proton affinities of maingroup-element hydrides and noble gases: trends across the periodic table,...

Proton Affinities of Maingroup-Element Hydrides and

Noble Gases: Trends Across the Periodic Table,

Structural Effects, and DFT Validation

MARCEL SWART, ERNST ROSLER, F. MATTHIAS BICKELHAUPT

Theoretische Chemie, Scheikundig Laboratorium der Vrije Universiteit, De Boelelaan 1083,NL-1081 HV Amsterdam, The Netherlands

Received 10 February 2006; Accepted 12 February 2006DOI 10.1002/jcc.20431

Published online in Wiley InterScience (www.interscience.wiley.com).

Abstract: We have carried out an extensive exploration of the gas-phase basicity of archetypal neutral bases

across the periodic system using the generalized gradient approximation (GGA) of the density functional theory

(DFT) at BP86/QZ4P//BP86/TZ2P. First, we validate DFT as a reliable tool for computing proton affinities and

related thermochemical quantities: BP86/QZ4P//BP86/TZ2P is shown to yield a mean absolute deviation of 2.0

kcal/mol for the proton affinity at 298 K with respect to experiment, and 1.2 kcal/mol with high-level ab initiobenchmark data. The main purpose of this work is to provide the proton affinities (and corresponding entropies) at

298 K of the neutral bases constituted by all maingroup-element hydrides of groups 15–17 and the noble gases, that

is, group 18, and periods 1–6. We have also studied the effect of step-wise methylation of the protophilic center of

the second- and third-period bases.

q 2006 Wiley Periodicals, Inc. J Comput Chem 27: 1486–1493, 2006

Key words: bases; basicity; cationic acids; density functional calculations; periodic table; proton affinities; thermo-

chemistry

Introduction

Designing new (and optimizing existing) approaches and routes

in organic synthesis requires knowledge of the thermochemistry

involved in the targeted reactions. In this context, the proton af-

finity (PA) of a reactant or intermediate species B often plays

an important role. This thermochemical quantity is defined as

the enthalpy change associated with dissociation of the conju-

gate acid [eq. (1)]:1–8

BHþ ! Bþ H� : �H ¼ PA: (1)

Overall reaction enthalpies and reaction barriers (and thus reac-

tion rates) are related to the PA, as soon as proton transfer

occurs somewhere along the cascade of elementary steps of a

reaction mechanism. This is often the case, as proton transfer is

ubiquitous in organic reaction mechanisms, either as simple pro-

ton transfer (PT) or as part of a more complex chemical trans-

formation, for example, base-induced elimination reactions that

may compete with nucleophilic substitution.9–13

Here, we focus on the proton affinities of the maingroup-ele-

ment hydrides and noble gases in the gas phase. Gas-phase pro-

ton affinities are obviously directly applicable to gas-phase

chemistry,3–6 but they are also relevant for chemistry occurring

in the condensed phase.1,14 On one hand, they reveal the intrin-

sic basicity of the protophilic species involved and, thus, they

shed light on how this property is affected by the solvent. On

the other hand, they can serve as a universal, solvent-independ-

ent framework of reference, from which the actual basicity of a

species in solution can be obtained through an (empirical) cor-

rection for the particular solvent under consideration.15–17 Ex-

perimental gas-phase proton affinities for neutral organic bases

have been reported,3–6 and corrected based on new experiments

or quantum-chemical studies.18 Unfortunately, only few bench-

mark CCSD(T) studies have been reported, and even less infor-

mation is available for bases with a heavier, that is, third and

higher period atom as protophilic center.4,7,8

The present study has three purposes. First, we wish to evaluate

the performance of density functional theory (DFT).19–26 This is

done by computing the 298 K reaction enthalpies DacidH298 of reac-

tion 1 (i.e., PA values) for a test set of 12 bases for which experi-

mental or highly accurate benchmark data are available.27–48 It is

anticipated here that the well-known BP8649,50 functional performs

very reasonably for our neutral model bases, similar to our previous

findings for anionic bases.51 Second, we aim at setting up a com-

Correspondence to: F. M. Bickelhaupt; e-mail: [email protected]

Contract/grant sponsor: The Netherlands Organization for Scientific

Research (NWO-CW).

This article contains Supplementary Material available at http://www.

interscience.wiley.com/jpages/0192-8651/suppmat

q 2006 Wiley Periodicals, Inc.

plete description of the proton affinities of the bases XHn consti-

tuted by all archetypal maingroup-element hydrides of groups

15–17 and the noble gases, that is, group 18, and periods 1–6.

Third, we have studied the influence of step-wise methylation of

the protophilic center X in species (CH3)mXHn–m (for periods 2

and 3), for example, PH3, CH3PH2, (CH3)2PH, (CH3)3P. In addi-

tion to our computed BP86/QZ4P//BP86/TZ2P values for the

298 K reaction enthalpy DacidH298 of all conjugate acids BHþ in

eq. (1) (that is, the proton affinity PA of all bases B ¼ XHn), we

also report the corresponding 298 K reaction entropies (DacidS298,provided as �TDacidS298 values), and 298 K reaction free ener-

gies (DacidG298).

Note that the series of in total 42 bases investigated in this

study covers large parts of the periodic system as well as a

number of important structural themes occurring in organic

chemistry. To the best of our knowledge, this series of bases

has never before been studied, in its full range, consistently with

one and the same method, either experimentally or theoretically.

We anticipate that the very consistency of our approach makes

our data particularly suitable for inferring accurate trends in

thermochemistry across the periodic system.

Methods

All calculations were performed with the Amsterdam Density

Functional (ADF) program developed by Baerends and

others.52,53 Molecular orbitals (MOs) were expanded using two

different large, uncontracted sets of Slater-type orbitals: TZ2P

and QZ4P.54 The TZ2P basis is of triple-� quality, augmented by

two sets of polarization functions (2p and 3d on H; d and f onheavy atoms). The QZ4P basis, which contains additional diffuse

functions, is of quadruple-� quality, augmented by four sets of

polarization functions (two 2p and two 3d sets on H; two d and

two f sets on heavy atoms). Core electrons (e.g., 1s for second pe-

riod, 1s2s2p for the third period, 1s2s2p3s3p for the fourth pe-

riod, 1s2s2p3s3p3d4s4p for the fifth period, 1s2s2p3s3p3d4s4p4dfor the sixth period) were treated by the frozen core (FC) approx-

imation.53 An auxiliary set of s, p, d, f, and g STOs was used to

fit the molecular density and to represent the Coulomb and

exchange potentials accurately in each SCF cycle. Scalar relativ-

istic corrections were included self-consistently using the Zeroth

Order Regular Approximation (ZORA).55

Energies and gradients were calculated using the local den-

sity approximation (LDA; Slater exchange and VWN56 correla-

tion) with nonlocal corrections49,50 due to Becke (exchange) and

Perdew (correlation) added self-consistently. This is the BP86

density functional, which is one of the three best DFT function-

als for the accuracy of geometries,57 with an estimated unsigned

error of 0.009 A in combination with the TZ2P basis set. In a

previous study51 on the proton affinity of anionic species, we

compared the energies of a range of other DFT functionals, to

estimate the influence of the choice of DFT functional. These

functionals included the Local Density Approximation (LDA),

Generalized Gradient Approximations (GGAs), meta-GGA and

hybrid functionals. The BP86 functional emerged as one of the

best functionals. The restricted and unrestricted formalisms were

used for closed-shell and open-shell species, respectively.

Table 1. Computeda–e and Experimentalf–h Proton Affinities at 298K PA (in kcal/mol)

of Neutral Bases.

Base BP86/TZ2Pa BP86/QZ4Pb CCSD(T)c–e Expt.f–h

NH3 202.6 203.2 204.1c 204.0f

CH2CO 192.2 193.1 196.0d 195.9g 6 0.7

(CH3)2CCH2 196.1 198.3 — 192.9h 6 0.4

CH3CHO 184.6 185.9 — 183.7f 6 0.4

CH3CHCH2 183.4 184.1 — 179.6f 6 0.7

CH2O 168.0 169.3 — 170.4f 6 0.3

H2S 170.1 170.6 — 168.5f 6 1.3

H2O 163.1 164.5 165.1d 165.2f 6 0.7

CH2CH2 163.5 164.3 — 162.6f 6 0.4

CO 141.9 143.3 141.8e 142.0f 6 0.7

CO2 127.6 129.1 129.3e 129.2f 6 0.5

N2 119.4 119.4 118.2e 118.0f

MAD/MD wrt CCSD(T)i 1.7/1.3 1.2/0.3 — 0.1/0.0

MAD/MD wrt exp.j 1.9/0.0 2.0/1.1 0.1/0.0 —

aThis work: BP86/TZ2P energies with ZPE correction at BP86/TZ2P.bThis work: BP86/QZ4P//BP86/TZ2P energies with ZPE correction at BP86/TZ2P.cCCSD(T)/aug-cc-pV5Z from ref. 61.dCCSD(T)/6-311Gþþ(3df,2pd)//MP2/6-31G (d, p) from ref. 59.eCCSD(T)/[5s4p3d2f]//MP2/[5s4p3d2f] from ref. 60.ffrom ref. 3.gfrom ref. 62.hfrom ref. 63.iMean absolute deviation (MAD)/mean deviation (MD) relative to CCSD(T).jMean absolute deviation (MAD)/mean deviation (MD) relative to experiment.

1487Proton Affinities

Journal of Computational Chemistry DOI 10.1002/jcc

Geometries were optimized using analytical gradient tech-

niques until the maximum gradient component was less than

1.0�10�4 atomic units (see Table S1 in the Supporting Informa-

tion). Vibrational frequencies were obtained through numerical

differentiation of the analytical gradients.53 Enthalpies at 298.15 K

and 1 atmosphere (DH298) were calculated from electronic bond

energies (DE) and vibrational frequencies using standard thermo-

chemistry relations for an ideal gas,58 according to eq. (2):

�H298 ¼ �Etrans;298 þ�Erot;298 þ�Evib;0 þ�ð�Evib;0Þ298þ�ðpVÞ: ð2Þ

Here, DEtrans,298, DErot,298, and DEvib,0 are the differences

between the reactant (i.e., BHþ, the conjugate acid) and prod-

ucts (i.e., B þ Hþ, the neutral base and the proton) in transla-

tional, rotational and zero point vibrational energy, respectively;

D(DEvib,0)298 is the change in the vibrational energy difference

as one goes from 0 to 298.15 K. The vibrational energy correc-

tions are based on our frequency calculations. The molar work

term D(pV) is (Dn)RT; Dn ¼ þ1 for one reactant BHþ dissociat-

ing to two products (B and Hþ). Thermal corrections for the

electronic energy are neglected.

Results and Discussion

Benchmarking and Validation of DFT

We begin with an exploration of the performance of our density

functional theory. To this end, we have computed the proton affinity

at 298 K (PA ¼ DacidH298) for a series of 12 neutral bases B, shown

in Table1, for which experimental data and ab initio theoretical

benchmark values are available. This series of bases covers PA val-

ues ranging from 118.0 for N2 through 204.0 kcal/mol for NH3 (see

Table 1, expt.). Table 1 compares our results for BP86, which

emerges as a good functional (vide infra), with CCSD(T)/6-

311þþG(3df,2p)//MP2/6-31G(d,p)59, CCSD(T)/[5s4p3d2f]//MP2/

[5s4p3d2f]60, and CCSD(T)/aug-cc-pV5Z61 benchmark calculations

as well as with experiment.3,18,62,63 As can be seen in Table 1, the

CCSD(T) benchmark data, where available, and experimental PA

values agree excellently, showing deviations of only 0.1 kcal/mol.

First, we have explored with BP86 the effect of carrying out

the DFT calculations with the TZ2P versus the very large QZ4P

basis set (see previous section). Already with the ‘‘smaller’’

TZ2P basis, that is, at BP86/TZ2P, we find PA values in reason-

able agreement with the CCSD(T) benchmark values, showing a

mean absolute deviation (MAD) value of 1.7 kcal/mol with

respect to the latter (see Table 1). Further improvements can be

achieved by going from the TZ2P to the QZ4P basis set. The

QZ4P basis set is not only more flexible and better polarized, it

also contains more compact functions (and also more diffuse

functions). One may therefore expect an improved description

of reaction 1 in which we go from a species XHnþ1þ involving

a formally cationic central atom X to a species XHn in which

the central atom has become formally neutral (and, likewise, an

initially, formally neutral H has become a proton). Thus, single-

point calculations were done at BP86/QZ4P using the BP86/

TZ2P geometries and enthalpy corrections. At this level of

theory, that is, at BP86/QZ4P//BP86/TZ2P, we achieve a signifi-

cant improvement of the MAD, which drops to 1.2 kcal/mol rel-

Table 2. Thermodynamic acidity properties (in kcal/mol) for neutral bases MemHn–mX at T ¼ 298 K.a

Group 15 Group 16 Group 17 Group 18

Base DH �TDS DG Base DH �TDS DG Base DH �TDS DG Base DH �TDS DG

Period 1

He 45.2 �5.9 39.3

Period 2

NH3 203.2 �8.2 195.0 OH2 164.5 �7.4 157.1 FH 117.4 �6.5 110.9 Ne 52.7 �5.6 47.1

MeNH2 214.0 �8.2 205.7 MeOH 179.2 �7.3 171.9 MeF 143.0 �5.9 137.1

Me2NH 220.5 �7.9 212.6 Me2O 188.0 �7.1 180.9

Me3N 225.0 �7.4 217.5

Period 3

PH3 185.3 �8.2 177.0 SH2 170.2 �7.5 162.7 CIH 135.9 �6.4 129.6 Ar 93.9 �5.4 88.5

MePH2 203.8 �8.2 195.6 MeSH 186.8 �7.5 179.4 MeCI 157.0 �6.1 150.9

Me2PH 217.9 �8.0 210.0 Me2S 200.4 �7.6 192.8

Me3P 228.9 �8.1 220.8

Period 4

AsH3 176.6 �8.2 168.3 SeH2 172.4 �7.5 164.9 BrH 141.9 �6.3 135.6 Kr 106.1 �5.2 100.9

Period 5

SbH3 175.4 �8.1 167.2 TeH2 178.3 �7.5 170.9 IH 151.8 �6.2 145.5 Xe 122.2 �5.1 117.1

Period 6

BiH3 161.4 �8.1 153.3 PoH2 180.9 �7.4 173.5 AtH 156.1 �6.2 150.0 Rn 129.2 �5.0 124.2

aComputed at BP86/QZ4P//BP86/TZ2P for the reaction MemHn–mXHþ ? H� þ MemHn–mX with n ¼ 3, 2, 1 and 0

for groups 15, 16, 17, and 18, respectively.

1488 Swart, Rosler, and Bickelhaupt • Vol. 27, No. 13 • Journal of Computational Chemistry


ative to the CCSD(T) benchmark data (see Table 1). The MAD

relative to experimental data is slightly higher, at 2.0 kcal/mol

with the QZ4P basis and 1.9 with the TZ2P basis. Furthermore,

BP86/QZ4P//BP86/TZ2P yields correct relative PA values over

the entire range of bases.

We have verified that the geometry does not differ signifi-

cantly if it is also computed with the QZ4P basis set (data not

shown). Thus, the full BP86/QZ4P//BP86/QZ4P energies differ

by less than 0.01 kcal/mol compared to the BP86/QZ4P//BP86/

TZ2P energies (tested for CH2CO).

In conclusion, BP86/QZ4P//BP86/TZ2P (with BP86/TZ2P

enthalpy corrections) emerges as a reliable approach for study-

ing trends in basicity of neutral bases in the following section.

Proton Affinities of Maingroup-Element Hydrides

Using the BP86/QZ4P//BP86/TZ2P approach (see previous sec-

tion), we have computed the proton affinities at 298 K (PA ¼DacidH298) and the corresponding entropies DacidS298 (provided

as �TDacidS298 values) and reaction free energies DacidG298 of

all maingroup-element hydrides of groups 15–17 and the noble

gases (i.e., group 18) and periods 1–6. The results are summar-

ized in Table 2 and Figure 1.

Along the series of second-period bases, we obtain the well-

known trend of a decreasing basicity as the PA falls from 203

to 165 to 117 to 53 kcal/mol along NH3, OH2, FH, and Ne (see

Table 2 and Fig. 1, upper). A striking change occurs from group

15 to the higher groups. Descending group 15, the PA decreasesbut descending one of the other groups (16–18), the PA

increases. Interestingly, as one can see in Figure 1, upper, this

causes the trend of a monotonic decrease in basicity along the

second period (P2) and, to a lesser extent, the third and fourth

periods (P3, P4) to change into a trend for the fifth and sixth

periods (P5, P6) where the PA along a period increases from

group 15 to 16 and then decreases again along groups 16, 17

and 18. In group 15, for example, the PA decreases from 195 to

177 to 168 to 167 to 153 along NH3, PH3, AsH3, SbH3 and

BiH3, whereas in group 16, the PA increases from 157 to 163 to

165 to 171 to 174 kcal/mol along OH2, SH2, SeH2, TeH2 and

PoH2 (see Table 2).

The above trends in PA of neutral maingroup-element

hydrides XHn (Fig. 1, upper) differ from those found previously

for the anionic conjugate bases XHn�1� of the maingroup-ele-

ment hydrides51 (Fig. 1, lower): the former (XHn) show an

inversion in the trend down a group if one goes from group 15

to group 16 while in the case of the latter (XHn�1� ) the PA

always decreases down a group (for numerical results, see Table 2).

But there is also an interesting analogy between the trends of

XHn and XHn�1� , which can be clearly recognized in Figure 1:

for both, the kink in the PA trend along a period occurs if

one goes from the trivalent base (group 15 for XHn, group 14

for XHn�1� ) to the bivalent base (group 16 for XHn, group 15

for XHn�1� ), for example, from BiH3 to PoH2 (Fig. 1, upper) or

from PbH3� to BiH2

� (Fig. 1, lower). The effect is most pro-

nounced for bases with a more heavy protophilic center in

which the valence ns AO is inactive. This suggests that the

effect, that is, the sudden increase in PA from a trivalent to a

bivalent base is associated with an active np-type lone pair

becoming available.

The corresponding reaction entropies for 298 K yield a rela-

tively small (but not entirely constant) contribution �T DacidS298of �6 to �8 kcal/mol. As a consequence, the Gibbs free ener-

gies DacidG298 show the same trends as the corresponding PA

values (see Table 2).

The interaction between the base HnX and the proton upon

formation of the conjugate acid HnXHþ induces a geometrical

deformation in the base. This goes with a strengthening of the

interaction (compared to the fictious situation in which the base

would keep its original geometry), but at the expense of a geo-

metrical preparation energy that is associated with bringing the

base from its own equilibrium structure into the geometry it

eventually adopts in the conjugate acid.64 We have analyzed

how this deformation energy behaves as a component of the

overall proton bond energy �DacidE by decomposing the latter

into the aforementioned geometrical preparation energy DEprep

Figure 1. Proton affinities PA (at 298 K) of the neutral bases con-

stituted by maingroup-element hydrides of groups 14–18 and peri-

ods 1–6 (P1–P6) (upper) and of the corresponding anionic conjugate

bases of groups 14–17 and periods 2–6 (P2–6) (lower), computed at

BP86/QZ4P// BP86/TZ2P. Note the different vertical scales in the

upper and lower diagram. [Color figure can be viewed in the online

issue, which is available at www.interscience.wiley.com.]



plus the actual interaction energy DEint between the deformed

HnX fragment and the proton in HnXHþ [eq. (3)].

HnXþ Hþ ! HnXHþ : ��acidE ¼ �Eprep þ�Eint: ð3Þ

Table3 shows the results of the proton bond-energy decomposi-

tion as well as the HXH angles in the bases HnX and their con-

jugate acids HnXHþ. The deformation energy DEprep is in all

cases much (at least one order of magnitude) smaller than the

interaction energy DEint which, therefore, determines the trend

in �DacidE and thus PA. Note that for the group 18 acids, the

deformation energy of the bases is zero, of course, because

here the base is monoatomic and can thus not be deformed.

Yet, a number of interesting observations observations can be

made. In the first place, for group 17 and 16, the deformation

energies DEprep are all relatively small and, descending the

group, they decrease systematically from about one-and-a-half

to a few hundredths of a kcal/mol. The small deformation

energy in groups 17 and 16 is ascribed to the relatively small

geometrical distortion of the base upon forming the conjugate

acid as both, base and acid, have comparable HXH valence

angles. The decrease of DEprep down a period is caused by the

reduction in H��H steric repulsion as the central atom X

becomes larger (see, e.g., refs. 65 and 66), as a consequence of

which the additional hydrogen atom in the acid can be

accomodated with a still smaller extent of deformation (see Ta-

ble 3). Most strikingly, however, the trend is reversed if one

descends in group 15. Now, instead of decreasing, the defor-

mation energy DEprep of the base increases from 0.76 up to

17.42 kcal/mol (Table 3). The explanation for this is that the

valence angles of the isolated base still decrease down the pe-

riod, from 106.448 to 89.888, as there is less and less H��H

repulsion. However, all conjugate acids of group 15 have a tet-

rahedral geometry with a constant HXH angle of 109.478.

Thus, down group 15, the difference between the HXH angle

of base HnX and conjugate acid HnXHþ increases and, conse-

quently, the extent of deformation for the HnX fragment in the

acid increases.

Methyl Substituent Effects

Finally, we have studied the effect on the PA of stepwise re-

placing all hydrogen atoms in second- and third-period neutral

bases XHn by methyl substituents, that is, by stepwise increas-

ing m from 0 to n in MemHn–mX (n ¼ 3, 2, 1, and 0 for group

15, 16, 17, and 18, respectively). The results are collected in

Table4. The PA increases with the number of methyl substitu-

ents for both second- and third-period neutral bases. For exam-

ple, along NH3, MeNH2, Me2NH, and Me3N, the PA increases

from 203 to 214 to 221 to 225 kcal/mol, which is in excellent

agreement with experimental gas-phase data of 204, 215, 222,

and 227 kcal/mol.3 In fact, for the six main group elements that

we studied, we find a mean absolute deviation of 0.7 kcal/mol

between theory and experiment for the PA change associated

with methyl substitution.

The above finding that methyl substitution increases the PA

of both second- and third-period maingroup-element hydrides

XHn contrasts with the behavior of their anionic conjugate bases

XHn�1� .51 In the case of the latter, the PA also increases for

third-period anionic bases but it decreases for the second-period.

Interestingly, the reason for this is not that a methyl group sta-

bilizes second-period anionic bases and destabilizes the third-pe-

riod anionic bases. In fact, the introduction of methyl groups

destabilizes in all cases both the base and the conjugate acid.

The opposite trends in basicity of the anionic conjugate bases

XHn�1� of the maingroup-element hydrides originate from the

fact that a second-period base is destabilized less than its corre-

sponding conjugate acid whereas a third-period base is destabi-lized more than its conjugate acid. This behavior is reminiscent

Table 3. Decomposition of Proton Bonding Energy �DacidE (in kcal/mol) of Cationic Acids HnXHþ, and

HXH Angles of HnX and HnXHþ (in deg).a

Period

Group 15 Group 16 Group 17 Group 18

Acid DEprep DEint �DacidE Acid DEprep DEint �DacidE Acid DEprep DEint �DacidE Acid DEprep DEint �DacidE

P1 HeH 0.0 �48.70 �48.70

P2 NH4� 0.76 �211.86 �211.10 OH3

þ 1.70 �172.76 �171.06 FH2� 1.48 �123.63 �122.15 NeH� 0.0 �55.65 �55.65

P3 PH4� 12.37 �202.95 �190.58 SH3

� 0.64 �175.85 �175.21 CIH2� 0.67 �140.52 �139.85 ArH� 0.0 �96.67 �96.67

P4 AsH4� 14.84 �196.37 �181.53 SeH3

� 0.11 �176.98 �176.87 BrH2� 0.23 �145.57 �145.34 KrH� 0.0 �108.60 �108.60

P5 SbH4� 15.34 �194.94 �179.60 TeH3

� 0.05 �182.24 �182.19 IH2� 0.10 �154.88 �154.78 XeHþ 0.0 �124.41 �124.41

P6 BiH4� 17.42 �182.57 �165.15 PoH3

� 0.02 �184.53 �184.51 AtH2� 0.07 �159.01 �158.94 RnH� 0.0 �131.31 �131.31

ffHXH XH3 XH4þ ffHXH XH2 XH3

þ

P2 NH4� 106.44 109.47 OH3

� 104.27 112.28

P3 PH4� 92.44 109.47 SH3

� 91.50 93.04

P4 AsH4� 90.93 109.47 SeH3

� 89.65 90.77

P5 SbH4� 90.71 109.47 TeH3

� 89.81 90.67

P6 BiH4� 89.88 109.47 PoH3

� 89.20 89.52

aSee eq. three. Computed at BP86/QZ4P//BP86/TZ2P for the reaction Hþ þ HnX ? HnXHþ with n ¼ 3, 2, 1, and

0 for groups 15, 16, 17, and 18, respectively.



of the situation of the halomethyl anions CH2X�, the PA of

which decreases along X ¼ F, Cl, Br, I. Very recently,67 we

have shown that this is not because of increasing �-stabilizationof CH2X

� by X. Rather, the latter continuously decreases alongthe series but more slowly so than the �-stabilization of the con-jugate acid CH3X.

To trace the origin of the methyl-substituent effects on the PA

of the present, neutral model bases, we have decomposed the pro-

ton-affinity energy DacidE, associated with acid-dissociation of the

cationic conjugate acid MemHn–mXHþ, into three partial reactions,

as shown in the thermochemical cycle of Scheme 1.

The first step, which is associated with an energy change

�DEC(m), is dissociation of all substituents of the cationic, con-

jugate acid MemHn–mXHþ (but not the acidic proton) to form

the n-fold cationic radical XHþn� (see Scheme 1, m ¼ number

of methyl substituents). The energy DEC is the stabilization of

the protophilic center X in the cationic conjugate acid MemHn–m

XHþ by all substituents, that is, the interaction with m methyl

groups (Me) and n hydrogen atoms (H). Next, the unsubstituted

acid XHþn� is dissociated into Xn� þ Hþ (see Scheme 1). The

corresponding reaction energy is the proton-affinity energy

DacidE of the neutral base Xn�. The third and last step, which is

associated with an energy change DEN0(m), is addition of all

substituents to the protophilic center Xn� to form the base

MemHn–mX (see Scheme 1, m ¼ number of methyl substituents).

The energy DEN0 is the stabilization of the protophilic center X

in the neutral base MemHn–mX by all substituents, that is, the

interaction with m methyl groups (Me) and n–m hydrogen atoms

(H). The computed proton-affinity energies DacidE, DEC and

DEN0 values are collected in Table 4.

The relationship between the proton-affinity energy DacidE(MemHn–mX) of the neutral base and the other energy terms of

the thermochemical cycle of Scheme 1 is summarized in eq. (4)

(m ¼ number of methyl substituents):

�acidEðMemHn�mXÞ ¼ �acidEðXn�Þ þ�EN0 ðmÞ ��ECðmÞ: (4)

Thus, the proton-affinity energy DacidE(MemHn–mX) of the base

MemHn–mX is determined by the proton-affinity energy

Table 4. Analysis of the Methyl-Substituent Effect on PA Energies DacidE (in kcal/mol) in Terms

of the Partial Reactions in Scheme 1.a

Base DEC DEN DacidE Base DEC DEN DEacidE

N triradical 85.25 P triradical 116.68

NH3 �434.06 �308.21 211.10 PH3 �321.42 �247.52 190.58

MeNH2 �418.79 �282.10 221.94 MePH2 �325.06 �232.78 208.96

Me2NH �402.68 �259.21 228.72 Me2PH �326.33 �219.87 223.14

Me3N �385.44 �237.28 233.41 Me3P �325.73 �208.22 234.19

O diradical 120.23 S diradical 162.95

OH2 �289.36 �238.53 171.06 SH2 �199.01 �186.75 175.21

MeOH �275.10 �209.45 185.88 MeSH �196.53 �167.74 191.74

Me2O �258.41 �183.61 195.03 Me2S �192.44 �149.97 205.42

F radical 85.21 Cl radical 128.32

FH �181.31 �144.37 122.15 ClH �120.05 �108.52 139.85

MeF �179.41 �116.69 147.93 MeCI �119.49 �86.70 161.11

aComputed at BP86/QZ4P//BP86/TZ2P. See also Figure 2.

Scheme 1. Relationship between PA values and methyl substituent

effect (see Table 4). [Color figure can be viewed in the online issue,

which is available at www.interscience.wiley.com.]

Figure 2. Effect of methyl substitution DDE on the energy DEN0(X)

of the maingroup-element hydrides MemHn–mX and on the energy

DEC(X) of the corresponding cationic conjugate acids MemHn–mXHþ

relative to the unsubstituted species (see Scheme 1), computed at

BP86/QZ4P//BP86/TZ2P (see Table 4). [Color figure can be viewed

in the online issue, which is available at www.interscience.wiley.com.]



DacidE(Xn�) of the neutral, unsubstituted, and deprotonated proto-

philic center Xn� plus the difference in stabilization DEN0(m) of

Xn� in the base MemHn–mX and the stabilization DEC(m) of

XHþn� in MemHn–mXHþ by m methyl (Me) and n hydrogen sub-

stituents (H)n�. The methyl-substituent effect on the proton-affin-

ity energy, that is, the change DDacidE(m) in this value if one

goes from 0 to m methyl substituents, therefore depends not

only on the change DEN0(m) � DEN0(0) in stabilization of the

neutral base but also on the change DEC(m) � DEC(0) in stabi-lization of the cationic conjugate acid.

This is the clue to understanding the origin of the methyl-

substituent effects on the PA of second- and third-period bases.

In Figure 2, we have plotted the changes in stabilization by the

substituents DDEN0 ¼ DEN0(m) � DEN0(0) and DDEC ¼ DEC(m)� DEC(0) for the second- and third-period bases MemHn–mX

and their conjugate acids MemHn–mXHþ. Now it is clear that

introducing a methyl substituent, that is, replacing a hydrogen

by the sterically more demanding methyl group, leads consis-

tently in almost all cases to a destabilization of the system. The

only exception is observed for the protonated phosphines, where

methyl substitution leads to a stabilization. However, more rele-

vant for the increase in the PA of second- and third-period bases

is that a methyl group destabilizes the neutral base more than its

corresponding cationic conjugate acid.

Conclusions

The Density Functional Theory emerges from our exploration of

42 model systems as a sound and computationally efficient alter-

native to highly correlated ab initio methods for computing pro-

ton affinities and related thermochemical quantities of neutral

bases across the periodic table. The BP86/QZ4P//BP86/TZ2P

approach achieves a mean absolute deviation of 1.2 kcal/mol for

the proton affinity at 298 K (DacidH298) with respect to high-

level ab initio CCSD(T) benchmark data, and of 2.0 kcal/mol

with experimental data. This makes us recommend the above

BP86 approach for obtaining accurate proton affinities of or-

ganic and inorganic species that either escape direct experimen-

tal observation and/or are computationally too demanding for

highly correlated ab initio methods such as CCSD(T).

The proton affinity along the archetypal second-period main-

group-element hydrides NH3, OH2, FH, and Ne decreases as va-

lence 2p AOs of the protophilic atom become more compact

and stable. This well-known trend changes if one descends in

the periodic table to higher periods. The proton affinity of the

maingroup-element hydrides XHn decreases down group 15, but

it increases down groups 16–18. This causes the proton affin-

ities along fifth- and higher period bases to first increase from

group 15 to group 16 and then to decrease again up to group

18. A similar behavior was previously found for the anionic

conjugate bases XHn�1� of the maingroup-element hydrides. In

both cases, the effect is most pronounced for the heavier ele-

ments, and it always occurs going from the trivalent base (group

15 for XHn, group 14 for XHn�1� ) to the bivalent base (group 16

for XHn, group 15 for XHn�1� ).

Introducing methyl substituents at the protophilic center has

the same effect on second-period and third-period neutral main-

group-element hydrides: both become more basic (e.g., along

PH3, MePH2, Me2PH, and Me3P), which concurs with experi-

mental data. The origin of this trend is that methyl substituents

destabilize the neutral maingroup-element hydride XHn morethan its cationic conjugate acid XHnþ1

þ .

Supporting Information

Cartesian coordinates of all species occurring in this study.

Acknowledgments

We thank Prof. Dr. N. M. M. Nibbering for helpful discussions.

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