Characterization of dihydrogen-bonded D–H ¯ H–A complexes on the basis of infrared and magnetic resonance spectroscopic parameters

Characterization of dihydrogen-bonded D–H ¯ H–A complexes on the basis of infrared and magnetic resonance spectroscopic parameters

Hubert Cybulski, Magdalena Pecul, and Joanna Sadlej^a)

Department of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland Trygve Helgaker

Department of Chemistry, University of Oslo, Box 1033 Blindern, N-0315 Oslo, Norway

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Received 14 March 2003; accepted 11 June 2003

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The structural, energetic, and spectroscopic properties of the dihydrogen-bonded complexes LiH¯H₂, LiH¯CH₄, LiH¯C₂H₆, and LiH¯C₂H₂are investigated. In particular, the interaction energy is decomposed into physically meaningful contributions, and the calculated vibrational frequencies, the magnetic resonance shielding constants, and inter- and intramolecular spin–spin coupling constants are analyzed in terms of their correlation with the interaction energy. Unlike the other three complexes, which can be classified as weak van der Waals complexes, the LiH¯C₂H₂ complex resembles a conventional hydrogen-bonded system. The complexation-induced changes in the vibrational frequencies and in the magnetic resonance shielding constants correlate with the interaction energy, as does the reduced coupling^2hJ_HXbetween the proton of LiH and hydrogen or carbon nucleus of the proton donor, while^1hJ_HHdo not correlate with the interaction energy. The calculations have been carried out using Møller–Plesset perturbation theory, coupled-cluster theory, and density-functional theory. © 2003 American Institute of Physics.

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DOI: 10.1063/1.1597633

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I. INTRODUCTION

Molecular spectroscopy represents an important

共

and sometimes the only

兲

method for the detection and character- ization of hydrogen bonds and other intermolecular interac- tions. Infrared spectra

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IR

兲

and nuclear magnetic-resonance

共

NMR

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iso- and anisotropic chemical shifts, in particular, have for a long time provided indirect evidence for hydrogen-bond formation through the changes that are mea- sured in the parameters relative to the monomers.^1–5Numer- ous experimental and theoretical studies have been carried out to correlate these changes with the hydrogen-bond geom- etry

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bond lengths and bond angles

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⁶ as well as with the hydrogen-bond type.⁷Moreover, progress in NMR spectros- copy has made it possible to use the nuclear spin–spin cou- pling constants not only as indirect evidence of hydrogen bonds⁸but also as direct evidence, following the recent dis- covery of intermolecular hydrogen-bond-transmitted spin–

spin coupling constants. Such couplings have been observed in biomacromolecules

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i.e., proteins^9–11 and nucleic acids^12,13

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and in fluorine-containing clusters.^14,15

Simultaneously with this experimental work, many the- oretical studies have been carried out. The coupling con- stants transmitted through hydrogen bonds have been calcu- lated for many complexes,6,7,14,16 –24including neutral dimers of simple organic and inorganic molecules,16,17,19,20fluorine- containing clusters,^14,18,22 and low-barrier hydrogen-bond complexes.^7,20,22,23Some effort has also been aimed at pre- dicting the coupling constants transmitted through bonds weaker than hydrogen bonds.^18,25–28In particular, the obser- vation of non-negligible intermolecular coupling constants in

van der Waal systems without hydrogen bonds such as CH₄¯HF¹⁸ and He¯He²⁶ show that the transmission of spin–spin couplings cannot necessarily be taken as evidence for covalency, as sometimes maintained.^10,29

Hydrogen bonds are usually formed between the posi- tively charged hydrogen of an A–H proton donor

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a weak acid

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and an electronegative atom B, representing the proton acceptor

共

a weak base

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. Recently, however, proton–hydride D–H^␦⫹¯^␦⫺H–A interactions have attracted some attention.

Such dihydrogen bonds

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DHBs

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, where D–H acts as a proton donor and H–A as an acceptor, have been the subject of many investigations.^{30– 42} Typical elements A that can ac- commodate this hydridic hydrogen, acting as proton accep- tors, are the transition metals and boron.32,33,36,37From x-ray and neutron diffraction, it is known that the H¯H distances are usually shorter than 2 Å and significantly smaller than the sum of the van der Waals radii of the hydrogens in the N–H¯H–Ir complex—for example, the H¯H distance has been reported as 1.8 Å.³³

Like conventional hydrogen bonds, dihydrogen bonds may find an application in supramolecular syntheses and in crystal engineering; they may also play an important role in catalytic processes.³⁷Because of the unusual character of the weak interaction, these complexes are interesting also from a theoretical point of view. So, even though the small dihydrogen-bonded systems have not been much studied ex- perimentally, they are ideal for theoretical investigations, which may provide not only useful information on the struc- ture and bonding of these complexes but also suggest future experiments.

The question we address in this paper is the spectro- scopic characterization of dihydrogen bonds and the possi- bility of their detection and characterization by optical and

a兲Author to whom correspondence should be addressed. Electronic mail:

[email protected]

5094

0021-9606/2003/119(10)/5094/11/$20.00 © 2003 American Institute of Physics

NMR spectroscopy. To answer this question, the IR frequen- cies and NMR parameters are evaluated for dihydrogen- bonded complexes and analyzed as potential parameters for the characterization of dihydrogen bonds by correlating them with interaction energies and intermolecular distances.

As DHB models, we have chosen the complexes LiH¯H₂, LiH¯C₂H₆, LiH¯CH₄, and LiH¯C₂H₂, all with LiH as the proton acceptor. The proton donors include H₂ and the C–H group from the hydrocarbons CH₄, C₂H₆, and C₂H₂. These molecules differ by the quadrupole mo- ment. Preliminary calculations have also been carried out for some other complexes such as LiH¯H₂O, LiH¯H₂CO, LiH¯HF, BH₃¯NH₃, and BH₃¯H₂O. However, since their DHB structures turned out not to be minima on the potential energy surface, these systems were not pursued fur- ther. On the other hand, calculations of the properties of the true DHB systems LiH¯HCN, LiH¯HNC, NaH¯HCN, NaH¯HNC, LiH¯HOH, NaH¯HOH, LiH¯C₂H₂ have been published.^41,42 For these systems, the intermolecular coupling constant ^1hJ_HH depends on the nature of the proton–donor group and the proton–acceptor metal hydride, as well as on the intermolecular distances H¯H.⁴²Their IR data were also reported, although the NMR shielding con- stants were not.⁴¹The present work, which extends the range of molecules studied to include van der Waals complexes with a weak H¯H interaction, can provide valuable insight about DHBs, as contrasted with conventional hydrogen bonds and weak van der Waals forces.

In the present paper, we examine whether there is a fun- damental difference between DHB and other van der Waals systems. To explore this issue, we have examined the spec- troscopic properties of the DHB complexes under study and their interaction energy, including its decomposition into in- dividual contributions. This decomposition is carried out within the framework of intermolecular perturbation theory, combined with the supermolecular scheme.^{43– 45}In this man- ner, we would like to establish whether DHBs share the properties of conventional hydrogen bonds such as electro- static stabilization⁴⁶ and to see how they may differ from weaker van der Waals interactions through H¯H contacts.

To elucidate the role of the individual contributions to the interaction energy such as the electrostatic, exchange, induc- tion, and dispersion components, we employ intermolecular Møller–Plesset perturbation theory

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IMPPT

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.^{43– 45} The re- sulting decomposition is unambigous, offering an opportu- nity to investigate the physical origin of the bonding effects.

In Sec. II of this paper, the methods employed for the optimization of the geometry, the calculation of the interac- tion energy and its decomposition, and the calculation of molecular properties are described. Next, in Sec. III, the re- sults of these calculations are discussed—in particular, the optimized structures, the interaction energies, the infrared spectra, and the NMR shielding constants and indirect spin–

spin coupling constants. A summary and main conclusions are presented in Sec. IV.

II. COMPUTATIONAL DETAILS

A. Calculation of equilibrium structure and interaction energy

1. Geometry optimization and vibrational frequencies The structures of all monomers and complexes were op- timized by means of frozen-core second-order Møller–

Plesset

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MP2

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perturbation theory. Except for the large LiH¯C₂H₆ complex, the structures were optimized using frozen-core fourth-order Møller–Plesset

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MP4

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theory and coupled-cluster single-and-double

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CCSD

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theory as well.

For the small LiH¯H₂ complex, a frozen-core optimization was also carried out using CCSD theory with a perturbative triples corrections

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CCSD

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T

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.⁴⁶ For comparison, geometry optimizations were carried out using density-functional theory

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DFT

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, used with the hybrid three-parameter Becke–

Lee–Yang–Parr

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B3LYP

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functional, as implemented in the

GAUSSIAN98 program.⁴⁷ In the geometry optimizations, no counterpoise corrections were made for the basis-set super- position error. The vibrational frequencies were computed within the harmonic approximation, at the respective level of theory.

For the geometry optimizations, the frequency calcula- tions, and the calculations of the interaction energy, we used the aug-cc-pVTZ basis.^48,49As shown,^50,51 this basis accu- rately reproduces geometries, frequencies, and electric prop- erties of the isolated molecules and their complexes.

2. The total interaction energy

The supermolecular interaction energy was obtained by substracting the energies of the monomers from those of the complex for each complex. The computed interaction ener- gies were corrected for basis-set superposition error follow- ing the prescription of Boys and Bernardi,⁵² and for the re- laxation of the monomer geometry during complex formation.⁵¹To relate the calculated interaction energy to the observed dissociation energy D₀, a correction for the differ- ence in the zero-point vibrational

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ZPV

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energies of the com- plex and the monomers was added. The ZPV correction was calculated in the harmonic approximation at the respective level of theory. The geometry optimizations as well as the calculation of vibrational frequencies and interaction ener- gies were carried out using theGAUSSIAN 98program.⁴⁷

3. The partitioning of the interaction energy

For more insight into the nature of the H¯H interaction, we have partitioned the interaction energy using IMPPT.^{43– 45,53}The IMPPT interaction-energy corrections are denoted by ⑀^{(i j)}, where i and j are the orders of the inter- molecular interaction operator and the intramolecular correc- tion operator, respectively.^{43– 45}

At the all-electron MP2 level, the total interaction energy is decomposed into a Hartree–Fock self-consistent field

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SCF

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contribution and a correlation contribution:

⌬

E^MP2⫽⌬E^SCF⫹⌬E⁽²⁾.

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1

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The SCF contribution is further decomposed into deforma- tion and Heilter–London parts:

⌬

E^SCF⫽

⌬

E_def^SCF⫹⌬E^HL.

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2

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The deformation energy

⌬

E_def^SCFis interpreted as an effect due to relaxation of orbitals in the Coulomb field of the partner under the restriction imposed by Pauli principle. We also consider the second-order IMPPT approximation to

⌬

E_def^SCF. It can be approximated as the induction response terms

⑀ind,r

(n,0), where the term ⑀ind,r

(20) is calculated by coupled- perturbed Hartee–Fock theory. The Heilter–London contri- bution to the SCF interaction energy, Eq.

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2

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is next decom- posed as

⌬

E^HL⫽⑀els (10)⫹⑀exch

HL ,

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3

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where⑀els

(10)and⑀exch

HL are electrostatic and exchange energies, respectively. Finally, the correlation correction to the MP2 interaction energy in Eq.

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1

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is represented as

⌬

E⁽²⁾⫽

⌬

E_exch⁽²⁾ ⫹⑀disp (20)⫹⑀els,r

(12),

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4

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where

⌬

E_exch⁽²⁾ is the second-order exchange correlation cor- rection, ⑀disp

(20) the dispersion correlation correction, and⑀es,r (12)

the second-order electrostatic correlation correction.

In the interpretation of our results, we shall focus on

⑀els (10), ⑀exch

HL ,

⌬

E_def^SCF, and⑀disp

(20). All terms⑀^{(i j)} were calcu- lated in the basis of the full complex. The IMPPT calcula- tions were carried out in aug-cc-pVDZ basis, and, for the smaller complexes, in the aug-cc-pVTZ basis, using the

TRURL 94package of Cybulski.⁵⁴

B. The calculation of NMR parameters 1. NMR shielding constants

The calculations of the NMR shielding constants were carried out at the all-electron MP2 level, using London orbitals.^55–57 The basis-set superposition error for the complexation-induced changes in the shielding constants was estimated using the counterpoise correction method.⁵² The shielding constants were calculated with the

GAUSSIAN 98 program,⁴⁷ using the aug-cc-pCVTZ basis ex- cept for the Li atom, for which no core–valence functions are available and the aug-cc-pVTZ-su1

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see later

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basis was used instead.

2. Nuclear spin–spin coupling constants

The indirect nuclear spin–spin coupling constants were calculated using CCSD theory and DFT. Unless otherwise indicated, all four nonrelativistic contributions to the spin–

spin coupling constants were calculated: the Fermi-contact

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FC

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term, the spin–dipole

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SD

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term, the paramagnetic spin–orbit

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PSO

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term, and the diamagnetic spin–orbit

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DSO

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term. The lithium coupling constants are given for the

7Li isotope. All NMR properties were calculated at the MP2/

aug-cc-pVTZ geometries.

The CCSD nuclear spin–spin coupling constants were calculated as unrelaxed second derivatives of the electronic energy, using a version of ACES II⁵⁸—see Ref. 59 and refer- ences therein. The B3LYP spin–spin calculations were car- ried out with a development version of the DALTON

program.⁶⁰The use of the inexpensive B3LYP model made it possible to carry out calculations at several different inter-

molecular distances, which would have been too expensive at the CCSD level. In addition, these calculations give us an opportunity to examine the performance of DFT for atypical systems such as DHB complexes.

The spin–spin coupling constants were calculated by means of aug-cc-pVDZ-su1

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11s5p2d/11s3p2d for C and Li, 6s2p/6s2p for H

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and aug-cc-pVTZ-su1

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12s6p3d2f/

12s4p3d2f for C, 13s6p3d2f/13s4p3d2f for Li, 7s3p2d/

7s3p2d for H

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basis sets. They are obtained from the stan- dard augmented correlation-consistent aug-cc-pVTZ basis sets of Dunning and co-workers^48,49by decontracting the s functions and by adding one tight s orbital.⁶¹Their suitability for the calculations presented here has been established in Refs. 16, 17, and 62.

III. RESULTS AND DISCUSSION

A. Geometry and energetic of the complexes

Figure 1 presents the optimized structures of the DHB complexes investigated in this study: LiH¯H₂, LiH¯CH₄, LiH¯C₂H₆, and LiH¯C₂H₂. Since these calculations were performed on model complexes for which the geometries and binding energies are experimentally unknown, no verifi- cation is possible. We also note that the optimized H¯H structures represent local minima of the potential energy sur- faces.

The geometrical parameters of the optimized structures are listed in Table I, while Table II contains the correspond- ing interaction energies D_e, the harmonic ZPV energies

⌬

E_ZPV, and the dissociation energies D₀. In the following, we base our discussion on the CCSD results or, when these are unavailable

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for LiH¯C₂H₆), on the MP2 results, as the most accurate ones.

FIG. 1. The structures of LiH¯H2, LiH¯CH4, LiH¯C2H6, and LiH¯C2H2.

Except for LiH¯C₂H₆, all complexes where a H–C bond donates a proton to the hydridic hydrogen of LiH have a colinear Li–H¯H–C arrangement. In addition, LiH¯H₂ is linear. Based on the H¯H separation, the complexes can be divided into two groups: LiH¯H₂, LiH¯CH₄, and LiH¯C₂H₆ have a long H¯H separation and can be clas- sified as weak van der Waals complexes, whereas LiH¯C₂H₂, with an intermolecular separation of 2 Å, has a dihydrogen bond strength comparable with that of conven- tional hydrogen bonds. As we shall see, this difference be- tween the three weak van der Waals complexes on the one hand and LiH¯C₂H₂ on the other hand is found in all the properties studied.

The Li–H distance of the proton acceptor is constant in the weak van der Waals complexes but shortened in LiH¯C₂H₂. The shifts in the proton–donor bond distance, however, are less systematic. As expected, the largest shift in the proton–donor CH bond length occurs for LiH¯C₂H₂.

More surprisingly, the CH bond in LiH¯CH₄changes in the opposite direction of the bond in LiH¯C₂H₆. We recall, however, that LiH¯C₂H₆has a nonlinear DHB bond, which may account for this difference.

The interaction energy in Table II follows the same trend as the interatomic distances, increasing in the sequence LiH¯H₂⬍LiH¯CH₄⬍LiH¯C₂H₆⬍LiH¯C₂H₂, which correlate with the quadrupole moment of the proton donors molecules. As for the bond distance, there is a difference between LiH¯C₂H₂ and the weak van der Waals com- plexes. In the van der Waals complexes, the energy minimum is very shallow—in fact, LiH¯H₂ is unstable in the sense that the minimum is not sufficiently deep to accomodate one vibrational energy level. By contrast, the interaction energy of LiH¯C₂H₂ is similar to those of neutral complexes with a single hydrogen bond such as in the water dimer.^63,64

The inclusion of the harmonic ZPV correction changes

TABLE I. Selected calculated geometrical parameters 共in Å兲 and their complexation-induced changes共in parentheses兲 of the LiH¯H₂, LiH¯CH₄, LiH¯C2H6, LiH¯C2H2complexes. All calculations are in the aug-cc-pVTZ basis set.

Parameter Model LiH¯H2 LiH¯CH4 LiH¯C2H6 LiH¯C2H2

r(H¯H) MP2 2.6016 2.5093 2.5001 1.9721

MP4 2.5739 2.4936 . . . 1.9758

CCSD 2.6388 2.5794 . . . 2.0370

CCSD共T兲 2.5901 . . . . . . . . .

B3LYP 2.5733 2.6287 2.6213^a 2.0040

r(Li–H) MP2 1.6047 (⫺0.0002) 1.6052 (⫹0.0003) 1.6060 (⫹0.0011) 1.6017 (⫺0.0032)

MP4 1.6082 (⫺0.0003) 1.6088 (⫹0.0003) . . . 1.6047 (⫺0.0037)

CCSD 1.6101 (⫺0.0004) 1.6104 (⫺0.0001) . . . 1.6060 (⫺0.0045)

CCSD共T兲 1.6101 (⫺0.0004) . . . . . . . . .

B3LYP 1.5893 (⫺0.0006) 1.5894 (⫺0.0005) 1.5896 (⫺0.0003)^a 1.5848 (⫺0.0051) r(H–X) MP2 0.7403 (⫹0.0029) 1.0872 (⫹0.0010) 1.0888 (⫺0.0003) 1.0733 (⫹0.0116)

MP4 0.7445 (⫹0.0029) 1.0905 (⫹0.0008) . . . 1.0752 (⫹0.0113)

CCSD 0.7455 (⫹0.0025) 1.0888 (⫹0.0003) . . . 1.0715 (⫹0.0094)

CCSD共T兲 0.7458 (⫹0.0028) . . . . . . . . .

B3LYP 0.7459 (⫹0.0030) 1.0886 (⫹0.0003) 1.0905 (⫺0.0005)^a 1.0734 (⫹0.0118)

aSaddle point.

TABLE II. Calculated interaction energy De, vibrational contribution to the interaction energy⌬EZPV, and the dissociation energy D0共in kJ/mol兲of the LiH¯H2, LiH¯CH4, LiH¯C2H6, LiH¯C2H2 complexes. All calculations are in the aug-cc-pVTZ basis.

Parameter Level LiH¯H2 LiH¯CH4 LiH¯C2H6 LiH¯C2H2

D_e MP2 ⫺2.98 ⫺3.20 ⫺3.93 ⫺17.78

MP4 ⫺3.20 ⫺3.48 . . . ⫺17.82

CCSD ⫺2.80 ⫺2.84 . . . ⫺16.04

CCSD共T兲 ⫺2.78 ⫺3.38^a ⫺4.11^a ⫺17.22^a

B3LYP ⫺2.10 ⫺1.48 ⫺1.39^b ⫺15.27

⌬EZPV MP2 5.17 2.37 1.49 4.61

MP4 5.22 2.23 . . . 4.67

CCSD 5.00 2.26 . . . 4.54

CCSD共T兲 5.15 . . . . . . . . .

B3LYP 5.49 2.29 - 4.24

D0 MP2 ⫹2.19 ⫺0.83 ⫺2.44 ⫺13.17

MP4 ⫹2.03 ⫺1.25 . . . ⫺13.16

CCSD ⫹2.20 ⫺0.58 . . . ⫺11.50

CCSD共T兲 ⫹2.37 . . . . . . . . .

B3LYP ⫹3.40 ⫹0.81 - ⫺11.03

aGeometry optimized at the MP2 level.

bSaddle point.

the interaction energy substantially—not only for LiH¯H₂, but for the other complexes as well. For example, judging from D_e, LiH¯CH₄ and LiH¯C₂H₆ have similar interac- tion energies, whereas the D₀ values indicate that the LiH¯C₂H₆ complex is significantly more stable. To under- stand this behavior, we recall that the minima of the three weak van der Waals complexes are very shallow, but ZPV corrections are calculated at the harmonic approximation.

For LiH¯H₂ system the potential could be very anharmonic one and that is why this system is unstable in this approxi- mation.

The geometry optimization was carried out at different ab initio levels. Usually, the accuracy of the results increases in the order MP2, CCSD, and CCSD

共

T

兲

, with the perfor- mance of MP4 being slightly unpredictable

共

due to the fre- quent nonconvergence of the Møller–Plesset series⁶⁵

兲

. In- deed, from Tables I and II, we see that the MP2 results are closer to CCSD than are the MP4 results—MP4 overesti- mates the binding energy and underesimates the intermolecu- lar distance. On the other hand, for the dipole moment and polarizability of LiH, the convergence of the MP2, MP4, CCSD series is smooth. For LiH¯H₂, there is essentially no difference between D_ecalculated at the CCSD and CCSD

共

T

兲

levels but the interatomic distances are different.

Since DFT has previously been used in studies of DHBs,^38,66it is of some interest to compare its performance relative to MP2 and CCSD. Concerning the intermolecular H¯H distance, we note that DFT performs well for the strong LiH¯C₂H₂ complex, just as for conventional hydro- gen bonds.^67,68For the three weak DHB complexes, the qual- ity of the DFT H¯H distances is poorer, although it should be pointed out that, in this case, the differences between MP2

共

and MP4

兲

results and the CCSD results are also substantial.

However, while MP2 consistently underestimates the bond distance relative to CCSD, DFT underestimates it for LiH¯H₂ but overestimates for LiH¯CH₄, suggesting a less predictable performance. We also note that the intramo- lecular LiH distance is significantly underestimated at the DFT level.

The inadequacy of DFT for the weakly bound complexes is more clearly noticeable from the interaction energies in Table II. While DFT is reasonably accurate for LiH¯C₂H₂, there are significant discrepancies between DFT and MP2/

MP4 for LiH¯H₂, LiH¯CH₄, and LiH¯C₂H₆. For ex- ample, with

⌬

E_ZPV included, LiH¯CH₄ is bound at the MP2 and MP4 levels but not at the DFT level. For LiH¯C₂H₆, on the other hand, the DHB structure opti- mized at the DFT level does not remain a minimum on the potential energy surface.

The reason for the failure of DFT to reproduce the struc- ture and energetics of the weak DHB complexes is probably the same as for other weakly interacting van der Waals complexes—in its present incarnation, DFT is incapable of a correct description of dispersion, which plays a crucial role in stabilizing these complexes.⁶⁹

B. The decomposition of the interaction energies The components of the interaction energy calculated by means of IMPPT to second order are presented in Table III.

For comparison with a conventional hydrogen-bonded sys- tem, we have included the results for the water dimer, calcu- lated in the same basis. An inspection of Table III shows that the classification of the complexes in two groups

共

the strong LiH¯C₂H₂ complex and the weak van der Waals com- plexes

兲

is valid also for the individual contributions to the interaction energy.

The decomposition of the interaction energy of LiH¯C₂H₂ in Table III is very similar to that of the water dimer⁵³—the main binding contributions come from the electrostatic energy ⑀els

(10), followed by the induction energy

共

expressed as either

⌬

E_def^SCFor ⑀ind,r

(20)) and the dispersion en- ergy⑀disp

(20). In both LiH¯C₂H₂ and H₂O¯H₂O, the weights of the electrostatic and exchange energies calculated with the Hartree–Fock monomer wave functions are such that their sum

⌬

E^HLis negative. Since⑀ind,r

(20) provides a good approxi- mation to

⌬

E_def^SCFfor the complexes in this group, the SCF exchange-deformation effects

共

estimated as

⌬

E_def^SCF⫺⑀ind,r

(20)) are small for these systems. The results in Table III thus suggest that there is no fundamental difference in the energy decomposition of DHB complexes and hydrogen-bond com- plexes of comparable strength.

For the three weak complexes LiH¯H₂, LiH¯CH₄, and LiH¯C₂H₆, the decomposition of the interaction en- ergy presents a different picture. Here, the large repulsive exchange term outweighs the attractive electrostatic term

TABLE III. Decomposition of the MP2 interaction energy共in kJ/mol兲of the LiH¯H₂, LiH¯CH₄, LiH¯C₂H₆, LiH¯C₂H₂complexes in the aug-cc- pVDZ共aD兲and aug-cc-pVTZ共aT兲basis sets共without monomer relaxation effects兲. Geometry optimized with a respective basis set.

LiH¯H2 LiH¯CH4 LiH¯C2H6 LiH¯C2H2 H2O¯H2O

aD aT aD aT aD aT aD aT aD aT

⌬E_{all el.}^MP2 ⫺2.57 ⫺3.00 ⫺2.88 ⫺3.25 ⫺3.58 ⫺17.88 ⫺18.69 ⫺19.97

⌬E^MP2 ⫺2.56 ⫺3.00 ⫺2.86 ⫺3.23 ⫺3.56 ⫺4.06 ⫺17.88 ⫺18.07 ⫺18.67 ⫺19.87

⌬E^HL 1.64 1.12 3.35 2.80 4.48 . . . ⫺2.41 . . . ⫺5.69 ⫺5.20

⑀exch

HL 6.23 5.48 8.01 6.88 9.41 . . . 27.52 . . . 29.42 29.91

⑀els

(10) ⫺4.58 ⫺4.36 ⫺4.66 ⫺4.08 ⫺4.94 . . . ⫺29.93 . . . ⫺35.11 ⫺35.10

⌬E_def^SCF ⫺2.45 ⫺2.22 ⫺2.91 ⫺2.60 ⫺3.35 . . . ⫺11.39 . . . ⫺9.67 ⫺9.90

⑀ind,r

(20) ⫺1.81 ⫺1.66 ⫺3.41 ⫺3.11 ⫺4.78 . . . ⫺13.80 . . . ⫺11.92 ⫺12.69

⑀disp

(20) ⫺2.74 ⫺2.79 ⫺4.41 ⫺4.34 ⫺6.11 . . . ⫺9.51 . . . ⫺9.31 ⫺10.74

⑀disp

(21) ⫺0.46 ⫺0.48 ⫺0.50 ⫺0.51 ⫺0.45 . . . ⫺0.24 . . . ⫺0.46 ⫺0.48

⑀els,r

(12) 0.23 0.24 ⫺0.08 ⫺0.07 ⫺0.15 . . . 2.48 . . . 0.25 0.39

⑀els

(10), making the Heitler–London interaction energy

⌬

E^HL positive. Among the remaining terms, the main attractive contribution comes from the dispersion term⑀disp

(20), although induction is also substantial. Moreover, the first-order corre- lation correction to the dispersion energy ⑀disp

(21) constitutes about 10% of ⑀disp

(20), much more than in LiH¯C₂H₂. In LiH¯C₂H₆ and LiH¯CH₄, the dispersion contribution is larger than the electrostatic contribution, at least in the aug- cc-pVTZ basis. By contrast, in LiH¯H₂, ⑀disp

(20) is smaller than⑀els

(10), which may be rationalized in terms of the small polarizability of H₂.

In short, the decomposition of the interaction energy of LiH¯C₂H₂ does not differ from that in the hydrogen bonded H₂O¯H₂O complex: the leading attractive term is the electrostatic energy, which outweighs the exchange–

repulsion term. By contrast, for LiH¯H₂, LiH¯CH₄, and LiH¯C₂H₆—already classified as weak van der Waals com- plexes on the basis of their total interaction energy—the en-

ergy decomposition confirms that they are indeed bound by dispersion, the electrostatic term being too small to compen- sate for the large exchange-repulsion term.

C. The vibrational harmonic frequencies

The vibrational harmonic frequencies of the DHB com- plexes were calculated at the MP2, MP4, CCSD, and B3LYP levels of theory, at their respective optimized geometries—

see Table IV. In the following, we discuss only the intramo- lecular complex modes—that is, the vibrational modes local- ized in one of the monomers. To facilitate this discussion, Table IV also contains the changes in the monomer param- eters induced by the formation of the DHB complex.

Concerning ␯

共

LiH

兲

stretching vibration, we note that complexation causes a large blueshift of about 50 cm^⫺1 in C₂H₂. In the weaker complexes, this mode is still blue- shifted but only by about 10 cm^⫺1 and correlated with the

TABLE IV. Selected calculated harmonic vibrational frequencies共in cm^⫺1) for the complexes and their shifts upon complexation at the MP2, MP4, CCSD, CCSD共T兲, and B3LYP levels of theory in the aug-cc-pVTZ basis.

Complex Level

␯共LiH兲 ␯共donor兲

␯dim. ⌬␯ ␯dim. ⌬␯

LiH¯H2

MP2 1424 8 ␯共HH兲 4466 ⫺51

MP4 1406 9 ␯共HH兲 4382 ⫺51

CCSD 1396 9 ␯共HH兲 4361 ⫺41

CCSD共T兲 1396 10 ␯共HH兲 4354 ⫺47

B3LYP 1430 10 ␯共HH兲 4359 ⫺58

LiH¯CH4

MP2 1424 8 ␯s(CH) 3057 ⫺12

␯as(CH) 3192 ⫺12

␯as(CH) 3195 ⫺9

MP4 1406 9 ␯s(CH) 3018 ⫺12

␯as(CH) 3141 ⫺13

␯as(CH) 3149 ⫺6

CCSD 1396 9 ␯s(CH) 3036 ⫺10

␯as(CH) 3150 ⫺13

␯as(CH) 3162 0

B3LYP 1429 9 ␯s(CH) 3019 ⫺10

␯as(CH) 3118 ⫺12

␯as(CH) 3127 ⫺3

LiH¯C2H6a

MP2 1429 13 ␯^(CuH) 3066 ⫺7

␯共CH兲 3069 ⫺6

␯共CH兲 3139 ⫺8

␯共CH兲 3143 ⫺4

␯共CH兲 3163 ⫺6

␯共CH兲 3168 ⫺1

LiH¯C2H2

MP2 1465 49 ␯^(CwC) 1945 ⫺23

␯as(CH) 3303 ⫺129

␯s(CH) 3494 ⫺40

MP4 1450 53 ␯^(CwC) 1931 ⫺24

␯as(CH) 3278 ⫺120

␯s(CH) 3462 ⫺40

CCSD 1440 53 ␯共CC兲 2025 ⫺19

␯as(CH) 3325 ⫺92

␯s(CH) 3492 ⫺38

B3LYP 1468 48 ␯共CC兲 2043 ⫺25

␯as(CH) 3275 ⫺137

␯s(CH) 3479 ⫺37

aSaddle point at the B3LYP level.

interaction energy. The large blueshift in LiH¯C₂H₂can be traced to the significant bond shortening of LiH—see Table I.

In the weaker complexes, the effect of complexation on the LiH bond length is very small, explaining the small change in the␯

共

LiH

兲

frequency.

In the proton donors, the stretching frequencies—that is,

␯

共

HH

兲

in H₂, ␯s(CH) and␯as(CH) in C₂H₂, ␯

共

CH

兲

in CH₄ and C₂H₆—are redshifted. As for␯

共

LiH

兲

, these shifts corre- late to some extent with the interaction energies. In C₂H₂, the asymmetric CH stretching band is shifted by about

⫺120 cm^⫺1 and the symmetric band by about ⫺40 cm^⫺1; in the weak complexes, ␯

共

CH

兲

changes of only about

⫺10 cm^⫺1 are observed. Clearly, these shifts reflect the changes in the CH bond lengths upon DHB formation—see Table I. The shift in the vibrational mode of H₂is substantial, in spite of the very small interaction energy in LiH¯H₂. This is understandable, considering the small reduced mass of H₂.

The DFT/B3LYP functional reproduces the stretching frequencies and their complexation shifts with an accuracy comparable with the MP2 method. The differences between MP2 frequencies and the MP4 or CCSD frequencies are also small.

D. The NMR shielding constants

The isotropic and anisotropic proton shielding constants and their counterpoise-corrected shifts upon complexation

⌬

␴cc, calculated at the MP2 and DFT/B3LYP levels of theory, are collected in Table V. The monomer-relaxation corrections

⌬

␴relax are listed separately. For LiH¯C₂H₆, only DFT calculations were carried out, the all-electron MP2 calculations being too expensive.

The shifts in the isotropic shielding constant of the ac- ceptor hydrogen in LiH are small. However, there is a dif- ference between LiH¯C₂H₂ and the weak van der Waals complexes. Whereas the LiH isotropic proton shielding in-

creases upon the formation of LiH¯C₂H₂, it decreases for the weaker complexes. The corresponding shift in the LiH proton shielding anisotropy is in the same direction and ex- hibits an inverse correlation with the intermolecular distance, although not with the interaction energy

共

the shift of 3.42 ppm in the shielding anisotropy of LiH¯C₂H₂ is relatively too small

兲

. For all complexes, the monomer relaxation con- tribution to the proton shift in LiH is negligible.

The shifts in the proton shielding constants in the proton donors are more substantial. Predictably, the largest shifts in the isotropic (⫺3.00 ppm) and anisotropic

共

6.07 ppm

兲

pro- ton shieldings occur in the strongest complex LiH¯C₂H₂, and they are similar to those previously calculated for H₂O¯C₂H₂.⁷⁰For the other complexes, the shifts in the iso- and anisotropic shielding constants are much smaller but in the same direction. The shift in the isotropic shielding corre- lates with the inverse of the intermolecular distance; for the anisotropy, the correlation is weaker. For example, in spite of similar intermolecular distances and interaction energies, the shift is much larger in LiH¯CH₄than in LiH¯C₂H₆. This difference probably arises since LiH¯CH₄, unlike LiH¯C₂H₆, has a colinear DHB structure, making the shielding tensor more anisotropic. Although the effect of monomer relaxation is more substantial for the donor proton than for the acceptor proton, it is significant only in LiH¯C₂H₂.

The proton shielding constants and their shifts calculated at the DFT level are very close to those at the MP2 level, probably because proton shielding shifts are mostly influ- enced by the magnetizability tensor of the neighboring molecule,⁷¹ which is rather insensitive to electron correlation.⁷² For the remaining shieldings such as those of

13C, the complexation-induced shifts calculated at the DFT and MP2 levels

共

not shown in Table V

兲

differ more since the electrostatic and dispersion effects are larger than the purely magnetic ones.⁷¹

TABLE V. Calculated isotropic and anisotropic shielding constants共in ppm兲in the complexes and their shifts upon complex formation at the MP2 and B3LYP level of theory. All calculations in the aug-cc-pCVTZ basis for H and C, and in the aug-cc-pVTZ-su1 basis for Li.

Complex ␴ ␴Li– H ␴H– X

Li–H H–X

⌬␴CC ⌬␴relax ⌬␴CC ⌬␴relax

MP2

LiH¯H2 iso 26.59 25.75 ⫺0.01 0.00 ⫺0.93 ⫺0.06

aniso 3.25 4.41 0.83 0.00 2.63 ⫺0.01

LiH¯CH4 iso 26.53 30.11 ⫺0.09 ⫺0.00 ⫺1.23 ⫺0.05

aniso 4.62 13.45 2.21 ⫺0.00 3.18 ⫺0.01

LiH¯C2H2 iso 26.85 27.09 0.23 0.01 ⫺2.61 ⫺0.39

aniso 5.82 21.83 3.40 0.02 6.29 ⫺0.22

B3LYP

LiH¯H2 iso 26.45 25.73 ⫺0.04 0.00 ⫺1.03 ⫺0.06

aniso 3.34 4.44 0.85 0.00 2.83 ⫺0.01

LiH¯CH4 iso 26.40 30.25 ⫺0.10 0.00 ⫺1.29 ⫺0.05

aniso 4.67 12.48 2.19 0.00 3.28 ⫺0.01

LiH¯C2H6 iso 26.44 29.68 ⫺0.05 0.00 ⫺1.14 ⫺0.03

aniso 4.65 10.05 2.18 ⫺0.01 1.16 ⫺0.03

LiH¯C2H2 iso 26.76 27.28 0.26 0.01 ⫺2.79 ⫺0.39

aniso 5.86 21.66 3.35 0.02 6.57 ⫺0.23

E. The intermolecular indirect nuclear spin–spin coupling constants

1. The spin–spin coupling constants at the equilibrium geometry

The intermolecular indirect nuclear spin–spin coupling constants of the complexes under investigation ^nhJ, calcu- lated at the CCSD and DFT levels in the aug-cc-pVDZ-su1or aug-cc-pVTZ-su1 basis sets, are tabulated in Table VI. Since coupling constants transmitted through strong dihydrogen bonds have already been discussed elsewhere,⁴² we focus here on the comparison of these parameters in strong com- plex LiH¯C₂H₂ and in the weak van der Waals complexes.

The initial discussion in this subsection is based on the CCSD results.

The most interesting coupling constants transmitted through Li–H¯H–X–W are probably the short-range inter- molecular proton–proton coupling constants ^1hJ_HH. These constants are relatively small and negative; they do not cor- relate with the interaction energy—at least not when the whole set of complexes is considered, since the largest cou- pling of ⫺0.95 Hz is observed for the weakest complex LiH¯H₂. However, when only complexes containing the Li–H¯H–C–W dihydrogen bond are compared, a qualita- tive correlation with the intermolecular distance is observed.

Except for^1hJ_HHin LiH¯H₂, the largest contribution to the

short-range intermolecular proton–proton couplings origi- nate from spin–orbit terms; in this respect, the short-range proton–proton intermolecular couplings resemble the long- range ones.^16,17

The^2hJ_LiHcouplings in LiH¯CH₄and LiH¯C₂H₆are negligible and dominated by the spin–orbit interactions. The corresponding couplings in LiH¯H₂ and LiH¯C₂H₂ are different in character, being larger (⫺0.30 Hz and

⫺1.02 Hz, respectively

兲

and dominated by the FC interac- tion. Clearly, no correlation with the interaction energy is observed for these coupling constants.

The intermolecular coupling constant^2hJ_HXbetween the hydrogen atom of LiH and the hydrogen or carbon atoms of the proton donor are positive and much larger than^1hJ_HH, in spite of the longer separation. The largest reduced coupling is observed for LiH¯C₂H₂ and the smallest for LiH¯H₂, so in this sense ^2hJ_HXcorrelates

共

qualitatively

兲

with the in- termolecular distance. However, the^2hJ_HCcoupling is larger for LiH¯CH₄ than for LiH¯C₂H₆, which is the opposite of the relation for the interaction energies

共

see Table II

兲

. This is probably caused by nonlinearity of dihydrogen bond in LiH¯C₂H₆.

The ^3hJ_LiX coupling constants are all positive. The smallest reduced coupling is observed in LiH¯H₂ and the largest in LiH¯C₂H₂. While^3hJ_LiCcorrelates well with the

TABLE VI. Intermolecular indirect spin–spin coupling constants J共in Hz兲calculated at CCSD and B3LYP levels of theory in the aug-cc-pVTZ-su1共aT-su1兲 basis and the aug-cc-pVDZ-su1共aD-su1兲basis.

Term

level/basis ^1hJHH 2hJLiH 2hJHX 3hJLiX 1hJHH 2hJLiH 2hJHX 3hJLiX

LiH¯H2 LiH¯CH4

FC ⫺1.10 ⫺0.34 3.64 1.89 ⫺0.57 ⫺0.06 2.90 0.99

DSO 0.71 0.03 ⫺0.27 ⫺0.10 1.55 0.17 0.02 ⫺0.01

PSO ⫺0.58 0.00 0.32 0.05 ⫺1.33 ⫺0.05 ⫺0.04 0.00

SD 0.01 0.01 ⫺0.02 0.00 0.01 0.01 0.06 0.01

CCSDÕaDsu1 À0.95 À0.30 3.67 1.84 À0.35 0.05 2.88 0.99

FC ⫺1.15 ⫺0.35 3.87 1.93 ⫺0.62 ⫺0.09 2.94 0.98

DSO 0.74 0.03 ⫺0.28 ⫺0.10 1.55 0.17 0.02 ⫺0.01

PSO ⫺0.66 0.00 0.32 0.05 ⫺1.33 ⫺0.05 ⫺0.04 0.00

SD 0.00 0.01 ⫺0.03 0.00 . . . . . . . . . . . .

CCSDÕaTsu1 À1.07 À0.30 3.88 1.89 À0.40 0.03 2.92 0.98

FC ⫺1.33 ⫺0.58 5.89 3.72 ⫺0.61 ⫺0.05 4.57 1.63

DSO 0.74 0.03 ⫺0.82 ⫺0.10 1.55 0.17 0.02 ⫺0.01

PSO ⫺0.66 0.00 0.32 0.12 ⫺1.34 ⫺0.12 ⫺0.04 0.01

SD 0.00 0.01 ⫺0.03 0.00 0.00 0.01 0.07 0.01

B3LYPÕaTsu1 À1.25 À0.54 5.89 3.73 À0.41 0.02 4.62 1.65

LiH¯C2H6 LiH¯C2H2

FC ⫺0.79 ⫺0.03 2.31 0.93 ⫺0.99 ⫺1.22 9.05 5.80

DSO 1.62 0.17 0.06 0.00 2.28 0.21 0.11 0.01

PSO ⫺1.18 ⫺0.04 ⫺0.06 0.00 ⫺1.63 ⫺0.04 ⫺0.09 0.00

SD . . . . . . . . . . . . ⫺0.02 0.03 0.11 0.01

CCSDÕaDsu1 À0.35 0.10 2.32 0.93 À0.37 À1.02 9.18 5.83

FC . . . . . . . . . . . . ⫺1.06 ⫺1.24 9.43 5.73

DSO . . . . . . . . . . . . 2.32 0.22 0.11 0.01

PSO . . . . . . . . . . . . ⫺2.01 ⫺0.06 ⫺0.14 0.00

SD . . . . . . . . . . . . ⫺0.06 0.03 0.11 0.02

CCSDÕaTsu1 . . . . . . . . . . . . À0.81 À1.06 9.51 5.76

FC ⫺0.94 0.01 3.50 1.49 0.05 ⫺1.59 11.64 8.68

DSO ⫺0.02 0.01 0.04 0.00 2.31 0.22 0.11 0.01

PSO ⫺1.43 ⫺0.12 ⫺0.06 0.01 ⫺2.04 ⫺0.13 ⫺0.15 0.00

SD 1.65 0.18 0.06 0.00 ⫺0.06 0.02 0.13 0.02

B3LYPÕaTsu1 À0.74 0.07 3.53 1.50 0.26 À1.48 11.72 8.70