixed Z as a function of the binding energies of binary complexes X:(HCNH)þ.

Figure 2 presents plots of the diminutive effect on binding energies of complexes X:(HCNH)þ:Z versus the binding energies of the binary complexes (HCNH)þ:Z, which are ordered along the x-axis according to increasing binding energy. In Figure 2 there are four sets of vertically stacked points, each stack having a different X but the same binary complex (HCNH)þ:Z. The trendlines shown in Figure 2 connect reduced binding energies of ternary complexes with the same X. In Figure 2 the trendlines as a function of X are ordered according to decreasing diminutive effects as HNC > HCN > HF > HCl > ClF Figure 2 indicates that the diminutive effect increases as the binding energies of both X:(HCNH)þ and (HCNH)þ:Z increase. Figure 3 provides the corresponding plots of the diminutive effect on ternary complexes X:(HCNH)þ:Z versus the binding 12680


The Journal of Physical Chemistry A energies of binary complexes X:(HCNH)þ, which are ordered along the x-axis according to increasing binding energy. The vertical stacks of points refer to complexes with the same X but different Z, and the trendlines indicate the best linear relationship among ternary complexes with the same Z. The trendline for NCH as Z lies significantly higher on the δ(δE) axis than the remaining trendlines, reflecting the significant weakening of the NHþ 3 3 3 N hydrogen bond in the ternary complexes relative to (HCNH)þ:NCH. The trendlines for Z = HF and HCl are superimposable, while that of ClF is slightly lower on the δ(δE) axis. Electron Density Analysis. The topological analysis of the electron density within the AIM methodology shows the presence of intermolecular bond critical points (bcp’s) in the binary and ternary complexes. Values of the electron density (F), Laplacian (r2F), and local total energy density (H) at bcp’s are reported in Table S4 of the Supporting Information. Previous

Figure 4. Electron density at the bcp (au) vs the H 3 3 3 A interatomic distance (Å). The exponential trendlines have correlation coefficients of 0.998 or greater.

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studies have demonstrated that hydrogen bonds can be characterized based on the signs of r2F and H.31 Thus, strong hydrogen bonds have negative values of both r2F and H, hydrogen bonds of intermediate strength have a positive r2F and a negative H, while weak hydrogen bonds have positive values of both parameters. Among the binary complexes, only HNC:HCNHþ and HCNHþ:NCH have negative values of both parameters, and these two have the greatest binding energies. These two complexes also have the highest electron densities at the NHþ 3 3 3 N and CHþ 3 3 3 C bcp’s. The remaining binary complexes have hydrogen bonds of intermediate strength with negative values of H and positive values of r2F, and reduced electron densities at bcp’s. Formation of a ternary complex is associated with reduced absolute values of r2F and H relative to the corresponding binary complexes, another indication that the presence of Z weakens the X 3 3 3 HCNHþ interaction and the presence of X weakens the HCNHþ 3 3 3 Z interaction. The electron densities are also reduced at the bcp’s. The most dramatic effects are observed in the ternary complexes formed from the most stable binary complexes HNC:HCNHþ and HCNHþ:NCH. The AIM results are a clear indication of diminutive cooperative effects. The complete topological analysis of the binary and ternary complexes provides a large number of bond critical points for the NHþ 3 3 3 A and CHþ 3 3 3 A hydrogen bonds, where A is C, N, F, or Cl. Plots of the electron density at the bcp versus the interatomic distance for these interactions yield the exponential relationships which are shown in Figure 4, in agreement with previous reports.32 The diagrams in Figure 5 are pictorial indications of how the presence of HNC as X changes the electron density distribution in the ternary complex HNC:HCNHþ:NCH relative to the binary complex HCNHþ:NCH, and how the presence of NCH as Z changes the electron density distribution in the same ternary complex relative to the binary complex HNC:HCNHþ. Thus, the formation of the CHþ 3 3 3 C hydrogen bond in the ternary complex results in a loss of electron density in the bonding region of the NHþ 3 3 3 N hydrogen bond relative to

Figure 5. Electron density changes at (0.0005 au in the ternary complex HNC:HCNHþ:NCH relative to (a) the binary complex HCNHþ:NCH and isolated HNC and (b) the binary complex HNC:HCNHþ and isolated NCH. Blue and yellow regions indicate a loss and gain of electron density, respectively. 12681



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Table 2. NH and NA Distances (R, Å) and Coupling Constants 1J(NH), 2hJ(NA), and 1hJ(HA) (Hz) for Complexes X:(HCNH)þ:Z for Fixed Z as a Function of X R(NH) þ

1

J(NH)

(HCNH)

1.015

148.1

HNC:(HCNH)þ:NCH HCN:(HCNH)þ:NCH

1.099 1.103

111.0 109.9

R(NA)

2.607 2.601

2h

J(NA)

23.7 24.2

1h

J(HA) 9.2 10.1

HF:(HCNH)þ:NCH

1.135

99.2

2.566

27.4

18.6

HCl:(HCNH)þ:NCH

1.142

96.4

2.560

27.9

20.6

ClF:(HCNH)þ:NCH

1.149

93.7

2.554

28.5

22.8

(HCNH)þ:NCH

1.260

56.5

2.520

32.0

56.5

HNC:(HCNH)þ:FH

1.036

134.5

2.625

82.1

53.0

HCN:(HCNH)þ:FH

1.037

134.7

2.619

84.4

53.6

HF:(HCNH)þ:FH HCl:(HCNH)þ:FH

1.043 1.044

134.8 134.6

2.594 2.593

93.0 93.2

54.8 54.9

ClF:(HCNH)þ:FH

1.045

134.6

2.589

95.2

55.1

(HCNH)þ:FH

1.051

133.9

2.570

102.5

55.4

HNC:(HCNH)þ:ClH

1.042

132.1

3.078

8.0

3.4

HCN:(HCNH)þ:ClH

1.044

132.3

3.071

8.2

3.4

HF:(HCNH)þ:ClH

1.053

131.5

3.040

9.2

3.4

HCl:(HCNH)þ:ClH

1.053

131.1

3.037

9.3

3.4

ClF:(HCNH)þ:ClH (HCNH)þ:ClH

1.055 1.063

131.0 129.4

3.033 3.009

9.4 10.3

3.4 3.2

HNC:(HCNH)þ:FCl

1.033

134.7

2.659

61.6

49.4

HCN:(HCNH)þ:FCl

1.035

135.0

2.652

63.6

50.3

HF:(HCNH)þ:FCl

1.042

134.9

2.621

71.9

53.8

HCl:(HCNH)þ:FCl

1.042

134.6

2.620

71.8

53.9

ClF:(HCNH)þ:FCl

1.044

134.6

2.615

73.8

54.6

(HCNH)þ:FCl

1.050

133.7

2.592

80.8

56.9

the binary complex, while the formation of the NHþ 3 3 3 N hydrogen bond results in a loss of electron density in the bonding region of the CHþ 3 3 3 C hydrogen bond relative to the binary complex. Thus, these diagrams provide further evidence of diminutive cooperative effects in these complexes. SpinSpin Coupling Constants. Table 2 presents selected distances and coupling constants for (HCNH)þ, binary complexes (HCNH)þ:Z and ternary complexes X:(HCNH)þ:Z for fixed Z as a function of X. Table 3 presents distances and spinspin coupling constants for (HCNH)þ, the binary complexes X:(HCNH)þ, and ternary complexes X:(HCNH)þ:Z for fixed X as a function of Z. The PSO, DSO, FC, and SD components of J are given in Tables S5 and S6, respectively, of the Supporting Information. (HCNH)þ:NCH and X:(HCNH)þ:NCH. That the cooperative effect of X on coupling constants is diminutive is most dramatically illustrated by 1J(NH), 1hJ(HN), and 2hJ(NN) for the NHþ 3 3 3 N hydrogen bond in the binary complex (HCNH)þ: NCH and ternary complexes X:(HCNH)þ:NCH. The variation of 1J(NH) as a function of the NH distance is illustrated in Figure 6. There are two references points, the first at (1.015 Å, 148.1 Hz) belonging to isolated (HCNH)þ and the second at (1.260 Å, 56.5 Hz) belonging to the binary complex (HCNH)þ:NCH, which has a symmetric proton-shared N 3 3 3 Hþ 3 3 3 N hydrogen bond, in which case 1J(NH) and 1hJ(HN) are equal. Values for the ternary complexes lie between these two extremes, with absolute values ordered as HNC > HCN > HF > HCl > ClF

which is the order of decreasing binding energies of binary þ . That is, as the strength of the complexes X:(HCNH) X 3 3 3 HCNHþ interaction increases, the cooperative diminutive effect causes the proton-shared character of the N 3 3 3 Hþ 3 3 3 N hydrogen bond to decrease as it moves toward a traditional NHþ 3 3 3 N hydrogen bond. This results in a shorter NH distance, and a greater absolute value of 1 J(NH). Figure 7 illustrates the variation of 2hJ(NN) and 1hJ(HN) as a function of the NN distance in the same complexes. The largest value of 2hJ(NN) is found for the binary complex which has the shortest NN distance because the hydrogen bond is symmetric. Formation of a ternary complex results in a loss of proton-shared character, and a decrease in 2hJ(NN) as the NN distance increases. The points at the extremes of the curve belong to the binary complex HCN 3 3 3 Hþ 3 3 3 NCH with its symmetric protonshared hydrogen bond and to the ternary complex HNC:(HCNH)þ:NCH in which the NHþ 3 3 3 N hydrogen bond has the least amount of proton-shared character due to the strength of the interaction with HNC. Thus, values of 2hJ(NN) decrease as the strength of the X 3 3 3 (HCNH)þ interaction increases. The decrease in 2hJ(NN) in going from (HCNH)þ:NCH to X:(HCNH)þ:NCH is dramatically different from the increase in the absolute values of 2hJ(N-A) in going from CNH:Z to X: CNH:Z and of 2hJ(C-A) in going from NCH:Z to X:NCH:Z. These changes in the neutral complexes are associated with synergistic cooperative effects. A related pattern is evident for 1hJ(HN), that is, 1hJ(HN) decreases in absolute value as the strength of the X 3 3 3 12682



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Table 3. CH and CA Distances (R, Å) and Coupling Constants 1J(CH), 2hJ(CA), and 1hJ(HA) (Hz) for Complexes X:(HCNH)þ:Z for Fixed X as a Function of Z R(CH) 1J(CH) R(CA) þ

2h

J(CA)

1h

J(HA)

1.078

329.2

HNC:(HCNH)þ:NCH

1.117

291.9

3.020

75.6

5.3

HNC:(HCNH)þ:FH

1.134

289.6

2.958

92.7

0.4

HNC:(HCNH)þ:ClH

1.135

289.1

2.957

93.2

0.1

HNC:(HCNH)þ:FCl

1.137

288.5

2.950

95.2

0.7

HNC:(HCNH)þ

1.158

279.3

2.899

112.1

8.9

HCN:(HCNH)þ:NCH

1.107

295.5

2.910

29.5

4.7

HCN:(HCNH)þ:FH

1.120

297.1

2.858

35.4

4.0

HCN:(HCNH)þ:ClH

1.121

296.5

2.855

35.7

3.9

HCN:(HCNH)þ:FCl

1.122

296.6

2.850

36.4

3.8

HCN:(HCNH)þ

1.134

293.9

2.811

41.6

2.5

HF:(HCNH)þ:NCH

1.083

304.8

2.896

118.1

42.7

HF:(HCNH)þ:FH

1.088

314.8

2.844

144.5

51.0

HF:(HCNH)þ:ClH

1.088

314.2

2.846

142.1

50.4

HF:(HCNH)þ:FCl

1.088

315.2

2.840

146.0

51.5

HF:(HCNH)þ

1.092

319.9

2.805

164.3

56.9

HCl:(HCNH)þ:NCH

1.087

302.1

3.382

10.5

3.1

HCl:(HCNH) :FH

1.095

311.7

3.319

13.1

3.7

HCl:(HCNH)þ:ClH

1.095

311.0

3.317

13.2

3.7

HCl:(HCNH)þ:FCl

1.096

311.9

3.310

13.5

3.8

HCl:(HCNH)þ

1.101

315.6

3.270

15.5

4.2

(HCNH)

þ

ClF:(HCNH)þ:NCH

1.082

303.0

2.962

78.4

30.4

ClF:(HCNH)þ:FH

1.088

313.9

2.896

100.6

38.8

ClF:(HCNH)þ:ClH

1.088

313.4

2.897

100.0

38.7

ClF:(HCNH)þ:FCl

1.089

314.4

2.890

102.8

39.7

ClF:(HCNH)þ

1.093

319.1

2.849

119.5

45.9

Figure 6. 1J(NH) vs the NH distance for NHþ 3 3 3 N hydrogen bonds in X:(HCNH)þ:NCH and (HCNH)þ:NCH.

(HCNH)þ interaction increases. Because the magnetogyric ratio of 15N is negative and that of 1H is positive, all of the reduced coupling constants 1hK(HN) are positive, indicating that the NHþ 3 3 3 N hydrogen bonds in these complexes should be classified as proton shared.33 The binary complex (HCNH)þ: NCH with the symmetric hydrogen bond has the greatest amount of proton-shared character, while HNC:(HCNH)þ: NCH has the least. As evident from Table S5, all of these coupling constants are dominated by the FC term.

Figure 7. 2hJ(NN) (green diamond, left axis) and 1hJ(HN) (red squares, right axis) vs the NN distance for NHþ 3 3 3 N hydrogen bonds in X:(HCNH)þ:NCH and (HCNH)þ:NCH.

Couplings Constants for the NHþ 3 3 3 A Hydrogen Bond in the Remaining Complexes. 1J(NH). There are three other

sets of complexes in which (HCNH)þ acts as the proton donor through the NH group: X:(HCNH)þ:FH, X:(HCNH)þ:ClH, and X:(HCNH)þ:FCl. For all of these, 1 J(NH) values for the ternary complexes lie between the monomer which has the largest absolute value, and the corresponding binary complex which has the smallest absolute value. The presence of X decreases the NH distance and increases the absolute value of the coupling constant. However, there is little variation in 1J(NH) in the ternary complexes for fixed Z as a function of X. 1J(NH) in all complexes is dominated by the FC term. 2h J(NA). The NA distance in these same complexes is shortest in the binary complex, and longest in the complex HNC:(HCNH)þ:Z. For complexes with NH 3 3 3 F hydrogen bonds, absolute values of 2hJ(NF) are largest in the binary complexes (HCNH)þ:FH and (HCNH)þ:FCl and smallest in the ternary complexes HNC:(HCNH)þ:FH and HNC:(HCNH)þ:FCl in which the X 3 3 3 (HCNH)þ interaction is strongest. The decrease in the absolute values of both of these coupling constants for a given Z tends to follow the order of increasing binding energies of the binary complexes X:(HCNH)þ, although when X is HF and HCl, 2hJ(NF) values are essentially equal. Finally, although values of 2hJ(NCl) for complexes X:(HCNH)þ:ClH follow the same pattern, the values of this coupling constant are small and differ by less than 2 Hz. All of the two-bond coupling constants are dominated by the FC term. 1h J(HA). For ternary complexes X:(HCNH)þ:FH and X:(HCNH)þ:FCl and the corresponding binary complexes (HCNH)þ: FH and (HCNH)þ:FCl, values of 1hJ(HF) are negative. Since the magnetogyric ratios of 1H and 19F are both positive, values of the reduced coupling constant 1hK(HF) are also negative, indicating that these are traditional NH 3 3 3 F hydrogen bonds.33 The largest negative values are found in the binary complex, while the smallest values belong to the ternary complexes with HNC as X. To interpret 1h J(HF) consistently with 2hJ(NF), the distance dependence of this coupling constant must be considered. Figure 8 presents a plot of 1h J(HF) versus the HF distance for the binary and ternary complexes with NHþ 3 3 3 F hydrogen bonds. In this plot there is a point at (0.922 Å, 508 Hz) belonging to 1J(HF) for the isolated FH

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Figure 8. 1hJ(HF) vs the HF distance for complexes with NHþF hydrogen bonds. The data points at short distances correspond to FH monomer and to the proton-bound homodimer (FH)2Hþ with a symmetric hydrogen bond. See text.

monomer. Another reference point at (1.147 Å, 188 Hz) corresponds to 1hJ(HF) for the symmetric, proton-shared hydrogen bond in the proton-bound dimer HF 3 3 3 Hþ 3 3 3 FH. As the HF distance increases, 1hJ(HF) decreases, and at some distance (in this case, about 1.4 Å) changes sign and becomes negative as the HF distance further increases. Between 1.4 and 1.7 Å, the smaller the absolute value of 1hJ(HF), that is, the closer it is to 0 Hz, the greater is the proton-shared character of the hydrogen bond. However, at some distance (about 1.7 Å) there is a minimum in the curve at which point 1hJ(HF) has its maximum negative value, and then the absolute value decreases with increasing distance, eventually asymptotically approaching 0 Hz. Thus, the NH 3 3 3 F hydrogen bonds in binary and ternary complexes with FH and FCl as Z are traditional, with the binary complexes having the most proton-shared character. The HF distance in the ternary complexes is greater than 1.7 Å, so decreasing absolute values of 1hJ(HF) indicate a further loss of proton-shared character. Although 1hJ(HF) is also dominated by the FC term, the PSO term makes a non-negligible contribution. Finally, 1hJ(HCl) is only 3.2 Hz for (HCNH)þ:ClH and 3.4 Hz in the corresponding ternary complexes, indicating that these hydrogen bonds are traditional but providing little additional information. Couplings Constants for the CHþ 3 3 3 A Hydrogen Bond. 1J(CH). 1J(CH) has its largest value (329 Hz) in (HCNH)þ and its smallest value (279 Hz) in the binary complex HNC:(HCNH)þ. The values in the ternary complexes HNC:(HCNH)þ:Z lie between these two extremes because the presence of Z shortens the CH distance and increases 1J(CH) relative to the binary complex, in the order NCH > FH > ClH > FCl which is the order of decreasing binding energies of binary complexes (HCNH)þ:Z. However, it should be noted that, unlike (HCNH)þ: NCH, HNC(HCNH)þ does not have a symmetric C 3 3 3 Hþ 3 3 3 C hydrogen bond. A complex optimized under the constraint that this bond be symmetric has a very short CC distance of 2.754 Å and a value of 1J(CH) of 132 Hz. In the set of complexes with HCN as X, 1J(CH) also has its smallest value in the binary complex HCN:(HCNH)þ, as expected. However, the values of this coupling constant in the ternary complexes HCN:(HCNH)þ:Z are similar, differing by less than 2 Hz. Even more interesting is the observation that in

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Figure 9. 1J(CH) vs the CH distance for the ternary complexes HF:(HCNH)þ:Z and ClF:(HCNH)þ:Z and the corresponding binary complexes with HF and ClF as X.

the remaining three sets of complexes HF:(HCNH)þ:Z, HCl:(HCNH)þ:Z, and ClF:(HCNH)þ:Z and the corresponding binary complexes, 1J(CH) has its largest value in the binary complex and its smallest value in X:(HCNH)þ:NCH, a pattern quite different from that of complexes with HNC as X. To understand these differences, it is necessary to consider the nature of the hydrogen bonds in these complexes, the variation in the CH distances, and the distance-dependence of 1J(CH). Relative to the complexes HNC:(HCNH)þ and HCN:(HCNH)þ, the character of the hydrogen bond in the binary complexes HF:(HCNH)þ, HCl:(HCNH)þ, and ClF:(HCNH)þ has changed significantly. These latter complexes have relatively low binding energies, and their hydrogen bonds have little proton-shared character. Formation of the ternary complexes further decreases the proton-shared character of the CHþ 3 3 3 A hydrogen bonds, as evident from the CH distances, which are longest in the binary complex and shortest in the ternary complex with Z = NCH, as expected. However, in contrast to the complexes with HNC as X, 1 J(CH) for complexes with FH, ClH, and FCl as X have their smallest values in the ternary complexes with Z = NCH, and their largest values in the corresponding binary complexes. Figure 9 illustrates that 1J(CH) for the binary and ternary complexes with HF and ClF as X increases as the CH distance increases, although the second-order trendline suggests that if the CH distance were further elongated, 1 J(CH) would begin to decrease. An increasing 1J(DH) with increasing DH distance for hydrogen bonds with DH as the proton donor group has been observed in previous studies.33 Thus, it is interesting that the presence of Z exhibits a diminutive effect on the CH distance but not on 1J(CH). The difference arises because of the nature of the dependence of 1J(CH) on the CH distance in these hydrogen-bonded complexes. 2h J(CA). The variation of 2hJ(CC) and 2hJ(CN) for complexes with HNC and HCN as X resembles the variation of 2hJ(NN) for the NHþ 3 3 3 N hydrogen bond for complexes X:(HCNH)þ:NCH. In complexes HNC:(HCNH)þ:Z and HCN:(HCNH)þ:Z with CHþ 3 3 3 C and CHþ 3 3 3 N hydrogen bonds, respectively, the shortest intermolecular distances and the largest absolute values of 2hJ(CC) and 2hJ(CN) are found in the binary complexes; the longest distances and smallest 12684



Figure 10. 1hJ(HC) vs the HC distance for the binary and ternary complexes with CHþC hydrogen bonds. The data point at short distance corresponds to an optimized structure of HNC 3 3 3 Hþ 3 3 3 CNH constrained to have a symmetric hydrogen bond.

absolute values are found in the corresponding ternary complexes HNC:(HCNH)þ:NCH and HCN:(HCNH)þ:NCH in which the interaction with Z is strongest. For these complexes, the order of increasing CC and CN distances and decreasing absolute values of 2hJ(CC) and 2hJ(CN) with respect to Z is the order of decreasing binding energies of the binary complexes (HCNH)þ:Z. For the remaining sets of complexes HF:(HCNH)þ:Z, HCl:(HCNH)þ:Z, and ClF:(HCNH)þ:Z, the shortest distances and largest values of 2hJ(CA) are once again found in the binary complex, and the longest distance and smallest value of 2hJ(CA) occur in the complex with NCH as Z. The order of increasing CA distance and decreasing 2hJ(CA) tends to follow the order of decreasing binding energies of the binary complexes (HCNH)þ:Z, although values for HF and HCl as Z are similar and are interchanged in complexes with CHþ 3 3 3 F hydrogen bonds. This interchange is also seen in the diminutive effects on the binding energies of the ternary complexes. 1h J(HA). 1hJ(HC) for HNC:(HCNH)þ and the corresponding ternary complexes HNC:(HCNH)þ:Z changes gradually from a small positive value in the binary complex to a small negative value in the ternary complex HNC:(HCNH)þ:NCH. Although the hydrogen bond in HNC:(HCNH)þ is not symmetric, it does have proton-shared character, as is apparent from the structure of this complex and from the positive value of the reduced coupling constant 1hK(HC). However, that this complex is far from symmetric can be seen from the plot in Figure 10, which illustrates the dependence of 1hJ(HC) on the HC distance. 1hJ(HC) is equal to 132 Hz for the complex constrained to have a symmetric hydrogen bond; þ9 Hz for the binary complex HNC:(HCNH)þ with an asymmetric protonshared hydrogen bond; and 5 Hz for the traditional hydrogen bond in HNC:(HCNH)þ:NCH. On this plot, an increasing negative value of 1hJ(HC) indicates decreasing proton-shared character, as these values fall on the short-distance side of the minimum in the trendline. In contrast, 1hJ(CN) values are positive for HCN:(HCNH)þ and HCN:(HCNH)þ:Z, which means that the reduced coupling constants 1hK(HN) are negative, indicating that all CH 3 3 3 N hydrogen bonds are traditional. The smallest negative value of this coupling constant is found for the binary complex, which indicates that its hydrogen bond has the most proton-shared character among this group; the largest negative

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value is found for HCN:(HCNH)þ:NCH, which has the least proton-shared character. In a plot of 1hK(HN) versus the HN distance, these points are found on the short-distance side of the minimum. That all of these complexes have some protonshared character can also be seen from the CH distances, which are significantly elongated relative to isolated (HCNH)þ and longer than those found in the three remaining sets of ternary complexes with HF, HCl, and ClF as X. 1h J(HF) and 1hJ(HCl) for the sets of complexes HF:(HCNH)þ:Z, ClF:(HCNH)þ:Z, and HCl:(HCNH)þ:Z are negative, so 1hK(HF) and 1hK(HCl) are also negative, a sign that the hydrogen bonds are traditional. However, as found for complexes X:(HCNH)þ:FH, X:(HCNH)þ:ClH, and X:(HCNH)þ:FCl, the largest absolute value in complexes with CHþ 3 3 3 A hydrogen bonds is also found for the binary complex and the smallest in the corresponding ternary complex with NCH as Z. Values of 1hJ(HF) and 1hJ(HCl) are found in plots of 1h J(HA) versus the HA distance at longer distances than that at which the minimum in the curve occurs. As for the complexes with NHþ 3 3 3 F hydrogen bonds, decreasing absolute values of 1h J(HF) and 1hJ(HCl) indicate decreasing proton-shared character. All 1hJ(HA) are dominated by the FC term, with the PSO term making small but non-negligible contributions to 1h J(HF).

’ CONCLUSIONS Ab initio calculations have been performed on a series of complexes in which (HCNH)þ is the proton donor and CNH, NCH, FH, ClH, and FCl (molecules X and Z) are the proton acceptors in binary complexes X:HCNHþ and HCNHþ:Z and ternary complexes X:HCNHþ:Z. These complexes are stabilized by CHþ 3 3 3 A and NHþ 3 3 3 A hydrogen bonds, with A being the electron-pair donor atom of molecules X and Z. The results of these calculations support the following statements. 1 The binding energies of ternary complexes X:HCNHþ:Z are less than the sum of the binding energies of the corresponding binary complexes X:HCNHþ and HCNHþ:Z, that is, cooperative effects are diminutive. The X 3 3 3 HCNHþ interaction is weakened by the presence of Z, and the HCNHþ 3 3 3 Z interaction is weakened by the presence of X. The diminutive effects tend to increase as the binding energies of corresponding binary complexes increase. 2 The results of AIM analyses indicate that ternary complexes have reduced electron densities at bond critical points relative to the corresponding binary complexes. In addition, values of the Laplacian and the local total energy at these points also provide evidence of diminutive cooperative effects. 3 Diminutive cooperative effects are also seen in coupling constants for the NHþ 3 3 3 A hydrogen bond in complexes X:HCNHþ:Z for fixed Z as a function of X. These effects are dramatic for complexes with NCH as Z for which 1J(NH) has its greatest value in the monomer; smallest value in the binary complex which has a symmetric proton-shared N 3 3 3 Hþ 3 3 3 N hydrogen bond; and intermediate values for the ternary complexes. Similarly, 2hJ(NN) and 1hJ(HN) have their largest absolute values in the binary complex, smallest in the complex HNC:HCNHþ:NCH, and decrease as the binding energy of the binary complex X:HCNHþ 12685


The Journal of Physical Chemistry A increases. Thus, as the strength of the X 3 3 3 HCNHþ interaction increases, the proton-shared character of the NHþ 3 3 3 N bond decreases. Corresponding NH, NN, and HN distances are consistent with these coupling constants. 4 For complexes X:HCNHþ:FH and X:HCNHþ:FCl, both 2h J(NF) and 1hJ(HF) are indicative of the same diminutive cooperative effects. The hydrogen bonds in these complexes are traditional hydrogen bonds, with the degree of proton-shared character greatest in the binary complex and least in the complex with HNC as X. 5 2hJ(CA) and 1hJ(HA) for complexes X:HCNHþ and X: HCNHþ:Z for fixed X as a function of Z also provide evidence for diminutive cooperative effects in these complexes. These effects are also observed for the CH distance, although the distance-dependence of 1J(CH) masks the diminutive effect in these complexes.

’ ASSOCIATED CONTENT

bS

Supporting Information. MP2/aug-cc-pVTZ structures and total energies of monomers and complexes; diminutive effects on energies of ternary complexes X:(HCNH)þ:Z for fixed Z as a function of X; results of AIM analyses; PSO, DSO, FC, and SD components of coupling constants. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]; [email protected].

’ ACKNOWLEDGMENT This work has been financed by the Spanish MICINN (CTQ2009-13129-C02-02) and Comunidad Autonoma de Madrid (Project MADRISOLAR2, ref S2009/PPQ-1533). The continuing support of the Ohio Supercomputer Center and CTI-CSIC is gratefully acknowledged. ’ REFERENCES (1) (a) Meot-Ner (Mautner), M. J. Am. Chem. Soc. 1978, 100, 4694. (b) Hirao, K.; Yamabe, S.; Sano, M J. Phys. Chem. 1982, 86, 2626. (c) Jucks, K. W.; Miller, R. E. J. Chem. Phys. 1988, 88, 6059. (d) Ruoff, R. S.; Emilsson, T.; Klots, T. D.; Chuang, C.; Gutowsky, H. S. J. Chem. Phys. 1988, 89, 138. (e) Jucks, K. W.; Miller, R. E. J. Chem. Phys. 1988, 88, 2196. (f) Kurning, I. J.; Lischka, H.; Karpfen, A. J. Chem. Phys. 1990, 92, 2469. (g) King, B. F.; Weinhold, F. J. Chem. Phys. 1995, 103, 333. (h) King, B. F.; Farrar, T. C.; Weinhold, F. J. Chem. Phys. 1995, 103, 348. (i) Karpfen, A. J. Phys. Chem. 1996, 100, 13474. (j) Cabaleiro-Lago, E. M.; Ríos, M. A. J. Chem. Phys. 1998, 109, 3598. (k) Nauta, K.; Miller, R. E. Science 1999, 283, 1895. (l) Juranic, N.; Macura, S. J. Am. Chem. Soc. 2001, 123, 4099. (m) Rivelino, R.; Chaudhuri, P.; Canuto, S. J. Chem. Phys. 2003, 118, 10593. (n) Chen, C.; Liu, M.-H.; Wu, L.-S. J. Mol. Struct. (THEOCHEM) 2003, 630, 187. (o) Alkorta, I.; Blanco, F.; Deya, P. M.; Elguero, J.; Estarellas, C.; Frontera, A.; Qui~nonero, D. Theor. Chem. Acc. 2010, 126, 1. (2) (a) Li, Q.; An, X.; Luan, F.; Li, W.; Gong, B.; Cheng, J.; Sun, J. J. Chem. Phys. 2008, 128, 154102. (b) Li, Q.; Wang, X.; Cheng, J.; Li, W.; Gong, B.; Sun, J. Int. J. Quantum Chem. 2009, 109, 1396. (c) Li, Q.; Liu, Z.; Cheng, J.; Li, W.; Gong, B.; Sun, J. J. Mol. Struct. (THEOCHEM) 2009, 896, 112. (3) Alkorta, I.; Rozas, I.; Elguero, J. Theor. Chem. Acc. 1998, 99, 116.

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Taylor, P. R.). BrillouinWigner perturbation theory was implemented by Pittner, J. (31) Rozas, I.; Alkorta, I.; Elguero, J. J. Am. Chem. Soc. 2000, 122, 11154. (32) Mata, I.; Alkorta, I.; Molins, E.; Espinosa, E. Chem.—Eur. J. 2010, 16, 2442. (33) Del Bene, J. E.; Elguero, J. In Computational Chemistry: Reviews of Current Trends; Leszczynski, J., Ed.; World Scientific Publishing Co. Pte, Ltd.: Singapore, 2006; Vol. 10, pp 229264.

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(HCNH)+:Z with X, Z = NCH, CNH, FH, ClH, and FCl - American

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