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The Badger−Bauer Rule Revisited: Correlation of Proper Blue Frequency Shifts in the OC Hydrogen Acceptor with Morphed Hydrogen Bond Dissociation Energies in OC−HX (X = F, Cl, Br, I, CN, CCH) Luis A. Rivera-Rivera,† Blake A. McElmurry, Kevin W. Scott, Robert R. Lucchese, and John W. Bevan* Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255, United States ABSTRACT: Potential morphing has been applied to the investigation of proper blue frequency shifts, Δν0 in CO, the hydrogen acceptor complexing in the hydrogen bonded series OC−HX (X= F, Cl, Br, I, CN, CCH). Linear correlations of morphed hydrogen bonded ground dissociation energies D0 with experimentally determined Δν0 free from matrix and solvent effects demonstrate consistency with original tenets of the Badger−Bauer rule (J. Chem. Phys. 1937, 5, 839−51). A model is developed that provides a basis for explaining the observed linear correlations in the range of systems studied. Furthermore, the generated calibration curve enables prediction of dissociation energies for other related but different complexes. The latter include D0 for H2O−CO, H2S-CO, and CH3OH−CO which are predicted by interpolation and found to be 355(13), 171(11), and 377(14) cm−1 respectively from available experimentally determined proton acceptor shifts. Results from this study will also be discussed in relation to investigations in which CO has been used as a probe of heme protein active sites.

1. INTRODUCTION The Badger−Bauer rule was initially applied to neutral closed shell hydrogen bonded complexes in 19371 following publication of the Badger rule for diatomic molecules.2 In the initially published paper,1 it was proposed that the enthalpy of formation of hydrogen bonds, ΔH, was linearly related to the infrared frequency shifts, Δν for hydroxylic electron acceptors involved in such hydrogen bonding. Since this time, it has been extensively used to correlate experimentally determined red frequency shifts of B−HO− and related stretching vibrations with intermolecular binding strengths for a large range of hydrogen bonded acceptors, B.3−5 A number of models have also been developed theoretically to account for the basis of the Badger−Bauer relationship.6−8 Further applications have, in addition, involved a wide range of studies including H−X red frequency shifts with force constants or bond length changes.7−9 There have been varying degrees of success with such correlations,10−14 in part due to a number of factors such as solvent and steric effects in experimental studies and the influence of anharmonicity.7,10,15,16 Despite these issues, Badger−Bauer relationships still continue to be invoked in a wide range of applications.17−24 These have also included proton acceptor carbonyl frequency shifts25,26 because of the facility of experimental measurements. In particular, spectroscopically determined frequency shifts on complexation are used as a means of qualitatively or quantitatively probing of the strength of noncovalent interactions as well as the environment of hydrogen bonded interactions. The accurate experimental determination of D0 for neutral ground state isolated hydrogen bonded complexes has been and continues to be an active field of research.27,28 Remarkably, © 2013 American Chemical Society

such D0 values have only been accurately determined for a relatively small number of systems under effectively isolated gas phase conditions or in supersonic molecular beams. In some respects, the Badger−Bauer relationship1 represents one of the earliest semiempirical attempts to obtain quantitative binding energies for a wide range of hydrogen bonded complexes, especially in condensed phases and comparable investigations have continued since. Recently, morphing methods29−37 have been developed and applied to generate potential functions for hydrogen bonded complexes. A primary objective of this work has been prediction of the properties of prototypical hydrogen bonded and halogen bonded complexes with significantly enhanced accuracy compared to standard ab initio calculations alone. Most importantly, this improvement in predictability should be relevant to determining either ground state D0 or equilibrium De dissociation energies as well as frequency shifts of either intramolecular frequencies in hydrogen atom acceptors or donors that result from complexation of such dimers. Traditionally, for hydrogen bonded interactions these have involved correlation of binding energies of the dimer with red frequency shifts of the hydrogen donor using the widely applied Badger−Bauer rule or some closely related variant of it.11 An alternative approach to be considered here, will investigate possible correlations of binding energies predicted on the basis of potential morphing approaches with experimentally determined proper blue frequency shifts of the hydrogen Received: June 13, 2013 Revised: July 23, 2013 Published: July 29, 2013 8477

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2.1. Ab Initio Potentials for OC−HX. The nonrelativistic ab initio interaction energies for the OC−HX complexes were calculated using the MOLPRO50−52 electronic structure package. The calculated ab initio potentials involved the following levels of theory/basis sets: (i) CCSD(T)/aug-ccpVTZ, (ii) MP2/aug-cc-pVQZ, and (iii) MP2/aug-cc-pVTZ, These potentials were corrected for the basis set superposition error (BSSE) using the counterpoise (CP) correction of Boys and Bernardi.53 In addition, the calculated CCSD(T)/aug-ccpVTZ potential was calculated without the CP correction. Details of the fitting of the ab initio potential and calculation of rovibrational energy levels have been given previously.54,55 In addition to the systems previously studied, we now report a 5-dimensional (5-D) investigation of OC−HBr. The new 5-D ab initio potentials for OC−HBr were calculated on a (R, r1, θ1, θ2, ϕ) grid including 48,560 points. The distances from the center of mass of 16O12C to center of mass of H79Br, R, were chosen to have the values of 3.00 Å, 3.75 Å, 4.25 Å, 4.50 Å, 4.75 Å, 5.25 Å, 6.25 Å, and 8.25 Å. The 16O12C bond length, r1, have the corresponding values of 1.007132 Å, 1.053438 Å, 1.128341 Å, 1.219632 Å, and 1.299542 Å. The angles θ1 and θ2 were selected to have the values of 5.0°, 10.0°, 30.0°, 50.0°, 70.0°, 90.0°, 110.0°, 130.0°, 150.0°, 170.0°, and 175.0°. Lastly, the dihedral angle ϕ was determined at values of 10.0°, 50.0°, 90.0°, 130.0°, and 170.0°. The additional values of ϕ = 190.0°, 230.0°, 270.0°, 310.0°, and 350.0° were obtained by symmetry. The 5-D grid was supplemented with additional points at all values of R and r1, and with ϕ = 0.0°, θ1 = 0.0°, 180.0°, and θ2 = 0.0°, 180.0°. In all calculations, the bond lengths of the H79Br monomer component were fixed at 1.41443 Å.56 Similarly to the 4-D29 morphed potential of OC−HBr, the experimental data used to morph the 5-D potential includes ground vibrational state microwave spectra57,58 and supersonic jet infrared spectra.59,60 Beside the ground vibrational state data and the low frequency bending vibration (ν15), we are now including the CO stretching vibration (ν2) and the combination band ν2 + ν15. 2.2. Compound-Model Morphing Method with Radial Correction. In the compound-model morphing method with radial correction (CMM-RC), the potential is generated as

acceptor. This is particularly so for hydrogen bond interactions38−41 that are free from matrix and solvent effects. Recently, DFT calculations17,21 have been used to model the stretching frequency νCO shifts within the protein matrices in which CO interacts with noncharged amino acids. Certain of these calculations indicated blue frequency shifts on complexation,17 which the authors found consistent with the Badger rule.2 Frequency shifts in CO associated with solute−solvent interactions have been the subject of previous theoretical treatment that also have direct relevance to the current work.42 A systematic investigation of the homologous series OC−HX (X = F, Cl, Br, I, CN, CCH) using both experimental and potential morphing29−37 approaches is presented here giving new insights into the applicability of tenets of the Badger− Bauer relationships. In particular, a model has been developed that determines the requirements for such relationships and could result in further adaptions and extended applicabilities through construction of a D0 vs Δν0 calibration curve. An application is now reported for the systematic investigation of proper OC blue frequency shifts on complexation with hydrogen bond dissociation energy for the series considered. Such shifts are different from the improper blue shifts of H−X vibrations43 that have recently been the subject of considerable attention.44,45 This series is selected in order to determine any correlations between D0 and Δν0 in this specified series and possible verification or otherwise of the Badger−Bauer rule1 to the observed proper blue frequency shifts. The magnitude of hydrogen acceptor blue frequency shifts observed in this series are frequently smaller in magnitude24,38,46 than corresponding HO−R and H−X stretching hydrogen bonded red shifts that have been measured. However, in the context of the current studies, experimentally determined blue frequency shifts for intramolecular vibrations in hydrogen bond acceptors have been determined precisely. Here, rovibrational analysis using supersonic jet spectroscopic methods38−41 have been investigated under effectively collisionless conditions free from matrix or solvent effects. In addition, prediction of zero-point energy corrected dissociation energies have been determined based on semiempirically generated morphed potentials as are intramolecular harmonic frequency shifts32 giving the opportunity to investigate in detail the applicability of the Badger− Bauer rule1 to these types of systems. The series chosen for investigation facilitates study because these complexes involve hydrogen bonded interactions that are linear or at least quasilinear under conditions, free from solvent or matrix effects rendering simplification of both spectroscopic and computational treatments.7 This is particularly so for correlating the results with both a model developed to account for the previously discussed observations and molecular calculations. Furthermore, the resulting linear correlation of D0 with Δν0 will be used to interpolate the dissociation energies of three other related hydrogen bonded complexes H2O−CO, H2S-CO, and CH3OH−CO not included in the prior analyses.47−49 The results will also be correlated directly with DFT calculations that have been used to model the stretching frequency νCO shifts within the protein matrices where CO interacts with different noncharged amino acids.17,19−21

CP VCMM ‐ RC(R ) = C1[VMP2(R′)]CP QZ + C 2{[VCCSD(T)(R ′)]TZ NOCP − [V CCSD(T)(R′)]TZ } CP + C3{[VCCSD(T)(R′)]TZ − [VMP2(R′)]CP TZ }

R′ = C4(R − R f ) + (1.0 + C5)R f (1)

where the Cα are the unitless morphing parameters. The reference or unmorphed potential, V(0) CMM−RC, is obtain by initially choosing C1 = 1.0, C2 = 0.0, C3 = 1.0, C4 = 1.0 and C5 = 0.0. The morphing parameters Cα are determined by using a regularized nonlinear least-squares optimization.61 In eq 1, the parameter C1 is the scaling parameter for the interaction energy of the dimer at the MP2/aug-cc-pVQZ level of theory including the CP correction for the BSSE. The second term gives correction for the BSSE at the CCSD(T) level of theory. The third term gives corrections for the correlation energy at the CCSD(T) level of theory. Lastly, the radial correction is included with the parameter C4 and C5. Not all of these parameters are varied in any given morphed potential. The quality of the fit of the experimental data is characterized by the root-mean-square (RMS) deviation of the experimental data

2. THEORETICAL METHODOLOGY The methodology for generating morphed potentials for the systems investigated has been extensively reported previously.29−37 Such methods will only be discussed briefly here. 8478

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Article

⎧ O expt − O calc(C ) ⎫2 ⎤ k α ⎬⎥ ∑⎨ k σ ⎭ ⎥⎦ k k=1 ⎩ M

1/2

⎪

⎪

⎪

⎪

The last term in eq 9 can be expanded using eq 4 as ⎛ ∂yi ⎞ dg dR e , i ⎜ ⎟ = i (R − Re , i(r ))Gi(R − Re , i(r )) − gi(r ) dr dr ⎝ ∂r ⎠ R

(2)

The value of the regularized parameter in the fitting procedure was γ = 10.0. 2.3. Model for Proper Blue Frequency Shift. In order to understand the source of the observed Δν0-D0 correlation, a simplified two-dimensional model including only the C−O bond length (r) and the distance between the C−O moiety and the HX component, R will be considered. The potential energy is written as νi (R, r) for the ith complex OC−HX. It will also be assumed that there is a reference potential F(y) which can be morphed to represent any of the specific complexes using the relationship Vi (R , r ) = Di(r )F(yi (R , r ))

Gi(R − Re , i(r )) − gi(r )(R − Re , i(r )) dR e , i dGi d(R − Re , i(r )) dr

So at (Re,i(re),re) ((∂yi)/(∂r))R|R=Re,r=re=−g(re)((dRe,i)/(dr))|r=re and then eq 9 becomes βi = −

H (0) = −

H

R = R e , r = re

dD =− i dr

⎛ 15 3 153 2⎞ d⎟ ωeχe = ω0⎜ c 2 + 3bd − d + ⎝4 2 8 ⎠

ai = (8)

=−

dr

2 r = re

d 2F + Di(re) 2 dr

x0 x02 αi and bi = β ℏω0 2ℏω0 i

⎛ ⎞ 1 Δωe , i = ω0⎜bi − b2 − 3aic ⎟ ⎝ ⎠ 2

⎡ ⎢⎛ ∂yi ⎞ ⎢⎜ ∂r ⎟ ⎝ ⎠R y=0 ⎢ ⎣

⎤2 ⎥ ⎥ ⎦ R = R e , r = re ⎥

(14)

(15)

(16)

Using eq 14, the shift in ωe is then given by (17)

As bi ≪ 1, in the cases considered here, to a good approximation, the middle term is neglected leading to

R R=R ,r=r e e

d2Di

(13)

These energy expressions are then applied to the proper blue frequency shift problem in two steps. First the values of k, c, and d are extracted from a power series expansion of the potential U(r) about r = re. In the case of CO, the derivatives were obtained from a Morse oscillator representation that reproduced the lowest three energy levels of the free monomer. In the complex, the same values for c and d are retained as in the free monomer and the values for a obtained from eq 8 and b from eq 11 give

(7)

r = re

⎡ ⎛ x ⎞2 ⎛ x ⎞3 ⎛ x ⎞4 ⎤ x ⎢ = ℏω0 a + b⎜ ⎟ + c ⎜ ⎟ + d⎜ ⎟ ⎥ ⎢⎣ x0 ⎝ x0 ⎠ ⎝ x0 ⎠ ⎝ x0 ⎠ ⎥⎦

and

and the second βi is given as ⎛ ∂ 2V ⎞ βi = ⎜ 2i ⎟ ⎝ ∂r ⎠

(1)

⎛ 1 81 2⎞ d⎟ ωe = ω0⎜1 + b − b2 − 3ac + ⎝ 2 4 ⎠

At equilibrium (Re,i,re), the first derivative is defined as αi with ⎛ ∂V ⎞ αi = ⎜ i ⎟ ⎝ ∂r ⎠ R

(12)

where x = r-re, x0 = √((ℏ)/(mω0)), and ω0 = √(k/m) . The value of ωe and ωeχe for the oscillator through second order in perturbation theory derived from the energies of the ν = 0, 1, and 2 vibrational states are

(6)

R

p2 1 + kx 2 2m 2

and the perturbation potential taken to be

⎛ ∂ 2V ⎞ dDi dF ⎛ ∂yi ⎞ d2Di d2F ⎜ 2i ⎟ = F ( y ) 2 + D + ⎜ ⎟ i i dr dy ⎝ ∂r ⎠ dr 2 dy 2 ⎝ ∂r ⎠ R R ⎡⎛ ∂y ⎞ ⎤2 ⎛ ∂ 2y ⎞ ⎢⎜ i ⎟ ⎥ + Di dF ⎜ i ⎟ ⎢⎣⎝ ∂r ⎠ ⎥⎦ dy ⎜⎝ ∂r 2 ⎟⎠ R

y=0

⎤2 ⎥ ⎥ r = re ⎦

(4)

Defining re as the value of r at the minimum in U, so that, ((dU)/(dr))|r=re = 0 and Re as the value of R at the minimum of the potential with D as minus the minimum of the potential at Re, that is ((∂Vi)/(∂R))r|R=Re,i,r=re) = 0 with Vi(Re,i,r) = −D(r) and V(∞,r) = 0. The reference potential F(y) is assumed to satisfy F(0) = −1 and F(∞) = 0 and ((dF)/(dy))|y=0 = 0. The radial scaling function Gi depends on the complex i but has the property that Gi(0) = 1. The r derivative of the potential can then be shown to be

R

r = re

⎡ dR e , i 2⎢ [gi(re)] ⎢ dr ⎣

(11)

(5)

⎛ ∂Vi ⎞ dDi dF ⎛ ∂y ⎞ ⎜ ⎟ = F(yi ) + Di ⎜ i ⎟ ⎝ ∂r ⎠ R dy ⎝ ∂r ⎠ dr

dr 2

d2F + Di(re) 2 dy

The shifts in ωe can now be obtained using second order perturbation theory with the zero’th order Hamiltonian taken to be

where r is the intramolecular coordinate, e.g. the CO stretch, and R is the intermolecular coordinate. The total potential V(Tot) would then be the sum of Vi and the asymptotic i intramolecular potential U(r) V i(Tot)(R , r ) = Vi (R , r ) + U (r )

d2Di

(3)

and yi (R , r ) = gi(r )(R − Re , i(r ))Gi(R − Re , i(r ))

(10)

Δωe , i ≈ ω0(bi − 3aic)

(18)

What is observed empirically is that the shift in frequency of the intramolecular vibration in complexes, Δωe,i, are a linear

(9) 8479

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function of the well depths of the intermolecular interaction Di(re) of the complexes. Considering the expression for the shifts given in eq 18 and the expressions given in eqs 16, 8, and 11, one way that this linear relationship can occur is if the expression for the r dependent well depths has an r dependence which just scales with the well depth of the complex so that Di(r) = Di(re) f (r), where f (r) is the same for all complexes. If this is true, then the shift in the frequencies can be expressed as ⎡ ⎛ ⎢ x 2 ⎜ d2f ℏΔωe , i = Di(re)⎢ 0 ⎜ − 2 ⎢⎣ 2 ⎜⎝ dr ⎡ ⎢ dR e , i ⎢ dr ⎣

+ r = re

⎤2 ⎞ ⎥ ⎟ + 3cx df 0 ⎥ ⎟⎟ dr r = re ⎦ ⎠

d2F dy 2

[gi(re)]2 y=0

⎤ ⎥ ⎥ r = re ⎥ ⎦

(19)

3. RESULTS The newly generated 5-D morphed potential for OC−HBr, V(3) CMM−RC, was obtained with the morphing parameters C1 = 1.0945(19), C2 = 0.1821(65), C3 = 1.0, C4 = 1.0 and C5 = 0.00776(13). These parameters give a root-mean-square, RMS of G = 1.3. CO blue frequency shifts Δν0 for OC−HX (X = F, Cl, Br, I, CN, CCH) have been measured experimentally previously35,36 and are given in Table 1 column 2 with the

Figure 1. Correlation (Badger−Bauer rule) for blue shift of CO stretch and dissociation energy D0 obtained from morphing. Interpolation gives D0 H2O−CO = 355(13) cm−1.

Table 2. Dissociation Energies Di, Parameters gi, dRe/dr, and Δωe for Model Calculations on OC−HX (X = F, Cl, Br, CN)a

Table 1. CO Blue Frequency Shifts and Dissociation Energies from Morphed Potentials for OC−HX (X = F, Cl, Br, I, CN, HCCH).a complex

Δν0

D0

O12C−HF 16 12 O C−H35Cl 16 12 O C−H79Br 16 12 O C−HI 16 12 O C−HCN 16 12 O C−HCCH

24.42677 12.22862 9.33346 5.2775 13.55011 6.0717

742.5(50) 414.2 325.56 210.99 468.26 233.36

16

a

complex 16

O12C−HF O12C− H35Cl 16 12 O C− H79Br 16 12 O C− HCN 16

a

Di

gi

dRe/dr

Δωe (model)

Δωe (potential)

1240.9 732.5

1.0774 1

0.9056 0.9965

28.3986 16.9064

29.6622 16.9064

595.7

0.9861

1.0159

13.7787

13.3692

656.3

0.9085

0.9841

14.5422

15.7238

Data in cm−1.

in Table 2. The corresponding plots for Di against Δωei for the model and potential are given in Figure 2. Table 3 contains data from CCSD(T)/aug-cc-pVQZ calculations for OC−HX (X = F, Cl, Br, I, CN, CCH, OH, SH) which are intended to supplement previous calculations and models as well as results reported in ref 17.

Data in cm−1.

corresponding D0 values in column 3. Figure 1 shows the plot of D0 against Δν0 of a linear fit to these points giving the straight line plot y = ax + b where a = 27.942 and b = 69.016 with R2 = 0.9984. Using values of Δν0 experimentally available for H2O−CO, H2S-CO and CH3OH−CO,47−49 it is now possible to interpolate respective values of D0 to be 355(13), 171(11) and 377(14) cm−1 under the assumption that the corresponding blue frequency shifts on complexation can be interpolated using the plot in Figure 1. In order to obtain suitable data for development of the model described in eq 19, the 1-D potentials in the intermolecular coordinate R and OC stretching coordinate r were generated from 5-D compoundmodel morphed potentials in OC−HX (X = F, Cl, Br, CN) and related data and parameters are given in Table 2. As an example calculation of the model proposed using the derived expression in eq 19, ωe = 2169.81358 cm−1 and ωeχe = 13.28831 cm−1 for CO, yields ω0 = ωe, x0 = 0.04760582 Å, c = −0.055336 and d = 0.003572. Using the OC−HCl complex as the reference complex to define the f(r) and F(y) functions, it is found that (df/dr) = −2.446 Å−1, (d2f/dr2) = 0.8643 Å−2 and (d2F/dy2) = 4.201 Å−2. The other parameters, derived from the morphed potentials of the complexes considered are then given

Figure 2. Correlation of Di from morphed potentials and the model (Section 2.3) with predicted harmonic frequency shifts in CO for OC−HX (X = F, Cl, Br, CN). 8480

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generated from extensive high resolution spectroscopic data. Moreover, these results are also relevant to prior spectroscopic investigations that deviate from linear characteristics complicating application of the Badger−Bauer rule.2−12 Specifically, they are indicative of the influence of anharmonicity as is apparent from the change in slopes relative to Figure 1. A second plot in Figure 2 gives a quantitative measure of the model proposed in Section 2.3. Data specific to the validity of the assumptions made in its derivation and the effective independence of f(r) are shown in Table 2. The terms in the expansion shown in Table 2 give the necessary requirements for the linear correlations associated with effective application of the Badger−Bauer rule. Clearly for the systems investigated and the range of binding energies involved, these requirements are met and can be compared with similar behavior observed in diatomic molecules.2,62 The harmonic corrected frequency shifts in CO that occur for the range of hydrogen bonded donors investigated are directly proportional to the equilibrium dissociation energies of the complexes. Furthermore, their product with the remainder of the function expressed in eq 19, reflects the observed almost linear dependence. Of additional interest is how this derived relationship correlates with an equivalent approach invoked by Hermansson44 to explain frequency shifts on hydrogen bonding that involved the expression ΔνOH ∝−E∥·(dμ∥free/drOH + 1/2· dμ∥ind /drOH). The current model, however, explicitly considers the dependence on De and includes an additional term that influences frequency shifts. It is relevant to note that a plot of Δωe against De for modeling neutral amino-acid−CO interactions generated from B3LYP calculations also gives a straight line through the origin. However, the slope of 83 blue shift is significantly different from that presented in this work (43.25 blue shift). We attribute this difference as due to the former calculations, treating the interaction as primarily electrostatic with no contributions due to dispersive effects. A corresponding plot based on CCSD(T)/aug-cc-pVQZ calculations for the OC−HX series considered in this work also gives a linear plot but in this case the gradient of 37.04 blue frequency shift is in better agreement with the plots more accurately determined in Figure 2. It is interesting also to consider applications of the results shown in the plot included in Figure 2. As an example the CO harmonic blue shift on complexation and its De calculated at the CCSD(T)/aug-ccpVQZ level for the complex H2O−CO can be compared with results interpolated from similar calculations to those used for the other OC−HX complexes considered as calibrants. Here the calculated value of Δωe for H2O−OC gives an interpolated value of De = 615 cm−1 from that plot which can be compared with the directly calculated value of 618 cm−1 (Table 3). The corresponding values for H2S-CO are 316 cm−1 and 326 cm−1, respectively. These calculations thus support the conclusion that these complexes have similar blue frequency shift behavior to the hydrogen bonded series OC−HX (X = F, Cl, Br, I, CN, CCH) (Figure 1) and from a calibration perspective can be categorized in the same group interactions for application of the Badger−Bauer rule.

Table 3. CO Harmonic Blue Frequency Shifts and Dissociation Energies from CCSD(T)/aug-cc-pVQZ Calculations for OC−HX (X = F, Cl, Br, I, CN, CCH, OH, SH)a complex 16

12

O C−HF O12C−H35Cl 16 12 O C−H79Br 16 12 O C−HI 16 12 O C−HCN 16 12 O C−HCCH 16 12 O C−H2O 16 12 O C−H2S 16

a

ωe (cm−1)

Δωe (cm−1)

r(CO)e (Å)

De (cm−1)

2189.76 2175.80 2172.51 2167.52 2175.92 2167.61 2174.25 2166.16

30.43 16.47 13.18 8.19 16.59 8.28 14.92 6.83

1.128560 1.129993 1.130332 1.130872 1.129959 1.130903 1.130207 1.131052

1211.36 686.19 564.34 398.38 600.02 367.14 618.32 326.18

The value ωe for free CO is 2159.33 cm−1.

4. DISCUSSION Figure 1 shows a linearly dependent plot (R2 = 0.9984) of D0 against the experimentally determined blue shift Δν0. This is indicative of a relationship that is consistent with the Badger− Bauer rule for the series investigated. This linear dependence, however, does not result in a straight line passing through the origin. This is not unexpected from a perspective based on the dissociation energies not being corrected for zero point energies and the frequency shifts in the different complexes not being corrected for anharmonicity as these quantities are expected to differ significantly for the range of complexes considered in the plot. However, if an uncorrected plot of this kind can be used as a reliable calibrant for determination of ground dissociation of other complexes based on experimentally determined and comparable blue shifts, then the approach could have significant wider implications. In the case of the complexes under consideration, the frequency shift, however, is not the traditional red frequency shift dependence associated with the proton acceptor as proposed by Badger and Bauer.1 Furthermore, a proper blue frequency shift of the hydrogen atom acceptor must also be distinguished from corresponding HX improper blue frequency shifts.42−44 Corresponding shifts associated with proton acceptors have been documented for carbonyl frequency shifts with change in enthalpy, ΔH, but in these cases such dependencies have been associated with red frequency shifts.26 Figure 2 is in many respects more meaningful as the variables, the dissociation energy De and Δωe for the CO stretching vibration are corrected for zero point energy and anharmonicity in the complexes considered. This makes the results directly comparable with calculations based on standard ab initio packages. Two plots are presented in Figure 2. The first derived from morphed potential energy data and the second from the model proposed in Section 2.3. Both plots give straight line dependences in complexes for which 5-D morphed potentials are available. The former has a slope of 43.37 blue frequency shift with R2 = 0.9997, and the latter with a slope of 43.86 blue frequency shift and R2 = 0.9989, each case giving a straight line through the origin. The former is interesting as it not only correlates with the linear dependence expected within the tenets of the original Badger−Bauer rule1 but corrections for anharmonicity and zero point energy effects giving a plot through the origin for the systems considered. The characteristics of this plot including its slope has significance for future applications as it has been predicted from accurately determined semiempirical compound morphed potentials

5. CONCLUSIONS Experimentally observed proper blue shifts Δν0 for the CO proton acceptor are demonstrated to have linear correlations with predicted hydrogen bonded dissociation energies D0 based on accurate semiempirical morphing methodologies. Such results are consistent with the original tenets of the Badger− 8481

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Bauer rule.1 In this series, such proper blue shifts contrast with traditionally directly measured H−X red shifts that frequently exhibit a corresponding nonlinear dependence. A model has now been formulated to rationalize the intrinsic characteristics of the systems studied and associated blue frequency shifts on complexation, particularly with respect to the Badger−Bauer relationship. Application of 5-D compound-model morphed potentials in formulating this model have provided criteria that correlate the linear dependence of Δωe with De and furthermore give insight into the influence of anharmonicity and zero point energy effects. In principle, similar approaches should be applicable to a range of hydrogen bonded interactions involving frequency shifts in acceptor vibrations including HCN, CH3CN, and NO. Results can also be compared with those previously generated in DFT calculations17 that asserts that the frequencies of νCO serve as a powerful tool to probe the surrounding environments of CO molecule inside protein matrices, as well as its orientations. In these investigations of the weak interactions between noncharged amino acids and CO revealed the effects of the protein’s microenvironments on the docked gas molecule, contributing insights into the accommodation and migration of small ligands within protein matrices. This in turn suggests the current studies of CO as hydrogen acceptor can provide quantitative information for using CO as a useful probe for delineating the structure−property−function relationship of heme-based sensors.18

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address †

L.A.R.-R.: Chemistry Department, University of Missouri, Columbia, Missouri 65211-7600 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

The National Science Foundation is thanked for supporting this research through Grant CHE-0911695. K.W.S. and B.A.M. also thank the Robert A. Welch Foundation for financial support in the form of predoctoral and postdoctoral fellowship under grant A-747. We also thank the Laboratory for Submm/ THz Science and Technology, the Laboratory for Molecular Simulation, and the Supercomputing Facility at Texas A&M University for providing support and computer time.

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