Ab initio molecular orbital calculations of the infrared spectra of interacting water molecules

Journal of Molecular Structure (Theo&em), 189 (1988) 241-265 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

241

AB INITIO MOLECULAR ORBITAL CALCULATIONS OF THE INFRARED SPECTRA OF INTERACTING WATER MOLECULES Part 1. Complexes of water with nitrogen, neon and argon

M.J. BRASLER, V.C.E. CARR, M.G. GERAZOUNIS, FORD*

N.R. JUGGA, G.A. YE0 and T.A.

Department of Chemistry, University of the Witwatersrand, Johannesburg, Africa)

Wits 2050 (South

(Received 16 November 1987)

ABSTRACT The infrared spectra of three water. - nitrogen, two water. * *neon and two water. - argon complexes have been predictedusing the GAUSSIAN-76 ab initio molecular orbital computer program package. The wavenumbers have been compared with those of the water monomer, calculated earlier, and with experimental data, where they were available. The intensities have also been compared with those of the monomer, and have been interpreted in terms of the derived atomic polar tensors. The structures, interaction energies (including the effects of basis set superposition error) and bonding properties of the complexes have been discussed.

INTRODUCTION

We have shown that it is possible to compute the infrared spectra (wavenumbers and intensities) of a variety of complexes between water and other small molecules, both of the hydrogen bonding (HOH- **NN, HOH* *.OC, HOH- - *CO, HOH. - *OHz, HOH- * *OCHz and HSH- * -OH,) and of the van der Waals type (Hz0 *. - Nz and Hz,O-*.CO, both planar and perpendicular) [ 11. In two of these cases we have also analysed the infrared intensity changes of the bonded OH-stretching bands (of HOH* * *OH, and HOH. *CO) [ 2 ] in terms of the King charge-charge flux-overlap (CCFO ) interpretation [ 3,4] of the atomic polar tensors ( APTs) [ 5,6]. However, later experience [ 7,8] showed that we had naively relied on the results of only a single pass of the geometry optimization routine of the GAUSSIAN-76 computer program [9,10] in order to determine the equilibrium geometries of the monomers and of the complexes. Because our procedure for calculating the Cartesian force constants, l

*To whom correspondence should be addressed.

0166-1280/88/$03.50

0 1988 Elsevier Science Publishers B.V.

242

and hence the wavenumbers, requires a knowledge of the absolute energy minimum for each molecule, or complex, it is necessary to ensure that the absolute minimum has been attained, by repeated cycles of the geometry optimization step; in some cases this required of the order of one hundred cycles [ 81. We have since [ 111 published corrected values of the minimum energies of the ten complexes studied earlier [ 1 J. In the light of these revised geometries and energies [ 111, and in view of the fact that we did not take basis set superposition error (BSSE) [ 121 into account in calculating the interaction energies of the various complexes [ 11, we have undertaken to repeat the computations of the infrared spectra of these and some additional, related, complexes. In this paper, we consider the three water - - -nitrogen complexes (linear hydrogen bonded HOH- *l NN, and planar and perpendicular H,O* - -N2). Our reason for studying the water - **nitrogen interaction [l] was that the first reported spectrum of water recorded using the matrix isolation technique was that observed by van Thiel et al. in nitrogen [ 131, and it is under matrix isolation conditions that one would most likely expect to observe evidence of the formation of the simple, hypothetical 1: 1 complexes that we have simulated in our calculations [ 11. Along with nitrogen, the most commonly used matrix gas in matrix isolation spectroscopy is argon, and we have also simulated two water- . *argon complexes, a linear HOH - - -Ar and a planar O-bonded HzO* - *Ar species. Since neon is also available to us, using the GAUSSIAN-76 program [ 9,101, we have also simulated the analogous HOH- *lNe and Hz00 *-Ne complexes. We report here the structures, bonding properties, interaction energies, wavenumbers and intensities of these complexes, and interpretations of the intensities in terms of the APTs and their charge, charge flux and overlap components. CALCULATIONS AND RESULTS

We have used the GAUSSIAN-76 computer program package [ 9,101, with the 4-31G basis set [ 141 for oxygen, hydrogen and nitrogen. For neon and argon we used the MINI-4 (43/4 and 433/43) basis sets of Huzinaga et al., respectively [ 15,161. The methods used for computing the wavenumbers and intensities have been described fully by Chin and Person [ 171, and are consistent with those which we have used earlier [ 1,7,8]. The calculations were carried out using an IBM 3083 computer. The computed minimum energy geometries are listed in Tables 1 and 2. As we pointed out before [ 111, the main effect of repeated geometry optimizations for the water- * nitrogen complexes was to reduce the minimum energy of the linear hydrogen bonded HOH* - *NN aggregate below those of the two van der Waals’ HzO- **Nz species. Table 3 shows the values of the interaction energies of the water- - ‘nitrogen l

243 TABLE 1 Calculated geometrical parameters of water-nitrogen Complex

complexes Bond angles

Bond lengths Bond

Length (pm)

Angle (degrees )

Linear OH*-*N bonded (C,)

F

(OH) (non-bonded) r(OH) (bonded) r(H-a-N) r(NN)

95.02 95.02 238.96 108.40

H6H 0HaT.N (ck) He .^NN (truns )

111.36 173.93 170.78

Planar O-bonded (C,,)

r(OH) r(O--.N) r(NN)

95.08 325.43 108.48

HOH N...d...N

111.34 19.19

HdH

111.27 18.97

Perpendicular O-bonded (C,,)

95.05

r(OH) ~(0.S-N)

328.98

r(NN)

108.44

N...&..N

TABLE 2 Calculated geometrical parameters of complexes of water with neon and argon Complex

Bond lengths

Bond angles

Bond

Length (pm)

Angle (degrees)

Linear OH- *-Ne bonded ( C.)

F

(OH) (non-bonded) r(OH) (bonded) r(H--*Ne)

95.03 94.99 238.50

H6H OH..^Ne (trans)

111.31 177.98

Planar 0. - *Ne bonded (C,, )

r(OH) r(O*-*Ne)

95.13 346.93

HGH

111.07

Linear OH-- *Ar bonded (C.)

F

95.01 94.95 255.67

HdH OH.^.Ar (trans)

111.41 176.29

HOH

111.19

(OH ) (non-bonded)

r (OH) (bonded)

r(H-**Ar) Planar 0.-*Ar bonded (C,)

r(OW

95.06

r(O-**fir)

372.44

TABLE 3 Calculated interaction energies of water-nitrogen Complex

Linear OH- - -N bonded Planar O-bonded Perpendicular O-bonded “See text for definition.

complexes

Energy” (kJ mol- ’ ) AE

BSSE

AE’

-7.30 -4.47 - 3.70

3.06 2.57 2.36

-4.24 - 1.90 -1.34

244 TABLE 4 Calculated interaction energies of complexes of water with neon and argon Complex

Linear Planar Linear Planar

Energy” (kJ mol- l)

OH. *.Ne bonded 0. *SNe bonded OH. - *Ar bonded 0. - *Ar bonded

AE

BSSE

AE’

-2.57 -0.02 -4.66 -0.01

2.98 0.11 6.28 0.43

0.41 0.09 1.62 0.42

*See text for definitions. TABLE 5 Calculated wavenumbers and intensities of the infrared bands of water-nitrogen Complex

Symmetry species

Mode

Assignment

0 (cm-‘)

Linear OH...N bonded (C,)

a’

*1

4130 3971 2679 1721 462 240 e

v9

Y(OH) (non-bonded) v(OH) (bonded) v(NN) 6( HOH) &OH-.-N) v(H..*N) G(H...NN) y(OH...N) y(H.,.NN)

Vl

vs(OH2)

v2

v(NN)

v3

S(

v2 V3 VP v5 V6 h a"

Planar O-bonded (C,)

Perpendicular O-bonded (G”)

al

V6

v4

HOH) v,(O...Nz)

a2

v5

tw(OH2)

h

v6

d0I-L)

b2

h

va(OH2)

h3

r(OH2)

v9

va(O---Nz)

Vl

vs(OH2)

%

v(NN)

al

*4

6(HOH) v,(O...N,)

a2

v5

tw(OH2)

b,

v0

v,(OH,)

V7

r(OH2)

v3

b2

“Negative eigenvaiue. bInactive.

V6

v,(O...N,)

v9

w(OH2)

380 220 3957 2683 1785 303 311 317 4121 301 209 3955 2683 1779 236 296 4115 215 289 252

complexes A (km mol-‘) 94

27 1.3 138 1.0 8.1 133 306 3.1 7.6 0.0 135 0.1

b

512 51 111 4.8 7.4 0.0 134 0.2 b

63 133 0.3 481

245

complexes, dE [ 111. These energies were corrected for BSSE [ 121 by the full counterpoise method [ 18 1, as advocated by Szczesniak and Scheiner [ 191, and as we have done for the linear and cyclic ammonia dimers [ 201. The BSSEs are also listed in Table 3. The entries in the column headed dE’ were derived by subtracting the BSSEs from the LIEvalues, as described earlier [20]. Table 4 contains the same information for the water complexes with neon and argon. It is evident from Table 4 that, while subtraction of the separated molecule, or atom, energies from that of the complex yields a negative value of dE for each complex, and therefore predicts an attractive interaction [ 201, subtraction of the BSSE from this energy difference results in a sign reversal of the interaction energy, so that all four complexes appear to suffer a repulsive interaction. The calculated wavenumbers and intensities for all seven complexes, determined as before [ 1,2,7,8], are collected in Tables 5-7, together with reasonable assignments

for all the normal modes.

As part of our procedure for calculating the infrared band intensities, a set of APTs [5,6] is determined for each atom of a complex. These APTs can be partitioned into their component charge, charge flux and overlap tensors, according to the CCFO model of King [ 3,4 1, as we have done for the water [ 21 and ammonia dimers [20] and the HOH. **CO complex [2]. Comparison of the total APTs, and of their C, CF and 0 components, of the oxygen, nitrogen and hydrogen atoms in the complexes with those in the water and ammonia monomers [ 71 has indicated the main source of the intensity increases for the bonded OH- or NH-stretching bands of the HOH. - *OHz, HOH. *-CO [21 and H2NH. - *NH3 [ 201 complexes. The total APTs and their components were TABLE 6

Calculatedwavenumbers and intensities of the infrared bands of water-neon complexes Complex Linear OH**.Ne bonded (G)

Symmetry species

P (cm-‘)

A

a”

u (OH) (non-bonded) u (OH) (bonded) 6(HOH) u(H*.*Ne) G(OH*.*Ne) y(OH*.*Ne)

4130 3974 1707 229 145 190

69 8.6 122 4.3 137 247

v.(W)

b,

6(HOH) v(O**.Ne) va(O&) r(OH,) w(OH,)

3920 1823 95 4107 181 a

29 82 1x10-6 59 141 0.0

a’

Planar O-bonded (G”)

*Negativeeigenvalue.

Mode

Assignment

(km mol-‘)

246 TABLE 7 Calculated wavenumbers and intensities of the infrared bands of water-argon complexes Complex

Symmetry species

Linear OH**.Ar bonded (C,)

Planar O-bonded (C,“)

Mode

0’

*1

a”

*2 *3 *4 *5 *,

al

*1 *2 *3

b,

*4 *5 *6

iJ (cm-‘)

A

v (OH) (non-bonded) v (OH) (bonded) S( HOH) v(H...Ar) G(OH...Ar) y(OH***Ar)

4111 3944 1671 151 a 288

38 71 80 4.5 67 229

*.(OHz) &OHz) v(O***Ar) *,(OHz) r(0I-h) w(0I-k)

3931 1830 263 4116 198 B

28 83 2x10-3 59 142 0.0

Assignment

(km mol-l)

“Negative eigenvalue.

calculated in a coordinate frame in which the bonded OH bond (HOH. - *NN, HOH. - *Ne and HOH- - *Ar), or the HOH angle bisector (planar and perpendicular H,O - l N2, and planar Hz0 *- .Ne and HzO* - *Ar ) lay along the z axis. These tensors are listed in Table 8-15. l

DISCUSSION

Structures

A considerable body of recent experimental and theoretical evidence indicates that intermolecular complexes between nitrogen and proton donors have linear, or nearly linear, XH - **NN fragments. Thus ClH. - *NN (matrix infrared [ 21,22 1, molecular beam electric resonance [ 23 ] and ab initio [ 24,25 ] ), FH*. *NN (matrix infrared [26,27] and ab initio [24,28] ), CH30H- - lNN (matrix infrared [26,27] and ab initio [24,28] ), CH30H* *-NN (matrix infrared and ab initio [ 29]), NCH- *lNN (pulsed nozzle Fourier transform microwave [ 30]), HOH- **NN (matrix infrared [ 271 and ab initio [28 ] ), HzNH* *NN (ab initio [ 281) and NNH+ (ab initio [ 311) are all linearly hydrogen bonded. Reed et al. [ 281, in their calculations using the 4-31G basis set, found that the separation of the oxygen atom from the NE N mid-point was 387 pm, the angle between the N z N axis and the line joining the 0 atom to the N = N midpoint was 3.8” and the angle between the water C, axis and 0.-*N=N midpoint line 49.6”. They kept the intramolecular water and nitrogen dimensions l

0.2742 0 - 0.0950

J&

“See ref. 7.

0.2742 0 0.0950

-0.5485 0 0

HI

0

Atom

0.4823 0

0

0 0.4823 0

0

0 - 0.9647

-0.1424 0 0.2265

0.1424 0 0.2265

-0.4531

0

0

0

0 0.4017 0 0 0.4017 0

0.4017 0 0 0.4017 0 0 0.4017

0

0

0.4017

0

0

- 0.8034

0

0.0554 0 0.0779

0.0554 0 -0.0779

-0.1109 0 0

0

- 0.8034 0 0 - 0.3034 0

Charge flux

Charge

0 0 0

0 0 0

0 0 0

- 0.0450

0

0.0379

0 - 0.0450

- 0.0379

0.0900

0

0

0

0 0.0807 0 0 0.0807 0

-0.1829 0 -0.1729

-0.1613 0

-0.1829 0 0.1729

0.3658 0 0

Overlap

-0.1803 0 -0.1302

0.1803 0 -0.1302

0.2603

0

0

Total atomic polar tensors, and their charge, charge flux and overlap contributions, of the water monomer in its original cartesian coordinate systema (units am e)

TABLE 8

0.0249 0 - 0.0059

N (non-bonded)

“See ref. 1.

-0.0107 0 0.0060

0.1298 0 0.0565

N (bonded)

H (non-bonded)

0

0.0269 0

0

-0.0149 0

0

0.4773 0

0

0.4813 0

-0.0016 0 0.0497

0.0243 0 -0.1432

- 0.0267 0 0.3821

- 0.0398 0 0.2906

0.0146 0 0

-0.0049 0 0

0.3956 0 0

0.4228 0 0

0.3516 0 - 0.0586

H (bonded)

0.0438 0 -0.5792

- 0.8281 0 0

0

- 0.4955 0 0.0016

0

- 0.9705 0

Charge

Total APT

Atom 0

0

0

0.0146

0 0

0

- 0.0049

0 0

0.0146 0

- 0.0049 0

0.3956

0 0

0

0.4228

0 0

-0.8281

0

0.3956 0

0.4228 0

0

-0.8281 0

0.0037 0 0.0344

-0.0032 0 -0.0521

0.0630 0 -0.0315

-0.0824 0 -0.0663

0.0189 0 0.1155

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

Charge flux

- 0.0026 0 0.0581 0.0066 0 - 0.0403

0.0347 0 - 0.2231 -0.0161 0 0.0951

-0.3289 0 0.0881

0.0112 0 0.0077

-0.0111 0 0.1846 -0.1024 0 - 0.0546

0.3136 0 -0.1140

0.0948 0 - 0.0020

Overlap

0.0123 0

0

0

0 - 0.0100

0.0817 0

0

0.0585 0

0

-0.1424 0

0

0.0145 0 - 0.0600

-0.0104 0 0.0848

0.0757 0 0.0411

- 0.0287 0 - 0.3169

-0.0510 0 0.2510

Total atomic polar tensors, and their charge, charge flux and overlap contributions, of the hydrogen bonded HOHe. *NN complex in its original cartesian coordinate system’ (units are e)

TABLE 9

0 0.4862 0

0 -0.0033 0

0 -0.0033 0

0.2564 0 -0.0829

-0.0236 0 0.0013

-0.0236 0 -0.0013

H(-xl

N(+x)

N(-xl

“See ref. 1.

0 0.4862 0

0.2564 0 0.0829

H(+x)

0.0649 0 0.0307

- 0.0649 0 0.0307

-0.1198 0 0.2402

0.1198 0 0.2402

- 0.0005 0 0

-0.0005 0 0

0.4043 0 0

0.4043 0 0

- 0.8075 0 0

0 0 -0.5418

-0.4656 0 0

0

0 -0.9656 0

Charge

Total APT

Atom 0

- 0.0605 0

0

-0.0005 0

0

0.4043 0

- 0.0005

0 0

- 0.0005

0

0

0.4043

0 0

0

0.4043

0 0

0

- 0.8075

0 0

0.4043 0

- 0.8075 0

- 0.0228 0 - 0.0042

- 0.0228 0 0.0041

0.0361 0 0.1144

0.0361 0 -0.1144

0 0

0

0

0

0

0 0

0

0

0 0

0 0.0137

0.0894

0 0.0134

- 0.0894

0 -0.0426

0.0549

- 0.0426

0

- 0.0549

0 0.0581

- 0.0003 0 0.0029

-0.0003 0 - 0.0029

-0.1840 0 -0.1973

0.1973

0

-0.1840

0.3153 0 - 0.0001

0 0

0

- 0.0266 0 0.0001 0

Overlap

Charge flux

- 0.0028 0

0

- 0.0028 0

0

0.0819 0

0

0.0819 0

0

-0.1583 0

0

- 0.0245 0 0.0176

0.0245 0 0.0178

-0.1747 0 -0.1215

0.1748 0 -0.1215

0.2076

0

0

Total atomic polar tensors, and their charge, charge flux and overlap contributions, of the planar Hz0 . . aNp complex in its original coordinate system” (units are e )

TABLE 10

“See ref. 1.

N(+Y)

N(-Y)

- 0.0073 0 0

-0.0073 0 0

- 0.0829

0

-0.0153 -0.Oc97

0

-0.0153 0.0007

0

0.4725 0

0

0.4725 0

0.0319

0 - 0.0590

0 0.0590 0.0319 - 0.0006 0 0

0

0

-0.ooo6

0.4038 0 0

-0.1245 0 0.2389

0.2789 0

H(-x)

0.4038 0 0

0.1245 0 0.2389

0.2789 0 0.0829

H(+x)

- 0.5414

0

0

- 0.8065 0 0

0

- 0.5431 0 0

0

-0.9144 0

Charge

Total AF’T

Atom 0

0 - 0.0006 0

0 - 0.0006 0

0.4038 0

0

0.4038 0

0

- 0.8065 0

0

- 0.0006

0 0

0 - 0.0006

0

0.4038

0 0

0.4038

0 0

- 0.8065

0

0 0

- 0.0009

-0.0010 0 0

0.0616 0 0.1144

0.0615 0 -0.1143

-0.1212 0 - 0.0002

Charge flux 0

- 0.0156 0.0023

0

0 - 0.0154 - 0.0023

-0.0168 0

0

0 -0.0168 0

0.0645 0

- 0.0761 0.0144

0

0.0761 0.0144

0

0.0462 0 - 0.0423

-0.0462 0 - 0.0423

0.0558

0 0

-0.0058 0 0

- 0.0058 0 0

-0.1865 0 -0.1973

-0.1865 0 0.1971

0.3846 0 0.0002

Overlap

0.0008 - 0.0030

0

0.0007 0.0030

0

0.0854 0

0

0.0854 0

0

-0.1723 0

0

0.0170 0.0180

0

-0.0171 0.0180

0

- 0.1706 0 -0.1226

0.1706 0.0002 -0.1227

0.2093

0 0

Total atomic polar tensors, and their charge, charge flux and overlap contributions, of the perpendicular H,O* **N, complex in ita original coordinate system” (units are e)

TABLE 11

z

0.3301 0 -0.0963

H (bonded)

Ne

0 0.0259

-0.0094

0.1418 0 0.0621

-0.4652 0 0.0157

0

H (non-bonded)

Total APT

Atom

-0.0138 0

-0.0018 0 -0.0430

0.0125 0 0.3633

0 0.4885 0 0

-0.0506 0 0.2123

0.0394 0 -0.5452

0 0.4851 0

0 -0.9638 0

0.0081 0 0

0.4012 0 0

0.3975 0 0

-0.8068 0 0

Charge

0 0 0.3975 0 0 0.4012 0 0 0.0081

0 0.4012 0 0 0.0081 0

0 0 - 0.8068

0 0.3975 0

0 -0.8068 0

0.0006 0 -0.0038

0.0439 0 -0.0486

-0.0874 0 -0.0315 -0.1191 0 -0.0282 -0.0018 0 -0.0504

0 0 0

0.0315 0 0.1512

0 0 0

0 0 0

-0.0181 0 0.0297

-0.3033 0 0.1107

0.0200 0 -0.0648

0.2987 0 -0.0681

0 0 0

0.0429 0 0.0839

Overlap

Charge flux 0.0894 0 -0.0726

0 0 -0.0007

0.1316 0 - 0.0096

0 0.0873 0 0 -0.0219 0

-0.0821 0 - 0.3364

- 0.0500 0 0.3343 0 0.0876 0

0 -0.1570 0

Total atomic polar tensors, and their charge, charge flux and overlap contributions, of the hydrogen bonded HOH. *.Ne complex in its original cartesian coordinate system (units are e )

TABLE 12

0

0

- 0.0029

0.2777 0 0

H(-xl

Ne

0.2777 0 0

H(+x)

-0.0011

0 0

0.0014 0

-0.1334 0 0.2255

0.1334 0 0.2255

0

0.4857 0

0

0.4857 0

0

- 0.4499

0 0

0

0.4015 0 0 0.0001 0

0.0001 0 0

0

0.4015 0

0

- 0.8030 0

0.4015 0 0

0.4015 0 0

- 0.8030 0 0

0

-0.5525 0 0

0

-0.9728 0

Charge

Total APT

Atom

0.0001

0

0

0.4015

0

0

0.4015

0 0

- ‘0.8030

0 0

0.0012 0 0

0.0573 0 0.1112

0.0573 0 -0.1112

-0.1135 0 0

Charge flux

0

0

0

0

0

0

0 0

0

0 0

0

-0.0012

0

0

0.0419 0 - 0.0455

-0.0419 0 -0.0455

0.0922

0

0

- 0.0041 0 0

-0.1811 0 -0.1112

-0.1811 0 0.1112

0.3640 0 0

Overlap

0.0013 0

0

0.0843 0

0

0.0843 0

0

-0.1698 0

0

0.0001

0 0

-0.1753 0 -0.1305

0.1753 0 -0.1305

0.2609

0

0

Total atomic polar tensors, and their charge, charge flux and overlap contributions, of the planar O-bonded H,O. **Ne complex in its original coordinate system (units are e )

TABLE 13

E

Ar

H (non-bonded)

0 0.4817 0

0 0.0143 0

0.1498 0 0.1214

0.0133 0 -0.0528

0.0170 0 0.2729

0.0016 0 0.3252

-0.0529 0 0.2825

0.0239 0 0

0.3997 0 0

0.3874 0 0

0.3202 0 -0.0965

H (bonded)

0 0.4781 0

-0.8110 0 0

0.0343 0 -0.5807

-0.4834 0 0.0279

0

0 -0.9741 0

Charge

Total APT

Atom

0 0.0239 0

0 0.3997 0

0 0.3874 0

0 -0.8110 0

0 0 0.0239

0 0 0.3997

0 0 0.3874

0 0 -0.8110

0.0002 0 -0.0095

0.0374 0 -0.0522

-0.0856 0 -0.0165

0 0 0

0 0 0

0 0 0

-0.0064 0 -0.1428

-0.1207 0 -0.0187

0.0450 0 0.2558

-0.0108 0 -0.0433

-0.2874 0 0.1737

0.0184 0 -0.0800

0.2797 0 -0.0504

0.0820 0 -0.0943

0.0480 0 0.0783

0 0 0

Overlap

Charge flux

0 -0.0096 0

0 0.0819 0

0 0.0907 0

0 -0.1631 0

0.0234 0 0.3919

0.1223 0 - 0.0558

- 0.0980 0 -0.3607

-0.0477 0 0.3246

Total atomic polar tensors, and their charge, charge flux and overlap contributions, of the hydrogen bonded HOH. -. Ar complex in its orginal cartesian coordinate system (units are e)

TABLE 14

- 0.0026 0 0

0.2780 0 0

H(-xl

Ar

0.2780 0 0

H(+x)

0

- 0.0035

0

0.0002 9 0

0.4015 0 0

-0.1330 0 0.2262

0.0014 0

0.4015 0 0

0.1330 0 0.2262

0

0.4861 0

0

0.4861 0

0

0

0

0.0002

0

0.0002 0

0.4015

0 0

0.4015

0 0

0

0.4015 0

0

0.4015 0

0

- .0.8032

0

0

-0.0014 0 0

0.0585 0 0.1120

0.0585 0 -0.1120

-0.1156 0 0

- ‘0.8032 0

0

-0.8032 0 0

0 -0.4490

0

-0.5533 0 0

0

0 - .0.9736

Charge flux

Charge

Total APT

Atom

0

0 0

0

0 0

0

0 0

0 0

0 0

- 0.0038

0

0

0.0433 0 - 0.0449

- 0.0433 0 - 0.0449

0 0.0936

-0.0015 0 0

0.1820 0 -0.1120

-0.1820 0 0.1120

0.3655 0 0

Overlap

0.0012 0

0

0.0846 0

0

0.0846 0

0

- 0.1704 0

0

0.0001

0

0

-0.1763 0 -0.1304

0.1763 0 -0.1304

0.2604

0

0

Total atomic polar tensors, and their charge, charge flux and overlap contributions, of the planar O-bonded H,O* - *Ar complex in its original coordinate system (units are e)

TABLE 15

:

at their monomer values (r(OH) =95.1 pm, H~H=111.2” andr(NN) =108.6 pm). These dimensions correspondto r(H***N) =237.6pm, OH*^*N=174.0” and H* -^NN = 176.2’) for comparison with our values (see Table 1) . Incidentally, Murto and Ovaska [ 291 obtained a value of 241 pm for (He -N) in the analogous complex CHBOH* *NN. For the planar HZ0 ***Nz species, Reed et al. derived a 0. **N = N mid-point separation of 320 pm [ 281, which compares with our 320.88 pm, and Murto and Ovaska’s 319 pm for CH30H* **NN [ 291. Our perpendicular H,O- **N, complex dimensions are essentially the same as those of the planar isomer. While we were unable to distinguish between the bonded and non-bonded OH bond lengths in HOH* - NN, we have found the bonded to be marginally shorter than the non-bonded lengths in HOH. - *Ne and HOH- - *Ar. This phknomenon is clearly related to the repulsive nature of these complexes, as noted above. However, the He **X and 0. - *X distances given in Table 2 are considerably shorter than the sum of the appropriate van der Waals’ radii, and this suggests attraction. Losonczy et al. [32] have determined a structure for HOH* *-Ne, with an 0.*-Ne distance of 363 pm (cf. our 333.49 pm) and a stabilization energy of 0.71 kJ mol-l, using a more extensive basis set than ours, but neglecting BSSE. Moreover, Bentley [ 331 has found a CZVHz0 - **Ne* species with an attractive potential of 24.12 kJ mol-’ at a 0. *-Ne* separation of 250 pm. Clearly the stability of the water- - -neon species is by no means settled. Losonczy et al. found that in the case of the hydrogen bonded HOH- *-Ar complex the well minimum appeared at a 0...Ar distance of 445 pm (cf. our 350.62 pm), with a depth of 0.08 kJ mol-’ [32]. They find, as we do, that the hydrogen bonding interaction between water and the second row element is weaker than that with the corresponding first row element, as expected. l

l

l

Bonding properties

Consideration of the molecular orbital coefficients of the various complexes presents no surprises. The ground state electronic configurations of the water and nitrogen monomers are [ 341

while those of the three C, hydrogen bonded complexes are HOH~~-NN:(1-9)(a’)2(la”)2(10a’)2(2a”)2 HOH-a-Ne:

(l-5) (~‘)“(lu”)~(6-7)

(u’)~(~u”)~(~u’)~

HOHa*-Ar:

(1-9)(u’)2(lu”)2(10-ll)(a’)2(2u”)2(12u’)2

256

In each of these three complexes, only one molecular orbital contains significant contributions from both the water molecule and the bonded partner. In the HOH. **NN complex, this is the 7~’ orbital. The complex 7~’ orbital is that formed from the water lbz o bonding orbital and one of the nitrogen lone pair orbitals. The remaining complex orbitals are essentially unperturbed H,O and Nz monomer orbitals, as indicated in Table 16. In the linear HOH* **Ne complex the orbital in question is the 7a’, and in the HOH. **Ar complex the lla’ orbital. While the HOH. **Ne 7~’ orbital is a combination of the water lbz with the neon 2p, orbital, the 11~’ orbital of HOH. - Ar combines the water 4u1 with the argon 3p, orbital. In the case of the non-hydrogen bonded, CzV,complexes, the electronic configurations are l

HzO’S’Nz (planar):

H20..*N2 (4~1 12(2b2

(lU1)2(2U~)2(lb2)2(~U~)2(4Ul)2(2b,)2(3b,)2

(perpendicular): J2(1b1

J2(5a,

J2(2b1

(la, )2(2u,)2(lb2)2(3u1)2 )2(6a,

)2(7a1 12(3b2

J2

H,O***Ne: (1-4)(u,)2(lb2)2(lb1)2(5u1)2(2b2)2(6u1)2(2b,)2 H,O**.Ar: (1-3)(~,)~(lb~)~(lb~)~(4-6)(~,)~(2b~)~ (7~~)2(3b2 )2(2b1 )2(301 )2(3b1 )” In both planar and perpendicular H,O **.N2, the 6u, and 7u1 orbitals both involve mixing of the water and nitrogen orbitals. The first of these combines TABLE 16 Molecular orbitals of the linear hydrogen bonded HOH. **NN complex Orbital

Energy (a.u. )

Apfiroximate description”

lfl’ 2a’ 3a’ 4a’ 5a’ 6a’ 7a’ 8a’ 9a’ la” 10a’ 2a”

- 20.503236 - 15.701169 - 15.697298 - 1.553091 - 1.339404 - 0.790667 -0.714504 - 0.650246 -0.645216 -0.645166 - 0.537256 - 0.487696

IWUa,) Nz(lqJ Wlud N,WJ Hz0 @ad N,(%) H,OUb,)+N,(2d

“See ref. 34.

N,(~cJ,) N,(llr:+lai;) N,(ln:-In;) H#(3aJ H,Otlb,)

257

mainly the water 3al with the nitrogen 2crporbital, while the second combines the water 3ai orbital with the nitrogen 3cr, Finally, for the O-bonded neon and argon complexes, the 6a, orbital of HzO* *Ne is essentially the unperturbed 3al water orbital, with a small contribution from the neon 2p, orbital, while the 7a, and 8ui orbitals of H,O- * *Ar mix the water 3u1 with the argon (3p, - 2p,), and with the argon (2p, - 3p,) combinations respectively. The coefficients of the molecular orbitals of all seven complexes are very little perturbed from their values in the orbitals of the isolated monomer molecules (or atoms ) , except for those orbitals indicated above which involve mixing of the sub-unit orbitals. This confirms the very weak intermolecular interactions which appear to characterize these particular complexes. l

Interaction energies

Reed et al. [ 281 have considered two water. - *nitrogen aggregates, a linear HOH- *-NN structure with an interaction energy of 7.3 kJ mol-l and a planar HzO* - *Nz complex, stabilized by 4.4 kJ mol-’ and characterized as a saddle point on the potential energy surface. These values coincide almost exactly with our dE values given in Table 3. Similarly, Murto and Ovaska obtained interaction energies of 6.8 and 4.9 kJ mold1 respectively for the linear and planar O-bonded methanol - - *nitrogen complexes, which values reduced to 4.1 and 2.3 kJ mol-l respectively after correction for BSSE [29]. Again, these energies are very similar to our dE and dE’ values for the water. **nitrogen complexes (see Table 3). It must be accepted, therefore, that the linear complex is the most stable water- - *nitrogen structure. We find that, after correcting for BSSE, the water- - -nitrogen energies, particularly those of the non-hydrogen bonded isomers, reduce to almost negligible proportions. This is to be expected for a very weak interaction, and is part of the justification for the widespread use of nitrogen as a matrix gas in matrix isolation spectroscopy. In the case of the neon and argon complexes, the interactions are so weak that correction for BSSE forces the interactions into the repulsive regime. Losonczy et al. [ 321, however, have found that the HOH- - -Ne and HOH- -. Ar complexes are stabilized, by 0.71 and 0.08 kJ mol-’ respectively, in the absence of BSSE. This illustrates how necessary it is to correct for BSSE in calculations of this type. The water* * - neon interaction energy rises dramatically, to 24.12 kJ mol-I, when Ne* ( 2p53s, ‘p3P) interacts with water along the water Cz axis [33]. However, under the conditions of our calculations, all four water- - - noble gas complexes depend on the neglect of BSSE for their attraction.

Wavenumbers - intramolecular modes

In comparing our calculated complex wavenumbers (Tables 5-7) with those of the water monomer ( v3 4110, Y, 3928 and Y, 1812 cm-’ [ 7]), it is convenient to divide the complexes into a hydrogen bonded group and a van der Waals’ group, although, in view of the weak interactions involved in all seven cases, this distinction may be over-rigorous. Nevertheless, it is based on the reduction in the extent of coupling between the water OH-stretching modes as the symmetry of the water molecule is lowered from C,, to C,. The non-equivalence of the two hydrogen atoms in the C, complexes is confirmed by their different Mulliken charges, as calculated by GAUSSIAN-76. The assignments of the normal modes to “Y(OH) (bonded)” and “Y(OH) (non-bonded)” (see Tables 5-7), however, are only approximate descriptions, as the graphical representations of the normal coordinates, derived as described earlier [ 8 1, show extensive involvement of both OH bonds in all OH-stretching modes (e.g. see Fig. 1). For the three linear OH . *X hydrogen bonded complexes, the “bonded” OHstretching wavenumber, Y,, is compared with the root mean square (RMS) monomer wavenumber, given by [ 35 ] l

l&S=

[j(v:‘+ii;)p

(1)

where P1 and 9, are the calculated stretching wavenumbers of the water monomer [ 71. Here, pRMs= 4020 cm- ‘. The expected downward shifts from DnMs (monomer) to D2 (complex), typical of hydrogen bonded complexes [ 361, amount to - 49 (N,), - 46 (Ne) and - 76 cm-’ (Ar ), which are all fairly insignificant. The “non-bonded” OH-stretching wavenumbers of the three complexes, Y,, are relatively constant. The HOH-bending wavenumber ( ZJ,for HOH- - *NN and v3 for HOH- *Ne and HOH* * lAr ), which is expected to increase on hydrogen bonding [ 36 1, actually decreases on complexation, with shifts of -91 (N2), - 105 (Ne) and - 141 cm-’ (Ar). For the four van der Waals’ complexes, in which the C,, symmetry of the water molecules is preserved, comparisons of the complex water wavenumbers directly with the corresponding wavenumbers of the water monomer [ 71 reveal no differences greater than 33 cm-l. These wavenumber data are all consistent with very weak interactions, whether of the hydrogen bonding or the van der Waals type, in all seven complexes. The calculated water- * - nitrogen spectra may be compared with those determined experimentally by Andrews and Davis, who studied water isolated in argon doped with nitrogen [ 271. New bands at 3731.8,2329.3 and 1599.7 cm-‘, not present in the spectra of the samples not containing nitrogen, were assigned to the bonded OH. - lN stretching, 14N= 14Nstretching and HOH bending vibrations of a HOH ***NN complex, yielding typical calculated/ experimental wavenumber ratios of 1.06, 1.15 and 1.08 respectively. The fact l

259

that bands at 2329.3 and 2251.5 cm-‘, attributable to v(14N s14N) and Y(‘~N= 15N) respectively, were observed in matrices of different isotopic compositions, confirms the hydrogen bonded structure, as the N = N stretching modes of the two van der Waals’ complexes are predicted to have zero intensity (see also ref. 1) . Comparison of the calculated water-.. noble gas spectra with experiment would require analysis of the spectra of water isolated in nitrogen, doped with argon or neon. To our knowledge, such spectra have not yet been reported, but there is a wealth of data on water isolated in pure noble gas matrices. Bondybey and English have assigned absorptions at 3782.7 (v,) and 1598.2 cm-l ( v2) to water monomers trapped in neon matrices [ 37 3. The v1monomer band is evidently too weak to be observed at the concentrations used. These wavenumbers correspond with our calculated 4130 and 1707 cm-l (linear HOH- l.Ne species) and 4107 and 1823 cm-’ (planar O-bonded structure) (see Table 6). The calculated/experimental wavenumber ratios are 1.09 and 1.07, and 1.09 and 1.14 respectively, suggesting that the linear hydrogen bonded complex may be the preferred isomer, in keeping with the relative interaction energies uncorrected for BSSE (see Table 4). Other unassigned bands have been reported at 3748.0,3732.5, 1631.9, 1617.4 and 1608.7 cm-’ in the water monomer absorption regions [ 371, and it is possible that these are due to water molecules trapped in different orientations in the neon matrix, and that the two structures considered here are among those orientations. The spectrum of water monomers in argon matrices consists of bands at 3733 (v,), 3638 (v,) and 1590 cm-’ (v,) [38]. Our calculated water---argon complex spectra contain bands at 4111,3944 and 1671 cm-’ (linear) and 4116, 3931 and 1830 cm-l (O-bonded) (see Table 7). The corresponding calculated/ experimental wavenumber ratios are 1.10,1.08 and 1.05 (linear) and 1.10,1.08 and 1.15 (O-bonded). As in the case of the water- *neon spectra, while the OH-stretching wavenumbers are virtually indistinguishable, there is a large difference between the HOH-bending wavenumbers of the hydrogen bonded and the van der Waals bonded isomers, and it is the spectra of the linear species which agree more closely with the observed spectra [ 37,381 than those of the O-bonded complexes. l

Wavenumbers - intermolecular modes The forms of the intermolecular modes of these complexes can be considered to be derived from the translations and rotations of the molecular fragments with respect to one another. For example, the hydrogen bond stretching modes, v(H**-N), v(H**-Ne) and y(H*--Ar), and the vibrations designated as v,(O***N,), v(O*-*Ne) and v(O***Ar) are clearly the out-of-phase translations of the two monomer sub-units along the intermolecular axis; the in-plane hydrogenbondbendingvibrations6(OH.*.N),6(H...NN),6(OHo*.Ne) and

6( OH* * *Ar ) and the V,(0. *N,) mode are the in-phase rotations of the fragments about axes perpendicular to the molecular plane; and the out-of-plane hydrogen bond bending modes y(OH* * N), y(H***NN), y(OH-**Ne) and y (OH* * *Ar ) are the in-phase rotations of the monomer species about axes in the molecular plane, perpendicular to the molecular axis. The remaining intermolecular modes, described as r( OHz), w ( OHz) and tw ( OHz) are simply librations of the water molecules about their three inertial axes, against the rest of the complex. The limitations of our wavenumber computation technique are most apparent for vibrational modes governed by very low force constants, such as the intermolecular modes considered here. Thus there are four examples of our calculations predicting negative eigenvalues for certain modes. This is not unusual [8]; negative eigenvalues have been cited as evidence for a particular structure representing a transition state on the intermolecular potential energy surface [391. Since we have considered at least two distinct structures for each combination, it is natural that at least one of them might correspond to a transition state. In addition, the precision with which the low wavenumbers are calculated is probably lower than in the higher wavenumber region, and this is the likely cause of some anomalies, e.g. the y (OH* *l Ne) and v (0. **Ne) modes appearing at lower frequency than those of their Ar counterparts, contrary to expectation, based on relative atomic masses. Since very few experimental spectroscopic data exist on such intermolecular vibrations, and since such information does not provide any significant new insights into the vibrational and energetic properties of these complexes, the calculated intermolecular wavenumbers will not be discussed further. l

l

Intensities - intramolecular modes

As well as the downward OH-stretching band wavenumber shift accompanying hydrogen bond formation [ 361, an increase in the OH-stretching band intensity is also usually observed, and Huggins and Pimentel have indicated that this intensity enhancement is often a more reliable criterion of hydrogen bond formation than the wavenumber shift [40]. The changes in the OHstretching band wavenumbers in all seven complexes were all found to be within 3% of the monomer RMS wavenumber. This suggests very little perturbation of the monomer wavenumbers due to complexation, and it is to be expected that in such weak complexes the water band intensities should not change significantly either. In the three hydrogen bonded complexes the bonded OH-stretching intensities range from 8.6 (Ne) through 27 ( N2) to 71 km mol-l (Ar). The v3 and vl intensities of the water monomer are 54.2 and 3.2 km mol- ’ respectively [ 71, giving a RMS intensity of 38.4 km mol-l. The bonded OH-stretching intensity of the HOH. *NN complex has a value 70% of this RMS intensity. In the case l

261

of HOH- **Ne it was found that the OH-stretching normal coordinates more closely resembled the coupled vi and v3 modes of the water monomer (see Fig. 1), hence the “bonded” OH-stretching intensity of 8.6 km mol-’ is much closer in value to the symmetric OH-stretching monomer intensity of 3.2 km mol-I. HOH. * - Ar appears to represent one of those examples in which a redistribution of intensity seems to have taken place, as discussed earlier for the ammonia dimers [a], and as indicated by Hogan and Steele [41]. The HOHbending intensity, by analogy with those of HOH- - *NN and HOH* **Ne (where the intensities are very similar to that of the monomer), appears to be about 65% too low, while the bonded OH-stretching intensity may be too high by the same factor. This would bring the intensity more into line with the monomer RMS value. The non-bonded OH-stretching intensities are not expected to be sensitive to hydrogen bonding and seem to vary in a random way, although the intensity for HOH. - *Ne is reasonably close to the antisymmetric OH-stretching intensity of the monomer [ 71. The bending intensities, with the exception of that of HOH. *l Ar, discussed above, undergo very little change from the monomer value. The planar and perpendicular Hz00 * Nz complexes have remarkably similar intramolecular water band intensities, which are also very similar to those of the monomer. Likewise, the intensities of the H,O* *lNe and HzO- - *Ar bands are virtually indistinguishable, and the antisymmetric OH-stretching intensities are very similar to that of the monomer. The sums of the intensities of the symmetric OH-stretching and HOH-bending modes of H,O* - -Ne and H,O- *-Ar are close to the sum of the monomer intensities, although the stretching intensities are too high and the bending too low; these are clearly two other cases of anomalous intensity redistribution [8,41]. l

Intensities - intermolecular modes Again, because of the absence of experimental data on these vibrations, discussion will be confined to the trends observed among similar modes. In the

b) Fig. 1. Calculated normal modes for the OH-stretching vibrations of the hydrogen bonded HOH. - *Ne complex: (a) “bonded” OH-stretching, (b) “non-bonded” OH-stretching.

262

three hydrogen bonded complexes, the hydrogen bond stretching intensities, V(H***N),V(H**.Ne) andv(H***Ar),arealllow (4.3to&lkmmol-‘).The in-plane bending modes, S(H.0 l NN), G(OH* . l Ne) and &OH*. l Ar) are of intermediate intensity (67 to 137 km mol-‘), while the out-of-plane bending vibrations, y(OH***N), y(OH***Ne) and y(OH***Ar), are, the most intense bands in their respective spectra (229 to 306 km mol-‘). In the four van der Waals’ complexes, the intermolecular stretching modes, y,(O*..Nz),y,(0.*.N2),~(0..*Ne) andv(O**.Ar) havenegligibleintensity, as do the w ( OHz) vibrations of Hz0 ***Ne and HzO***Ar. The w(OH,) intensities of planar and perpendicular HzO*.*Nz (512 and 481 km mol-’ respectively), however, are the highest in the spectra of these two species. The r ( OHz) mode intensities of all four complexes are very similar, being clustered in the range 111 to 142 km mol-‘. Atomic polar tensors

The total APTs of the water monomer, given in Table 8, were determined en route to the calculation of the monomer band intensities, and were referred to a Cartesian coordinate system in which the z axis coincided with the C, axis, with the oxygen atom in the positive direction, and the 3czplane was the molecular plane [ 7 ] (see Fig. 2a). The partitioning of the APTs into their charge, charge flux and overlap components, as described earlier [2,20], yielded the remaining columns of Table 8. In the same way, the APTs and their component tensors were calculated for the seven complexes, with the four van der Waals’ complexes in the same Cartesian frame as the monomer and the three hydrogen bonded complexes oriented with the bonded OH bond along the z axis and with the non-bonded hydrogen atom in the +x, -z quadrant, as shown in Fig. 2b. These quantities are collected in Tables 9-15. In order to compare the oxygen and hydrogen APTs of the hydrogen bonded complexes with those of the monomer, it was necessary to rotate the monomer APTs about the y axis by

“‘\;~._~ “‘1 ”

z

__________

x,7

1

/

/ “2

(Q)

(b)

Fig. 2. Cartesian coordinate systems for: (a) the water monomer; (b) the hydrogen bonded HOH***X complexes (X=N2, Ne, Ar).

-0.4635 0 0.0445

0.3524 0 -0.0869

0.1311 0 0.0445

0

HI

H2

"SeeFig. 2.

Total APT

Atom 0.0445 0 -0.5181

0 -0.0029 0.4823 0 0 0.3697

0 -0.0415 0.4823 0 0 0.1464

0 -0.9647 0

_ _

0.4017 0 0

0.4017 0 0

-0.8034 0 0

Charge

0 0.4017 0

0 0.4017 0

0 -0.6034 0

0.0259 0 0 0 0.0936 0

._ _ __ _.

_

0 0.0410 0 0 0 0 0.4017 -0.0478 0

0 -0.0669 0 0 0 0 0.4017 -0.0458 0

0 0 -0.8034

charge fhlx 0.2940 0 -0.0491

-_

_

-0.3116 0 0.0923

_ _

-0.0878 0 -0.0306

-0.0059 0.0176 0 0 0.0774 -0.0431

0.0936 0 -0.0468

Overlap - 0.0491 0 03322

._

__

0 0.0848 0.0807 0 0 -0.0015

0 -0.0357 0.0607 0 0 -0.3307

0 -0.1613 0

Total atomic polar tensors, and their chargp, charge flux and overlap contributions, of the water monomer, rotated into the cartesian coordinate system of the hydrogen bonded complexes” (units are e)

TABLE 17

264

124.38”,which is equivalent to bringing the monomer H, atom in Fig. 2 into coincidence with the z axis [ 201. (The value of the monomer HOH bond angle necessary to determine this angle of rotation was taken from ref. 7.) This rotation transforms the monomer APTs into the coordinate system of the complex. The rotated monomer APTs and their component tensors are reported in Table 17. The APTs of the van der Waals’ complexes, of course, require no such rotation. Comparison of the APTs of the three hydrogen bonded complexes (Tables 9,12 and 14) with the rotated monomer APTs (Table 17) indicates that the only major changes that occur in these quantities are in the P,, element of the bonded hydrogen atom. This is the element representing the change in the z component of the molecular dipole moment with the displacement of the bonded hydrogen atom along the z axis, or in the direction of the hydrogen bond, and this finding is consistent with our previous conclusions regarding the water [ 2 ] and ammonia dimers [ 201 and the water - - carbon monoxide complex [ 21. Further examination of Tables 9,12,14 and 17reveals that the changes in the Pz elements are located chiefly in the charge flux components, again as found previously [ 2,201. This appears to be a typical situation for a hydrogen bonded structure. The total APTs of the bonded N, Ne and Ar atoms in the three hydrogen bonded complexes are characterized by particularly low values, except for the minor exceptions of P,“, and Pg, indicating that very little intermolecular charge transfer occurs as a result of complex formation. This provides further evidence for the weakness of the intermolecular bonding in these complexes. In the case of the four van der Waals’ complexes, comparison of the total APTs of the atoms of the water molecules (Tables 10,11,13and 15) with those of the unrotated water monomer (Table 8) shows very minor changes in every case. This is also true of the various components of the APTs, of course, and it emphasizes the fundamental differences between the weakly hydrogen bonded complexes on the one hand and the van der Waals’ aggregates on the other. The conclusion regarding the changes in OH-stretching band intensity consequent upon hydrogen bond formation is that such changes are due mainly to the changes in the charge flux tensor elements of the bonded hydrogen atoms, while in the case of the van der Waals’ complexes negligible changes in the total APTs are manifested in no significant changes in the OH-stretching intensities being apparent. ACKNOWLEDGEMENTS

One of us (T. A. F. ) acknowledges financial support from the Foundation for Research Development of the South African Council for Scientific and Industrial Research, and the University Senate Research Committee. We are grateful for stimulating discussions with Professor J. C. A. Boeyens..

265 REFERENCES

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