Chemical Physics 276 (2002) 45±68
www.elsevier.com/locate/chemphys
Water adsorption and hydrolysis in the Si2O4, P2O5 and
P4O10 systems ± essential roles of the phosphate
system in biosynthesis
J.R. Tobias Johnson a,*, Itai Panas b
b
a
Department of Chemistry, Inorganic Chemistry, Goteborg University, S-412 96 Goteborg, Sweden
Department of Inorganic Environmental Chemistry, Chalmers University of Technology, S-412 96 Goteborg, Sweden
Received 9 July 2001; in ®nal form 24 October 2001
Abstract
Successive water addition to the mononuclear species SiO2 …g† and PO2 …OH†…g†, as well as the corresponding binuclear Si2 O4 …g† and P2 O5 …g† molecules, is studied by means of density functional theory. Hydrolysis of
…HO†3 SiOSi…OH†3 …g† is found to be slightly endothermic, and only an asymmetric energy minimum is found for
this silicic acid dimer. Four stable conformations are determined for the pyrophosphoric acid system
…HO†2 OPOPO…OH†2 …g†. Depending on the choice of reference structure and basis set, the hydrolysis energetics ranges
from 14±26 kJ/mol exothermic to 3±7 kJ/mol endothermic. In general, the hydrolysis reaction is best described as a near
zero-energy process. Signi®cant di€erences in the water chemistry of the ®nal monomeric products, Si…OH†4 …g† and
PO…OH†3 …g†, appear in the ®rst solvation shell. Connecting the P±OH and P@O groups by water bridges results in a
greater tendency for proton delocalization in PO…OH†3 …g†, than is observed when water is used to connect two Si±OH
groups in Si…OH†4 …g†. Taking the properties of pyrophosphoric acid as model for the P±O±P bridge in adenosine
triphosphate (ATP), the results of the present study support the notion that this molecule and its hydrolysis products
provide a nano-scale bu€er, which is essential for sustaining biosynthesis by controlling the proton and water activities. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction
Silicon dioxide (SiO2 (s), silica) and phosphorus
pentoxide (P2 O5 (s)) display intricate and important chemical behaviors with water. A common
denominator for both groups comprises the hy-
*
Corresponding author.
E-mail address: [email protected] (J.R.T.
Johnson).
drolyzed species, silicates and phosphates, of
which particularly the former belongs to the most
important and complex among all commercial
bulk chemicals. Silica alone is known to have as
many as 22 di€erent phases [1], a majority of which
base their structures on a SiO4 tetrahedron building block. Still, there exists also a six-coordinated
high-pressure phase of SiO2 (coesite). The origin of
the multitude of phases is found in the varied arrangements and connectivities of the silica tetrahedra in the bulk. Many silicates contain chains or
0301-0104/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 3 0 1 - 0 1 0 4 ( 0 1 ) 0 0 5 5 1 - 1
46
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
sheets of such tetrahedra, which are interconnected
through Si±O±Si bridges.
The industrially most used form of phosphorous is orthophosphoric acid, OP…OH†3 or equivalently H3 PO4 . One desired quality of this acid
comprises its capacity to bu€er solutions at very
di€erent pH values (from strongly alkaline to
acidic) [1]. Another important reason for the great
applicability of phosphates originates from their
role in biochemistry, e.g., in teeth and bones, as
well as in the essential molecules adenosine triphosphate (ATP) and DNA. Thus many fertilizers
and nutrients have phosphates as main components. Their chemical role in the cell is to participate in hydrolysis and condensation reactions.
One crucial feature of the biochemical molecule
ATP is associated with the release of a formal
energy equivalent when P±O±P or P±O±C bridges
are hydrolyzed. This ``energy release'' has been
argued to drive biosynthesis. In its most naive
form, the exothermicity of one chemical process is
suggested to drive a second reaction in the wanted
direction [2]. This scenario must be deemed exceedingly complicated, as it involves exact and
quantitative intermolecular energy transfer. Here,
support is presented for the signi®cantly simpler
understanding of the biophosphate system constituting a ``micro-bu€er'', which controls the detailed thermodynamic conditions, i.e., the proton
and water activities, in the immediate vicinity of
the reaction site, thus determining the conditions
for biosynthesis.
Acknowledging the similarities in the water
chemistry of the phosphates and silicates, it becomes interesting to learn of detailed similarities
and di€erences in their water chemistry by employing quantum chemical techniques. A comprehensive understanding of similarities and in the
water chemistry among the oxides of the 3p, 4p
and 3d elements is sought. Thus, the present study
is bracketed by two parallel investigations on the
water chemistry of the 3p oxides. The ®rst study
concentrated on the binuclear hydroxides or a
hydrated complexes of the AlO(OH) and Al2 O3
systems [3]. The second investigation is on the
water chemistry of the highly covalent SO2 …OH†2 ,
ClO3 …OH† and ArO4 systems and the dehydrated
binuclear species of the former two [4].
The principles for the present investigation were
outlined in two previous works on the water
chemistry of some transition metal oxides [5,6].
Two types of reactions are considered. The ®rst
type comprises water addition to mononuclear
species, which results either in the formation of
hydrated complexes, or the conversion of an M@O
group into a corresponding dihydroxide unit. The
second type comprises degradation of a polynuclear oxide species by successive hydrolytic cleavage of M±O±M bridges. Here, M is taken to be Si
or P, and both mononuclear and binuclear species,
as well as the conversion between the two, are
described.
Results are presented for the reactions:
SiO2 …g† ‡ H2 O…g† ! SiO2 H2 O…g†
SiO2 H2 O…g† ! SiO…OH†2 …g†
SiO…OH†2 …g† ‡ H2 O…g† ! SiO…OH†2 H2 O…g†
SiO…OH†2 H2 O…g† ! Si…OH†4 …g†
Si…OH†4 …g† ‡ nH2 O…g† ! Si…OH†4 …H2 O†n …g†
…R1†
Si2 O4 …g† ‡ H2 O…g† ! Si2 O3 …OH†2 …g†
Si2 O3 …OH†2 …g† ‡ H2 O…g† ! Si2 O2 …OH†4 …g†
Si2 O2 …OH†4 …g† ‡ H2 O…g† ! Si2 O…OH†6 …g†
Si2 O…OH†6 …g† ‡ H2 O…g† ! 2Si…OH†4 …g†
…R2†
PO2 …OH†…g† ‡ H2 O…g† ! PO2 …OH† H2 O…g†
PO2 …OH† H2 O…g† ! PO…OH†3 …g†
PO…OH†3 …g† ‡ nH2 O…g† ! PO…OH†3 …H2 O†n …g†
…R3†
P2 O5 …g† ‡ H2 O…g† ! P2 O4 …OH†2 …g†
P2 O4 …OH†2 …g† ‡ H2 O…g† ! P2 O3 …OH†4 …g†
P2 O3 …OH†4 …g† ‡ H2 O…g† ! 2PO…OH†3 …g†
…R4†
2. Methods and computational details
The B3LYP hybrid functional [7] was selected
for the calculations in the present study. This
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
choice was made on the basis of the high-quality
results obtained previously in analogous investigations. These comprise two studies on scandium
oxides [8,9] and one on germanium oxides and
hydroxides [10]. Most important though, for the
present e€ort are the two investigations on water
addition to transition metal oxides [5,6]. In all
cases, the computational results were in very close
agreement with available experimental data. This
expected success of the B3LYP hybrid density
functional approach requires some comments.
Experience on a vast number of systems tells of the
robustness of the particular choice on mixing exchange and correlation terms for this functional.
Only when ambiguity in the occupation of the
Kohn±Sham orbitals exists, results can be expected
to become unreliable. This is because the conventional Kohn±Sham strategy is ill de®ned in cases
where the proper electronic density description
requires partial orbital occupations, as in bond
forming and bond breaking regions on the ground
state potential energy surface (PES). Such anticipated pathological systems are carefully avoided in
our DFT investigations. While this constraint may
appear troublesome, a similar warning ¯ag is associated with the applicability of non-degenerate
perturbation theories, such as Mùller±Plesset 2nd
order perturbation method (MP2), and indeed also
coupled-cluster methods, such as CCSD(T), at
times. As the accuracy of DFT has been demonstrated previously [5,6,8±10], the high-cost eciency very much favors it before any explicitly
correlated wave function based method. The
agreement with ab initio results is repeatedly shown
here by comparisons to a number of high-level
calculations on SiO2 …g†, using MP2 and CCSD(T).
The B3LYP calculations were performed on the
Si and P oxides, oxyhydroxides and hydroxides as
outlined in the (R1)±(R4) reaction steps by employing the GA U S S I A N 98 program package [11].
Molecular structures were determined by calculating analytical Hessians, and characterized by
their stabilities and vibrational spectra. The choice
of basis set requires some comments. The mediumsized 6-311+G(d, p) basis set (denoted by (M)),
used for all atoms, appears fully sucient for describing the energetics and structures in general.
However, the description of Si±O and P±O bond-
47
ing can be improved by selecting larger basis sets.
This is most important for the Si and P atoms,
where calculations on important structures were
complemented by full optimizations using the
maximal 6-311+G(3df) basis sets on these atoms
(denoted by (L)). For O and H, 6-311+G(d, p)
describes the bonding suciently well. The smaller
6-311G basis sets for O and H atoms in conjunction with the 6-311G(d) basis sets for Si and P were
employed (denoted by (S)) for predicting structures. Although these are reasonable, for some
reactions the energetics becomes wrong. This occurs when the polarization around the core molecule is altered, e.g., by deprotonation. If this e€ect
is taken account for, the (S) basis set can be employed on large clusters, in order to reduce computational costs. All calculations were carried out
on closed shell singlet systems, i.e., the ground
states of the investigated species in their highest
oxidation state.
3. Results and discussion
The present e€ort comprises a systematic investigation of a stepwise addition of molecular
water to the mononuclear SiO2 …g† and PO2 …OH† …g†
molecules, as well as to the corresponding binuclear Si and P oxide systems. One part of this investigation follows closely a similar study on the
mononuclear transition metal oxides [5], as similar
reactions of H2 O with Si@O and P@O bonds are
considered. In addition, the present investigation
includes the hydrolysis of Si±O±Si and P±O±P
bridges. The latter reactions are in line with the
corresponding study on binuclear transition metal
oxide clusters [6], as these reactions increase the
number of Si±OH or P±OH units by two in each
H2 O addition step. A third issue regarding the
initial steps towards micro-solvation is addressed
as follows.
Comparing the stability of any hydrated molecule to the corresponding system where the water
molecule has been hydrolyzed involves full geometry optimization of all reactants and products.
The structures are established as corresponding to
local minima on the ground state PES by determining the vibrational spectra. Because two or
48
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
more minima exist on the PESs for several of the
model species, it becomes important for the
chemical understanding to complement structural
characteristics by determining interconnecting
paths between the minima. Such calculations involve evaluating relative stabilities of local minima
along possible reaction coordinates.
Summaries of geometrical parameters and vibrational frequencies for the structures are provided
in Tables 1±4, and illustrated in Figs. 1±4.
3.1. SiO2 …g† ‡ nH2 O
SiO2 …g† (Fig. 1(a)) is a linear molecule of D1h
symmetry. The largely covalent Si@O bond dis (M) and 1.51 A
(L/XL), distances are 1.52 A
playing only small basis set e€ects. Despite the
small size of SiO2 …g† and the general importance
of silicates, experimental and computational data
are scarce in the literature. This is probably due to
the high reactivity of the Si@O bonds in SiO2 …g†.
The IR-active vibrational frequencies have been
determined in Ar matrix to be 1416 and 273 cm 1
by Schn
ockel [12] and by Andrews and McClusky
[13]. Calculations on the Hartree±Fock (HF) level
have been performed by Pacansky and Hermann
[14] and by Ystenes [15], but no investigation appears to have been done using high-level ab initio
techniques. A DFT study, using small basis sets of
DZ quality, has been done by Brinkmann et al.
[16]. This gap in the available data is bridged in
this investigation by comparing our B3LYP results with bond distances and frequencies from
MP2 and CCSD(T) optimizations. While the
Si@O bond is somewhat longer using MP2 (1.53 A
(M) and 1.52 A (L/XL)), the CCSD(T) results
(M) and 1.515 A
(XL)) follow the B3LYP
(1.52 A
data very closely. The vibrational frequencies
display larger basis set e€ects for MP2 and
CCSD(T) than was found for B3LYP, and apparently the (L) or (XL) basis sets are required for
these two methods. All three methods appear to
agree on the low frequency (299 cm 1 (B3LYP/
XL), 295 cm 1 (MP2/XL) and 297 cm 1
(CCSD(T)/XL)), and they come out around 25
cm 1 above the experimental value. This is expected for harmonic frequencies without matrix
e€ects. However, there is some deviations for the
high frequency (1445 cm 1 (B3LYP/XL), 1416
cm 1 (MP2/XL) and 1424 cm 1 (CCSD(T)/XL)).
It appears that both the MP2 and CCSD(T) potentials are too shallow, as anharmonicity would
lower the frequencies further. In general, all three
methods reproduce the experimental results very
well, which is not the case for e.g., HF (too short
Si@O bonds and too high-vibrational frequencies,
cf. Table 1). The computational cost eciency
though strongly favors B3LYP, as the MP2 2nd
derivatives are takes 12 times longer and the
CCSD(T) frequencies as much as 72 times longer
time, exploiting similar resources on the same
parallel computer.
The degree to which the covalence in the
O@Si@O p-system is sub-optimal can be appreciated from the reactivity of SiO2 to water. Initial
hydration involves the formation of the
SiO2 H2 O…g† complex (Fig. 1(b)). A structure
with C2v symmetry is adopted for the complex,
(M)
displaying a long Si OH2 bond (1.93 A
(L)), equivalent Si@O bonds and a
and 1.89 A
158±159° O@Si@O bond angle. Although complex
formation is exothermic by 81 kJ/mol (M) and 88
kJ/mol (L), no intramolecular hydrogen bonds are
formed. These ®gures are expected to have high
accuracy, based on the above agreement on
SiO2 …g† between the B3LYP, MP2 and CCSD(T)
methods, and the close structural and energetical
agreement between B3LYP and MP2 on the more
loosely bonded SO3 H2 O…g† complex (S OH2
[4].
bond: 2.37±2.39 A)
Subsequent addition of the adsorbed water
molecule to one of the Si@O bonds produces
SiO…OH†2 …g† (Fig. 1(c)), which is accompanied by a
175 kJ/mol (M) and 184 kJ/mol (L) energy gain.
Although the reaction involves overcoming a
transition state, the considerable stability of the
SiO2 H2 O…g† complex makes oxydihydroxide
production very likely once the intermediate hydrate has been formed. The total exothermicity of
this reaction becomes 256 kJ/mol (M) and 272 kJ/
mol (L). Interestingly, SiO2 …g† displays a 60±100 kJ/
mol higher reactivity in this step than GeO2 …g† does
when forming the corresponding GeO…OH†2 [10].
The di€erences in reactivities between the (M) and
(L) basis sets are mainly assigned to a poorer describtion of the energetics of the Si@O bond in (M).
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
49
Table 1
and bond angles A (deg.), and ranges of vibrational frequencies …cm 1 †, together with normal mode
Summaries of bond lengths R (A)
symmetries and the number of vibrations in each group, for the SiO2 ‡ nH2 O system
SiO2
D1h
(M)
D1h
(L)
D1h
(XL)
D1h
(HF/M)
D1h
(HF/L)
D1h
(HF/XL)
D1h
(MP2/M)
D1h
(MP2/L)
D1h
(MP2/XL)
D1h
(CCSD(T)/M)
D1h
(CCSD(T)/XL)
R…Si@O†: 1.516
Pu …1 vib:†: 286
R…Si@O†: 1.509
Pu …1 vib:†: 281
R…Si@O†: 1.509
Pu …1vib:†: 299
R…Si@O†: 1.478
Pu (1 vib.): 342
R…Si@O†: 1.473
Pu (1 vib.): 332
R…Si@O†: 1.473
Pu (1 vib.): 359
R…Si@O†: 1.526
Pu (1 vib.): 267
R…Si@O†: 1.521
Pu (1 vib.): 264
R…Si@O†: 1.522
Pu …1 vib:†: 295
R…Si@O†: 1.520
Pu (1 vib.): 267
R…Si@O†: 1.515
Pu (1 vib.): 297
SiO2 H2 O
C2v
(M)
R…Si@O†: 1.527
R…Si O†: 1.931
Cs
(L)
C2v
(L)
SiO…OH†2 H2 O
C1
(1-M)
C1
(2-L)
rg=u …2 vib:†: 999±1448
rg=u (2 vib.): 998±1445
rg=u …2 vib:†: 1115±1604
rg=u (2 vib.): 1121±1604
rg=u (2 vib.): 1119±1599
rg=u (2 vib.): 974±1440
rg=u (2 vib.): 975±1428
rg=u …2 vib:†: 966±1416
rg=u …2 vib:†: 979±1434
rg=u (2 vib.): 980±1424
A…O@Si@O†: 180.0
A…O@Si@O†: 180.0
A…O@Si@O†: 180.0
A…O@Si@O†: 180.0
A…O@Si@O†: 180.0
A…O@Si@O†: 180.0
A…O@Si@O†: 180.0
A…O@Si@O†: 180.0
A…O@Si@O†: 180.0
A…O@Si@O†: 180.0
A…O@Si@O†: 180.0
A…O@Si@O†: 159.3
A…O@Si O†: 100.3
A…H±O±H†: 114.1
A1 ‡ A2 ‡ B1 ‡ B2 …4 ‡ 1 ‡ 2 ‡ 3 vib:†: 158±1575
A1 ‡ B2 …1 ‡ 1 vib:†: 3749±3872
R…Si@O†: 1.518
R…O±H†: 0.968
A…O@Si@O†: 157.7
R…Si O†: 1.893
A…Si O±H†: 119.6
A…O@Si O†: 101.1
A…H±O±H†: 113.9
A0 ‡ A00 …6 ‡ 4 vib:†: 191±1566
A0 ‡ A00 …1 ‡ 1 vib:†: 3733±3852
SiO…OH†2
C2v
(M)
C1
(2-M)
rg=u (2 vib.): 992±1446
R…O±H†: 0.967
A…Si O±H†: 122.9
R…Si@O†: 1.525
R…O±H†: 0.963
R…Si±O†: 1.627
A…Si±O±H†: 116.9
A1 ‡ A2 ‡ B1 ‡ B2 …4 ‡ 1 ‡ 2 ‡ 3 vib:†: 305±1274
R…Si@O†: 1.514
R…O±H†: 0.963
R…Si±O†: 1.615
A…Si±O±H†: 116.1
A1 ‡ A2 ‡ B1 ‡ B2 …4 ‡ 1 ‡ 2 ‡ 3 vib:†: 311±1292
R…Si@O†: 1.534
R…Si±O†: 1.615±1.625
R…O±H†: 0.961±0.981
A (17 vib.): 71±1622
R…Si@O†: 1.537
R…Si±O†: 1.641±1.652
R…Si O†: 1.993
R…O±H†: 0.961±0.970
A (17 vib.): 153±1596
R…Si@O†: 1.527
R…Si±O†: 1.628±1.640
R…O H†: 1.906±1.987
A…Si±O±H†: 110.9±117.6
A…Si±O H†: 98.9
A…O±H O†: 142.0
A (4 vib.): 3541±3896
A…Si±O±H†:
115.4±116.2
A…Si O±H†: 105.4±117.0
A…H±O±H†: 109.6
A (4 vib.): 3730±3894
A…Si±O±H†:
114.8±115.6
A…O@Si±O†: 128.3
A…O±Si±O†: 103.5
A1 ‡ B2 …1 ‡ 1 vib:†: 3875±3877
A…O@Si±O†: 128.0
A…O±Si±O†: 103.9
A1 ‡ B2 …1 ‡ 1 vib:†: 3874±3876
A…O@Si±O†: 125.7±127.3
A…O±Si±O†: 106.9
A…H±O±H†: 107.4
A…H±O H†: 97.6±136.0
A…O@Si±O†: 125.0±126.8
A…O@Si O†: 98.4
A…O±Si±O†: 103.2
A…O±Si O†: 95.0±98.0
A…O@Si±O†: 124.8±126.4
A…O@Si O†: 98.0
50
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
Table 1 (Continued )
R…Si O†: 1.966
R…O±H†: 0.961±0.971
A (17 vib.): 166±1595
Si…OH†4
S4
(M)
S4
(L)
Si…OH†4 H2 O
C1
(M)
C1
(L)
Si…OH†4 2H2 O
C1
(1-M)
C2
(2-M)
C1
(3-M)
R…Si±O†: 1.646
R…O±H†: 0.960
A ‡ B ‡ E …4 ‡ 5 ‡ 4 vib:†: 198±982
R…Si±O†: 1.634
R…O±H†: 0.960
A ‡ B ‡ E …4 ‡ 5 ‡ 4 vib:†: 190±994
R…Si±O†: 1.631±1.667
R…O±H†: 0.960±0.974
R…O H†: 1.911±2.000
A…O±Si±O†: 105.0±117.2
A…O±H O†: 141.5±151.0
A…H±O±H†: 106.6
R…Si±O†: 1.716±1.724
R…Si O†: 2.091±2.107
R…O±H†: 0.961±0.968
A…O±Si±O†: 89.6±172.0
A…O±Si O†: 83.7±95.2
A…O Si O†: 177.9
A…H±O±H†: 108.0±108.8
A (31 vib.): 85±1596
A (8 vib.): 3750±3874
R…Si±O†: 1.630±1.671
A…O±Si±O†: 105.2±117.8
R…O±H†: 0.961±0.974
A…O±H O†: 141.8±152.4
R…O H†: 1.891±1.995
A…H±O±H†: 106.7
A (31 vib.): 28±1624
A (8 vib.): 3615±3894
R…Si±O†: 1.620±1.674
A…O±Si±O†: 103.4±118.0
R…O±H†: 0.960±0.984
A…O±H O†: 161.0±170.8
R…O H†: 1.739±1.832
A…H±O±H†: 106.5±106.9
A (8 vib.): 3408±3901
R…Si±O†: 1.613±1.671
R…O±H†: 0.960±0.997
R…O H†: 1.679±1.921
A (38 vib.): 50±1686
A…O±Si±O†: 104.2±118.0
A…O±H O†: 156.8±167.8
A…H±O±H†: 106.5±106.9
A…H±O H†: 100.8±123.5
A (10 vib.): 3174±3897
Proceeding further along this line, it is observed
that there are two optional coordinations for the
SiO…OH†2 H2 O…g† complex. Either, H2 O is allowed to bridge between one hydroxide and the
Si@O, forming a nearly planar con®guration (Fig.
1(d)) or water is allowed to coordinate directly to
Si (Fig. 1(e)). Despite the long hydrogen bonds
the bonding energy for the former
(1.91±1.99 A),
A…O±Si±O†: 103.5
A…O±Si O†: 95.7±98.9
A…O±Si±O†: 106.4±115.9
A…Si±O±H†: 118.4
A ‡ B ‡ E …1 ‡ 1 ‡ 1 vib:†: 3897±3900
A…O±Si±O†: 106.3±115.9
A…Si±O±H†: 117.8
A ‡ B ‡ E …1 ‡ 1 ‡ 1 vib:†: 3898±3901
A (24 vib.): 39±1624
A (6 vib.): 3623±3900
R…Si±O†: 1.618±1.654
A…O±Si±O†: 105.2±116.9
R…O±H†: 0.960±0.974
A…O±H O†: 141.5±152.7
R…O H†: 1.890±2.023
A…H±O±H†: 106.6
A (24 vib.): 39±1620
A (6 vib.): 3625±3902
A (31 vib.): 35±1645
Si…OH†4 3H2 O
C1
(M)
A…Si O±H†: 101.9±116.2
A…H±O±H†: 109.6
A (4 vib.): 3714±3894
A…Si±O±H†:
117.0±118.2
A…Si±O H†: 109.7
A…H±O H†: 91.4±127.5
A…Si±O±H†:116.9±117.6
A…Si±O H†: 109.0
A…H±O H†: 90.5±128.3
A…Si±O±H†:
111.8±112.6
A…Si O±H†: 102.0±111.4
A…Si±O±H†:
116.7±117.5
A…Si±O H†: 110.0
A…H±O H†: 90.7±127.6
A…Si±O±H†:
115.4±123.5
A…Si±O H†: 126.5
A…H±O H†: 100.8±123.5
A…Si±O±H†:
115.7±119.5
A…Si±O H†:
115.7±122.2
complex is 42 kJ/mol (M), while the latter gives an
additional 14 kJ/mol (M). The reason for the
higher stability of the complex where water is
(M) and
bonded directly to Si (Si OH2 : 1.99 A
1.97 A (L)), as compared to the H bonded complex, is that for both systems the bond to the
complex relaxes only the Si±OH bonds, not the
Si@O bond. This relaxation e€ect becomes largest
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
51
Table 2
and bond angles A (deg.), and ranges of vibrational frequencies …cm 1 †, together with normal mode
Summaries of bond lengths R (A)
symmetries and the number of vibrations in each group, for the …SiO2 †2 ‡ nH2 O systems
OSiO2 SiO
D2h
(M)
R…Si@O†: 1.512
A…O@Si±O†: 135.7
R…Si±O†: 1.680
A…O±Si±O†: 88.6
Ag ‡ B1u ‡ B2g=u ‡ B3g=u …3 ‡ 2 ‡ 3 ‡ 4 vib:†: 110±1338
R…Si@O†: 1.502
A…O@Si±O†: 135.5
R…Si±O†: 1.666
A…O±Si±O†: 89.0
Ag ‡ B1u ‡ B2g=u ‡ B3g=u …3 ‡ 2 ‡ 3 ‡ 4 vib:†: 121±1356
D2h
(L)
HOSiO3 SiOH
C2
(M)
R…Si±O†: 1.602±1.737
R…Si±Si†: 2.071
A ‡ B …10 ‡ 9 vib:†: 128±1178
(HO)OSiOSiO(OH)
Cs
(1-M)
Cs
(2-M)
OSiO2 Si…OH†2
C2
(M)
R…Si@O†: 1.516±1.518
R…Si±O†: 1.620±1.650
R…O±H†: 0.964
R…O H†: 2.185
A0 ‡ A00 …13 ‡ 6 vib:†: 38±1306
R…Si@O†: 1.517±1.527
R…Si±O†: 1.612±1.670
R…O±H†: 0.963±0.978
R…O H†: 2.045
A0 ‡ A00 …13 ‡ 6 vib:†: 64±1306
R…Si@O†: 1.516
R…Si±O†: 1.619±1.706
R…O±H†: 0.960
A ‡ B …10 ‡ 9 vib:†: 104±1314
…HO†OSiOSi…OH†3
C1
(1-M)
C1
(2-M)
…HO†2 SiO2 Si…OH†2
D2
(M)
…HO†3 SiOSi…OH†3
C2
(1-M)
C2
(1-L)
A…Si±O±Si†: 91.4
A…Si±O±Si†: 91.0
R…O±H†: 0.961
A…Si±O±Si†: 73.7±73.9
A…Si±O±H†: 123.3
A…O±Si±O†: 87.2±128.0
A ‡ B …1 ‡ 1 vib:†: 3897±3898
A…Si±O±H†:
118.3±118.4
A…Si±O H†: 107.0
A…H±O H†: 134.7
A0 …2 vib:†: 3769±3852
A…Si±O±H†:
118.3±120.4
A…Si±O H†: 120.4
A…Si±O±Si†: 145.4
A…O@Si±O†: 124.6±130.2
A…O±Si±O†: 102.4±107.5
A…O±H O†: 139.3
A…Si±O±Si†: 129.7
A…O@Si±O†: 120.3±129.9
A…O±Si±O†: 107.5±110.5
A…O±H O†: 146.9
A0 …2 vib:†: 3565±3860
A…Si±O±H†: 121.6
A…O@Si±O†: 135.0
A…Si±O±Si†: 91.4
A…O±Si±O†: 87.3±114.2
A ‡ B …1 ‡ 1 vib:†: 3910
R…Si@O†: 1.523
A…Si±O±H†:
R…Si±O†: 1.602±1.646
116.2±119.8
R…O±H†: 0.960±0.963
A (1 vib.): 22i
A (25 vib.): 30±1298
A (4 vib.): 3862±3904
R…Si@O†: 1.530
A…Si±O±H†:
R…Si±O†: 1.611±1.676
117.6±119.5
R…O±H†: 0.960±0.969
A…Si@O H†: 94.8
R…O H†: 2.308
A (26 vib.): 38±1306
A (4 vib.): 3769±3852
R…Si±O†: 1.629±1.690
A…Si±O±H†: 119.2
R…O±H†: 0.960
A ‡ B1 ‡ B2 ‡ B3 …7 ‡ 6 ‡ 7 ‡ 6 vib:†: 85±1016
A ‡ B1 ‡ B2 ‡ B3 …1 ‡ 1 ‡ 1 ‡ 1 vib:†: 3909±3912
R…Si±O†: 1.639±1.654
A…Si±O±H†: 116.2±119.0
R…O±H†: 0.960±0.964
A…Si±O H†: 103.0
R…O H†: 2.599
A…H±O H†: 137.5
A (1 vib.): 9i
A (32 vib.): 41±1080
A (6 vib.): 3839±3901
R…Si±O†: 1.628±1.642
A…Si±O±H†: 115.3±118.6
R…O±H†: 0.960±0.964
A…Si±O H†: 103.4
R…O H†: 2.489
A…H±O H†: 137.0
A (33 vib.): 34±1082
A (6 vib.): 3834±3903
A…Si±O±Si†: 161.9
A…O@Si±O†: 125.9±129.0
A…O±Si±O†: 104.2±115.0
A…Si±O±Si†: 129.6
A…O@Si±O†: 121.6±123.6
A…O±Si±O†: 103.4±108.9
A…O±H O†: 138.2
A…Si±O±Si†: 91.3
A…O±Si±O†: 88.7±118.5
A…Si±O±Si†: 133.6
A…O±Si±O†: 103.2±113.9
A…O±H O†: 129.8
A…Si±O±Si†: 131.5
A…O±Si±O†: 103.3±113.8
A…O±H O†: 131.8
52
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
Table 2 (Continued )
C1
(2-M)
C1
(2-L)
HO3 SiOSi…OH†3 H2 O
C1
(M)
R…Si±O†: 1.630±1.658
A…Si±O±H†: 115.8±119.0
R…O±H†: 0.960±0.966
A…Si±O H†: 106.6
R…O H†: 2.222
A…H±O H†: 131.9
A (33 vib.): 25±1105
A (6 vib.): 3799±3904
R…Si±O†: 1.618±1.645
A…Si±O±H†: 115.2±118.6
R…O±H†: 0.960±0.966
A…Si±O H†: 106.6
R…O H†: 2.196
A…H±O H†: 132.9
A (33 vib.): 15±1112
A (6 vib.): 3800±3906
R…Si±O†: 1.628±1.665
R…O±H†: 0.960±0.980
R…O H†: 1.802±2.132
A (40 vib.): 35±1647
A…Si±O±H†: 114.9±118.8
A…Si±O H†: 108.3
A…H±O H†: 110.5±132.8
A…H±O±H†: 106.5
A (8 vib.): 3508±3901
for the second structure. It can be noted that the
exothermicity for the formation of the Fig. 1(e)
complex depends little on the choice of basis set
(59 kJ/mol (M) and 60 kJ/mol (L)).
The subsequent reaction, from the complex in
Fig. 1(e) to Si…OH†4 …g† (Fig. 1(f)), becomes exothermic by 195 kJ/mol (M) and 199 kJ/mol (L).
Thus the total energy release for the water addition
to the second Si@O (254 kJ/mol (M) and 259 kJ/
mol (L)) becomes somewhat lower than for addition to the ®rst. In total the SiO2 …g† ‡ 2H2 O…g†
reaction is exothermic by 509 kJ/mol (M), which is
about 100 kJ/mol higher than found for the corresponding Ge system [10]. The product, orhtosilicic acid, has been subject to several quantum
chemical investigations in the past [17±22], though
the focus has mainly been on the orientation of the
four Si±OH groups. In the optimal structure, these
are arranged so that each H atom points toward
an adjacent O atom, which result in S4 symmetry
[21]. This was indeed also observed for the optimal
structure of Ge…OH†4 [10]. Possibly more interesting is the fact that the structure of Si…OH†4 does
not display a tetrahedral con®guration on the O
atoms. Rather, the arrangement of O atoms
around Si could be described as a ¯attened tetrahedron, which contains two di€erent O±Si±O bond
angles (106° and 116° (M) and (L)). This is again
very similar to what was obtained for Ge…OH†4
[10]. This ¯attened tetrahedron coordination is in
contrast to the Ti…OH†4 molecule, which despite
the lower molecular symmetry displays a perfectly
tetrahedral oxygen coordination around the cen-
A…Si±O±Si†: 141.3
A…O±Si±O†: 103.5±114.8
A…O±H O†: 137.6
A…Si±O±Si†: 139.9
A…O±Si±O†: 103.9±114.7
A…O±H O†: 138.3
A…Si±O±Si†: 140.4
A…O±Si±O†: 101.8±115.0
A…O±H O†: 140.9±167.0
tral atom [5]. It is suggested that Td symmetry
cannot be sustained among neutral mononuclear
oxyhydroxides of the p-elements. In fact, the only
exception to this rule comprises ArO4 [4]. Thus,
the reason why systems such as SiO44 , PO43 ,
SO42 , ClO4 and ArO4 do display Td symmetry is
rather found in the packing of four exactly
equivalent ligands on a sphere. In contrast, the 3dshell of e.g., Ti does indeed possess the necessary
¯exibility to produce a truly tetrahedral covalent
bonding. The dominant basis set e€ect for
Si…OH†4 …g† is observed on the Si±O bond distances, which decrease with an enlarged basis set
(M) vs. 1.63 A
(L)).
(1.65 A
Introduction of additional H2 O molecules initiates the formation of a solvation shell around the
orthosilicic acid molecule by hydrogen bonding to
the Si±OH groups. For Si…OH†4 H2 O…g† (Fig. 1
(g)) there exists only one structure, namely the one
where the H end of one Si±OH group binds to
water, and where one H end of water binds to O in
another Si±OH group. This, however, results in
(M) and
elongated hydrogen bonds (1.91±2.00 A
1.89±2.02 A (L)), which consequently are not very
strong. The energy released upon binding is only
27 kJ/mol (M) and 26 kJ/mol (L). The reason for
the poor binding will discussed further. Here, it is
stated to be due to the lack of drive for proton
(electron pair) delocalization, originating from the
bridging between the two equivalent OH groups.
Water does not assist in further relaxing any strain
in the molecule. The only observed structural e€ect
is seen in the O±Si±O bond angles. It is gratifying
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
53
Table 3
and bond angles A (deg.), and ranges of vibrational frequencies (cm 1 ), together with normal mode
Summaries of bond lengths R (A)
symmetries and the number of vibrations in each group, for the PO2 …OH† ‡ nH2 O systems
PO2 …OH†
Cs
(M)
Cs
(L)
PO2 …OH† H2 O
C1
(1-M)
C1
(1-L)
C1
(2-M)
C1
(2-L)
PO…OH†3
C3
(M)
C3
(L)
P…OH†3 H2 O2
C1
(M)
R…P@O†: 1.462±1.469
R…P±O†: 1.600
A0 ‡ A00 …6 ‡ 2 vib:†: 391±1440
R…P@O†: 1.450±1.456
R…P±O†: 1.579
A0 ‡ A00 …6 ‡ 2 vib:†: 404±1472
C1
(L)
PO…OH†3 H2 O
C1
R…O±H†: 0.969
A…P±O±H†: 112.1
R…P@O†: 1.468±1.474
A…P±O±H†: 112.2
R…P±O†: 1.605
A…P O±H†:
R…P O†: 2.184
107.0±108.2
R…O±H†: 0.967
A…H±O±H†: 107.5
A …15 vib:†: 154±1611
A …3 vib:†: 3759±3860
R…P@O†: 1.456±1.462
A…P±O±H†: 111.6
R…P±O†: 1.584
A…P O±H†:
R…P O†: 2.119
105.5±105.9
R…O±H†: 0.966±0.968
A…H±O±H†: 107.7
A (15 vib.): 181±1614
A (3 vib.): 3748±3848
R…P@O†: 1.464±1.478
A…P@O H†: 108.7
R…P±O†: 1.579
A…P±O±H†: 111.0
R…O±H†: 0.962±0.998
A…O±H O†:
R…O H†: 1.694±2.195
124.9±159.7
A (15 vib.): 73±1609
A (3 vib.): 3221±3896
R…P@O†: 1.451±1.464
A…P@O H†: 108.2
R…P±O†: 1.558
A…P±O±H†: 111.0
R…O±H†: 0.962±1.000
A…O±H O†:
R…O H†: 1.676±2.204
125.1±161.2
A (15 vib.): 83±1608
A (3 vib.): 3186±3894
R…P@O†: 1.476
R…P±O†: 1.606
A ‡ E …5 ‡ 5 vib:†: 171±1291
R…P@O†: 1.462
R…P±O†: 1.588
A ‡ E …5 ‡ 5 vib:†: 173±1323
A…P±O±H†:
112.2±114.0
A…P±O H†: 115.8
A…H±O H†:
109.8±119.5
A (5 vib.): 3461±3837
R…P±O†: 1.627±1.725
R…O±H†: 0.968±0.972
A (22 vib.): 120±1201
R…P±O†: 1.610±1.708
R…O±H†: 0.962±0.966
A (22 vib.): 112±1208
R…P@O†: 1.472
A…O@P@O†: 134.6
A…O@P±O†: 111.8±113.7
A0 (1 vib.): 3788
A…O@P@O†: 134.1
A…O@P±O†: 112.2±113.8
A0 …1 vib:†: 3787
A…O@P@O†: 132.8
A…O@P±O†: 111.3±113.6
A…O@P O†: 95.0±96.0
A…O±P O†: 93.8
A…O@P@O†: 132.2
A…O@P±O†: 111.6±113.4
A…O@P O†: 95.7±96.0
A…O±P O†: 94.7
A…O@P@O†: 132.0
A…O@P±O†: 113.7±114.3
A…H±O±H†: 107.7
A…H±O H†: 101.4±129.4
A…O@P@O†: 131.5
A…O@P±O†: 113.9±114.6
A…H±O±H†: 107.7
A…H±O H†: 99.9±129.0
R…O±H†: 0.965
A…O@P±O†: 116.3
A…P±O±H†: 113.0
A…O±P±O†: 101.9
A ‡ E …1 ‡ 1 vib:†: 3834±3837
R…O±H†: 0.965
A…O@P±O†: 116.1
A…P±O±H†: 112.5
A…O±P±O†: 102.1
A ‡ E …1 ‡ 1 vib:†: 3839±3841
R…P±O†: 1.613±1.706
R…O±O†: 1.450
R…O±H†: 0.964±0.984
R…O H†: 1.753±2.220
A (22 vib.): 44±1535
P…OH†5
C1
(M)
R…O±H†: 0.968
A…P±O±H†: 112.9
A…O±P±O†: 94.5±101.5
A…O±O±H†: 101.3±101.8
A…O±O H†: 113.4
A…O±H O†: 161.9±166.3
A…O±P±O†: 88.0±176.5
A…P±O±H†: 109.4±113.4
A (5 vib.): 3796±3866
A…O±P±O†: 88.2±176.5
A…P±O±H†: 109.4±113.4
A (5 vib.): 3807±3867
A…P±O±H†:
A…O@P±O†: 113.4±117.2
54
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
Table 3 (Continued )
(1-M)
C1
(2-M)
C1
(2-L)
PO…OH†3 2H2 O
C1
(1-M)
C1
(2-M)
PO…OH†3 3H2 O
C3
(1-M)
C1
(2-M)
C1
(3-M)
R…P±O†: 1.581±1.631
R…O±H†: 0.962±0.987
R…O H†: 1.753±2.220
111.5±115.4
A…P±O H†: 112.3
A…O±H O†:
125.0±161.2
A (22 vib.): 43±1612
A (5 vib.): 3390±3896
R…P@O†: 1.488
A…P@O H†: 107.6
R…P±O†: 1.585±1.612
A…P±O±H†:
R…O±H†: 0.962±0.989
110.2±113.7
R…O H†: 1.773±1.970
A…O±H O†: 138.2±154.8
A (22 vib.): 42±1618
A (5 vib.): 3367±3890
R…P@O†: 1.474
A…P@O H†: 107.0
R…P±O†: 1.566±1.5922
A…P±O±H†:
R…O±H†: 0.962±0.989
111.0±113.4
R…O H†: 1.764±1.969
A…O±H O†:
139.6±155.2
A (22 vib.): 44±1619
A (5 vib.): 3360±3888
R…P@O†: 1.502
R…P±O†: 1.583±1.603
R…O±H†: 0.962±0.988
R…O H†: 1.780±1.974
A…P@O H†:
107.6±107.8
A…P±O±H†:
111.0±113.7
A…O±P±O†: 100.4±107.3
A…H±O±H†: 106.8
A…H±O H†: 97.0±132.3
A…O@P±O†: 114.0±117.0
A…O±P±O†: 100.8±106.0
A…H±O±H†: 107.2
A…H±O H†: 93.4±127.7
A…O@P±O†: 113.8±116.8
A…O±P±O†: 101.3±106.6
A…H±O±H†: 107.0
A…H±O H†: 91.64±127.2
A…O@P±O†: 112.9±116.2
A…O±P±O†: 101.4±108.4
A…H±O±H†: 107.2
A…H±O H†: 92.0±128.6
A…O±H O†: 139.3±155.2
A (29 vib.): 33±1622
A (7 vib.): 3377±3889
R…P@O†: 1.484
A…P@O H†: 128.7
A…O@P±O†: 111.2±119.2
R…P±O†: 1.573±1.620
A…P±O±H†:
A…O±P±O†: 102.8±105.9
R…O±H†: 0.961±1.008
112.3±116.5
A…H±O±H†: 106.7±107.3
R…O H†: 1.603±1.770
A…O±H O†:
A…H±O H†: 101.0±123.7
162.5±171.8
A (29 vib.): 31±1662
A (3 vib.): 2986±3498
A (4 vib.): 3827±3888
R…P@O†: 1.517
R…P±O†: 1.586
R…O±H†: 0.962±0.985
R…O H†: 1.817±1.996
A…P@O H†: 125.7
A…P±O±H†: 106.8
A…H±O±H†: 107.0
A…H±O H†: 92.9±128.0
A…O@P±O†: 113.2
A…O±P±O†: 105.5
A…O±H O†: 139.7±151.5
A ‡ E …12 ‡ 11 vib:†: 29±1617
R…P@O†: 1.483
R…P±O†: 1.563±1.646
R…O±H†: 0.962±1.042
R…O H†: 1.489±2.004
A ‡ E …3 ‡ 3 vib:†: 3436±3890
A…P@O H†: 121.6
A…O@P±O†: 111.0±120.5
A…P±O±H†:
A…O±P±O†: 102.3±105.5
111.0±115.7
A…H±O±H†: 106.6±107.0
A…P±O H†: 118.9
A…H±O H†: 103.5±126.9
A…O±H O†: 152.8±172.2
A (36 vib.): 48±1667
A (9 vib.): 2428±3893
R…P@O†: 1.498
A…P@O H†:
A…O@P±O†: 110.0±117.9
R…P±O†: 1.573±1.605
106.8±125.7
A…O±P±O†: 103.2±107.0
R…O±H†: 0.962±1.006
A…P±O±H†:
A…H±O±H†: 106.7±107.3
R…O H†: 1.612±1.980
111.2±116.9
A…H±O H†: 92.0±128.9
A…O±H O†: 139.7±170.0
A (36 vib.): 32±1655
A (9 vib.): 3018±3890
to note that the energy di€erence between the (M)
and (L) basis sets has virtually disappeared for
Si…OH†4 H2 O…g†. The deviations on energetics for
larger complexes using (M) can thus be estimated
to 2 kJ/mol, which anyway is within the expected
accuracy for DFT methods. Still, an improved
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
55
Table 4
and bond angles A (deg.), and ranges of vibrational frequencies …cm 1 †, together with normal mode
Summaries of bond lengths R (A)
symmetries and the number of vibrations in each group, for the …PO2 …OH††2 ‡ nH2 O systems
OPO3 PO
D3h
(M)
O2 POPO2
C2
(M)
C2
(L)
R…P@O†: 1.450
R…P±P†: 2.111
R…P±O†: 1.694
A…O@P±O†: 128.6
A01 ‡ A002 ‡ E0 ‡ E00 …3 ‡ 2 ‡ 3 ‡ 2 vib:†: 237±1443
R…P@O†: 1.459±1.462
R…P±O†: 1.627
A ‡ B …6 ‡ 4 vib:†: 57±655
R…P@O†: 1.447±1.450
R…P±O†: 1.605
A ‡ B …6 ‡ 4 vib:†: 42±684
O2 POPO…OH†2
C1
(M)
…HO†OPO2 PO…OH†
C2v
(1-M)
C2h
(2-M)
…HO†2 OPOPO…OH†2
C1
(1-S)
C1
(1-M)
C1
(1-L)
C2
(2-S)
C2
(2-M)
A…P±O±P†: 77.1
A…O±P±O†: 85.3
A…O@P@O†: 136.7
A…P±O±P†: 134.3
A…O@P±O†: 110.7±112.6
A ‡ B …2 ‡ 3 vib:†: 960±1461
A…O@P@O†: 136.3
A…P±O±P†: 132.6
A…O@P±O†: 111.0±112.6
A ‡ B …2 ‡ 3 vib:†: 996±1492
R…P@O†: 1.459±1.476
A…P±O±H†: 113.4±116.0
R…P±O†: 1.578±1.688
A…P±O H†: 105.2
R…O±H†: 0.966±0.977
A…O±H O†: 138.5
R…O H†: 2.000
A (22 vib.): 60±1429
A (2 vib.): 3613±3817
A…P±O±P†: 131.0
A…O@P@O†: 133.5
A…O@P±O†: 110.7±117.7
A…O±P±O†: 100.8±104.3
R…P@O†: 1.461
A…P±O±H†: 112.8
A…P±O±P†: 93.9
R…P±O†: 1.594±1.656
A…O@P±O†: 116.4±120.0
R…O±H†: 0.967
A…O±P±O†: 86.1±104.8
A1=2 ‡ B1=2 …12 ‡ 10 vib:†: 100±1362
A1 ‡ B2 …1 ‡ 1 vib:†: 3817±3818
R…P@O†: 1.462
A…P±O±H†: 112.9
A…P±O±P†: 93.9
R…P±O†: 1.592±1.656
A…O@P±O†: 116.5±119.9
R…O±H†: 0.966
A…O±P±O†: 86.1±104.8
Ag=u ‡ Bg=u …11 ‡ 11 vib:†: 100±1352
Ag ‡ Bu …1 ‡ 1 vib:†: 3817±3818
R…P@O†: 1.470±1.474
A…P±O±H†: 118.6±123.0
R…P±O†: 1.581±1.653
A…P±O H†: 112.4
R…O±H†: 0.969±0.977
A…H±O H†: 127.0
R…O H†: 2.064
A (29 vib.): 39±1332
A (4 vib.): 3632±3767
R…P@O†: 1.463±1.468
A…P±O±H†: 113.0±115.3
R…P±O†: 1.589±1.651
A…P±O H†: 111.2
R…O±H†: 0.965±0.966
A…H±O H†: 124.0
R…O H†: 2.301
A (29 vib.): 37±1340
A (4 vib.): 3780±3835
R…P@O†: 1.455±1.450
A…P±O±H†: 112.7±115.5
R…P±O†: 1.571±1.625
A…P±O H†: 109.9
R…O±H†: 0.965±0.967
A…H±O H†: 135.6
R…O H†: 2.463
A (29 vib.): 30±1372
A (4 vib.): 3806±3836
R…P@O†: 1.467
A…P±O±H†: 119.0±119.5
R…P±O†: 1.585±1.640
A…P±O H†: 111.4
R…O±H†: 0.969±0.981
A…H±O H†: 128.0
R…O H†: 1.973
A ‡ B …15 ‡ 14 vib:†: 69±1359
A ‡ B …2 ‡ 2 vib:†: 3541±3759
R…P@O†: 1.460
A…P±O±H†: 113.4±113.8
R…P±O†: 1.593±1.636
A…P±O H†: 109.9
R…O±H†: 0.965±0.973
A…H±O H†: 133.0
R…O H†: 2.060
A ‡ B …15 ‡ 14 vib:†: 60±1365
A ‡ B …2 ‡ 2 vib:†: 3693±3830
A…P±O±P†: 139.4
A…O@P±O†: 114.7±119.6
A…O±P±O†: 98.2±103.0
A…O±H O†: 138.5
A…P±O±P†: 134.3
A…O@P±O†: 113.8±118.6
A…O±P±O†: 98.8±106.8
A…O±H O†: 124.0
A…P±O±P†: 134.4
A…O@P±O†: 113.6±118.0
A…O±P±O†: 99.5±106.4
A…O±H O†: 117.2
A…P±O±P†: 133.9
A…O@P±O†: 116.4±117.2
A…O±P±O†: 96.7±105.5
A…O±H O†: 136.8
A…P±O±P†: 133.3
A…O@P±O†: 114.9±116.2
A…O±P±O†: 98.0±105.8
A…O±H O†: 138.4
56
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
Table 4 (Continued)
C2
(2-L)
C1
(3-S)
C1
(3-M)
C1
(3-L)
C2
(4-M)
C2
(4-L)
R…P@O†: 1.448
A…P±O±H†: 112.3±114.0
R…P±O†: 1.573±1.614
A…P±O H†: 108.2
R…O±H†: 0.966±0.971
A…H±O H†: 129.7
R…O H†: 2.071
A ‡ B …15 ‡ 14 vib:†: 54±1393
A ‡ B …2 ‡ 2 vib:†: 3708±3828
R…P@O†: 1.478±1.492
A…P±O±H†: 118.0±122.0
R…P±O†: 1.576±1.636
A…P@O H†: 105.7
R…O±H†: 0.969±0.987
A…O±H O†: 138.5
R…O H†: 1.974
A (29 vib.): 65±1346
A (4 vib.): 3443±3778
R…P@O†: 1.461±1.483
A…P±O±H†: 112.6±113.9
R…P±O†: 1.585±1.635
A…P@O H†: 105.0
R…O±H†: 0.965±0.982
A…O±H O†: 143.7
R…O H†: 1.947
A (29 vib.): 68±1353
A (4 vib.): 3523±3834
R…P@O†: 1.449±1.469
A…P±O±H†: 112.6±113.0
R…P±O†: 1.568±1.619
A…P@O H†: 104.2
R…O±H†: 0.965±0.983
A…O±H O†: 145.0
R…O H†: 1.902
A (29 vib.): 59±1381
A (4 vib.): 3501±3835
R…P@O†: 1.482
A…P±O±H†: 111.4±112.9
R…P±O†: 1.586±1.642
A…P@O H†: 104.0
R…O±H†: 0.965±0.977
R…O H†: 2.163
A ‡ B …15 ‡ 14 vib:†: 79±1274
A ‡ B …2 ‡ 2 vib:†: 3629±3832
R…P@O†: 1.468
A…P±O±H†: 111.8±112.6
R…P±O†: 1.567±1.621
A…P@O H†: 103.0
R…O±H†: 0.965±0.978
R…O H†: 2.103
A ‡ B …15 ‡ 14 vib:†: 75±1304
A ‡ B …2 ‡ 2 vib:†: 3605±3838
…HO†2 OPOPO…OH†2 H2 O
C1
(M)
R…P@O†: 1.464±1.485
A…P±O±H†: 112.5±119.9
R…P±O†: 1.561±1.667
A…P@O H†: 130.7
R…O±H†: 0.962±1.009
A…H±O±H†: 107.3
R…O H†: 1.594±1.772
A…H±O H†: 103.0±118.8
A (36 vib.): 39±1639
A (4 vib.): 2963±3881
P4 O10
Td
(M)
Td
(L)
P4 O6
Td
(M)
Td
(L)
P4
Td
(M)
Td
(L)
A…P±O±P†: 133.6
A…O@P±O†: 114.7±115.8
A…O±P±O†: 99.4±105.7
A…O±H O†: 138.6
A…P±O±P†: 125.9
A…O@P±O†: 116.0±118.6
A…O±P±O†: 95.9±105.9
A…P±O±P†: 124.9
A…O@P±O†: 110.0±118.5
A…O±P±O†: 96.6±106.4
A…P±O±P†: 125.8
A…O@P±O†: 110.6±118.0
A…O±P±O†: 98.2±106.5
A…P±O±P†: 117.0
A…O@P±O†: 109.0±119.0
A…O±P±O†: 101.0±104.5
A…O±H O†: 136.8
A…P±O±P†: 117.3
A…O@P±O†: 109.5±118.9
A…O±P±O†: 101.8±104.3
A…O±H O†: 138.3
A…P±O±P†: 137.7
A…O@P±O†: 109.8±117.9
A…O±P±O†: 101.9±113.6
A…O±H O†: 158.0±173.7
R…P@O†: 1.448
A…O@P±O†: 117.0
A…P±O±P†: 124.6
R…P±O†: 1.634
A…O±P±O†: 101.0
A1 ‡ E ‡ T1 ‡ T2 …2 ‡ 3 ‡ 3 ‡ 4 vib:†: 239±786
A1 ‡ T2 …1 ‡ 2 vib:†: 975±1420
R…P@O†: 1.435
A…O@P±O†: 116.7
A…P±O±P†: 124.0
R…P±O†: 1.612
A…O±P±O†: 101.3
A1 ‡ E ‡ T1 ‡ T2 …2 ‡ 3 ‡ 3 ‡ 4 vib:†: 245±820
A1 ‡ T2 …1 ‡ 2 vib:†: 1013±1453
R…P±O†: 1.676
A…O±P±O†: 99.0
A1 ‡ E ‡ T1 ‡ T2 …2 ‡ 2 ‡ 2 ‡ 4 vib:†: 278±914
R…P±O†: 1.655
A…O±P±O†: 99.3
A1 ‡ E ‡ T1 ‡ T2 …2 ‡ 2 ‡ 2 ‡ 4 vib:†: 284±940
R…P±P†: 2.220
A…P±P±P†: 60.0
A1 ‡ E ‡ T2 …1 ‡ 1 ‡ 1 vib:†: 360±597
R…P±P†: 2.204
A…P±P±P†: 60.0
A1 ‡ E ‡ T2 …1 ‡ 1 ‡ 1 vib:†: 367±608
A…P±O±P†: 127.7
A…P±O±P†: 127.3
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
57
Fig. 1. Structures in the SiO2 …g† ‡ 5H2 O…g† system: (a) SiO2 …g† …D1h †, (b) SiO2 H2 O…g† …C2v †, (c) SiO…OH†2 …g† …C2v †, (d) and
(e) SiO…OH†2 H2 O…g† …C1 †, (f) Si…OH†4 …g† …S4 †,(g) Si…OH†4 H2 O…g† …C1 †, (h), (i) and (j) Si…OH†4 2H2 O…g† …C1 † and
(k) Si…OH†4 3H2 O…g† …C1 † together with relative stabilities and energetics for some hydrolysis reactions.
quality on bond distances can be obtained if a
larger basis set is used.
There are three di€erent possibilities for binding
a second solvating water molecule. The least favorable coordination type for Si…OH†4 2H2 O…g†
is the binding of all six O atoms to Si (Fig. 1(h)).
Typical features include elongated bond distances
Si OH2 : 2.10 A).
Forming this
(Si±O: 1.72 A,
strained structure is endothermic by 127 kJ/mol
(M), as compared to the monohydrate, but it is a
local energy minimum. This structure is thus taken
to exemplify a six-coordinated Si con®guration,
elsewhere known only in high-pressure phases of
SiO2 (s) [1].
The second type of dihydrate complex (Fig.
1(i)) has each of the H2 O bonded to two Si±OH
groups and displays C2 symmetry. Binding the
second water molecule is as exothermic (27 kJ/mol
(M)), as was the ®rst. The hydrogen bonding in the
Fig. 1(i) structure is rather poor though, as re¯ected in the in rather long O H bonds (1.89±
The hydrogen bonding is signi®cantly
2.00 A).
improved if the second water molecule is allowed
to connect to the ®rst, thus forming a water dimer
58
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
ligand (Fig. 1(j)). The O H bond distances are
and this structure
notably shortened (1.74±1.83 A),
is 12 kJ/mol (M) more stable than the structure in
Fig. 1(i). The total binding energy for the second
water ligand thus becomes 39 kJ/mol (M). From
this energy gain it can be concluded that the H2 O
dimer is a better ligand to use for modeling the
solvation shell, than a single water molecule. It can
also be hypothesized, that binding four monomer
or dimer ligands to the Si…OH†4 core will preserve
its original symmetry.
The ®nal water complex in this study is the
trihydrate, Si…OH†4 3H2 O…g† (Fig. 1(k)). It is included as a reference structure to compare with
similar trihydrates for e.g., perchloric acid, which
display deprotonation and the formation of an ion
pair [4]. The complex in Fig. 1(k) does not display
such a behavior, and although the central O H
bond is shortened, some others are elonagated
This is re¯ected in the
(range: 1.68±1.93 A).
binding energy for the third water molecule, which
again becomes 27 kJ/mol (M), typical of adding
one H2 O…g† monomer. The main point with this
structure is though to show that nano-scale acidity
does not appear in Si…OH†4 …g†, which is in agreement with its Brùnsted alkalinity.
3.2. Si2 O4 …g† ‡ nH2 O
The Si2 O4 molecule consists of a central Si2 O2
ring
and
two
terminal
Si@O
bonds.
O@Si—O2 ˜Si@O is planar (Fig. 2(a)), analogous to
Ge2 O4 [10], and it is formed when dimerizing the
SiO2 molecule (Fig. 2(b)). The fusion of two Si@O
bonds into a ring is exothermic by 341 kJ/mol (M)
and 378 kJ/mol (L). The energy released by this
reaction is approximately 90±130 kJ/mol higher
than what was found for the corresponding
Fig. 2. Structures in the Si2 O4 ‡ 4H2 O system: Si2 O4 : (a) OSiO2 SiO …D2h †, (b) 2 SiO2 …D1h †; Si2 O5 H2 : (c) HOSiO3 SiOH …C2 †, (d) and
(e) HO…SiO†O…SiO†OH …Cs †, (f) OSiO2 Si…OH†2 …C2 †; Si2 O6 H4 :(g) and (h) HO…SiO†OSi…OH†3 …C1 †, (i) …HO†2 SiO2 Si…OH†2 …D2 †,
(j) 2 SiO…OH†2 …C2v †; Si2 O7 H6 : (k) …HO†3 SiOSi…OH†3 …C2 † and (l) …C1 †; Si2 O8 H8 : (m) 2 Si…OH†4 …S4 † and (n) …HO†3
SiOSi…OH†3 H2 O …C1 † together with relative stabilities and energetics for some hydrolysis reactions.
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
dimerization of GeO2 [10], which seems reasonable
due to the better bonding between Si±O than
Ge±O. The 37 kJ/mol basis set e€ect on reaction
energies, which is also observed through the
shorter Si±O bond lengths using the (L) basis set
(M) vs. 1:50 ‡ 1:67 A
(L)), corre(1:51 ‡ 1:68 A
sponds to the e€ect on the SiO2 …g† ‡ H2 O…g† reaction (2 16 kJ/mol). It is thus reasonable to
assign this e€ect to description of SiO2 …g†, where
the insuciency of (M) really a€ects the energetics.
However, earlier investigations at the HF [14,22]
and pseudo-potential levels [23] on the dimerization of SiO2 found much higher reactivities, i.e., in
the range 450±520 kJ/mol. A somewhat later paper
[24] compared results from MP2, DFT-GGA and
experiment. Both theoretical methods were found
to be in agreement with the experimental results,
and the formation energy for Si2 O4 was calculated
to be 354 kJ/mol, using DFT-GGA. A similar
consistency between MP2 and B3LYP results was
also found for the germanium oxides [10].
There are two di€erent types of reactive sites for
water addition to OSiO2 SiO, comprising the
Si±O±Si bridges and the terminal Si@O bonds.
Cleavage of one bridge results in a planar
HO±…O@Si†±O±…Si@O†±OH chain, which displays
one structure (Fig. 2(d)) similar to that found for
its Ge analogue [10]. In contrast though, the intramolecular hydrogen bond between the two
Si±OH groups is signi®cantly weaker (O H: 2.19
than what was found for the Ge system, and the
A)
Si±O±Si bond angle is rather open (145°). A second type of planar chain structure was found for
(OH)OSiOSiO(OH). It displays a geometry, where
the proton of one Si±OH group points toward one
Si@O unit (Fig. 2(e)). The hydrogen bond is
and the Si±O±Si bond
somewhat shorter (2.04 A)
angle more acute (129°). These e€ects stabilize the
latter structure by 7 kJ/mol (M), as compared to
the former.
While hydrolysis of one Si±O±Si bridge in Si2 O4 ,
to form the most stable chain structure, is exothermic by 162 kJ/mol (M), the high reactivity of
the terminal Si@O bonds determines the
O@Si—O2 ˜Si—…OH†2 cluster structure (Fig. 2(f)) to
be the global minimum for Si2 O5 H2 . In fact, the
Si2 O2 ring based cluster is 130 kJ/mol (M) more
stable than the chain, making water addition to one
59
of the terminal Si@O bonds in Si2 O4 exothermic by
292 kJ/mol (M). The 27 kJ/mol lower exothermicity, that is observed when comparing the conversion from the ®rst Si-chain type to the cluster to the
similar conversion of the Ge systems [10], is attributed to the higher reactivity of the Si@O bond,
as compared to the Ge@O bond. Previous studies
on the Si2 O5 H2 system suggested it to be a triplebridged HO±SifO3 gSi±OH cluster (Fig. 2(c))
[25,26]. However, this structure is the least stable of
the three (2 kJ/mol above the ®rst chain type). This
is in agreement with the stability ordering obtained
for the structures found for Ge [10].
The principal sites for addition of a second
water molecule comprise the remaining Si@O
groups. Consequently, the reactivities become rather independent on reactant structure, and the
relative stability ordering from seen for the
Si2 O5 H2 systems remain. There exist two chain
structures for OH±…Si@O†±O±Si…OH†3 . Reacting
one Si@O group in the ®rst Si2 O5 H2 chain structure (Fig. 2(d)) releases 281 kJ/mol (M), and produces a structure (Fig. 2(g)) with a very wide
Si±O±Si bond angle (161°). No hydrogen bonding
remains in this system, and it turns out to be a
transition state. Allowing for one ±‰…OH†2 SiŠ±OH
group to interact with the Si@O gives a 5 kJ/mol
(M) stabilization, and produces an energy minimum (Fig. 2(h)), which has a bonding situation
reminiscent of that in Fig. 2(e). Indeed, the rather
acute Si±O±Si bond angle (130°) is recovered, despite the fact that the O H bond distance (2.30
must be deemed too long to be classi®ed as a
A)
hydrogen bond. Surely, such ``intramolecular hydrogen bonds'' have only negligible in¯uence on
the bond angle of the Si±O±Si bridge. Rather, it is
the overall ligand-backbone and ligand±ligand
Pauli repulsions that become decisive for determining the Si±O±Si bond angles.
The global minimum for Si2 O6 H4 comprises the
Si2 O2 ring based cluster (Fig. 2(i)). This
…HO†2 ˜Si—O2 ˜Si—…OH†2 cluster displays D2 symmetry. It resembles the corresponding Ge based
system [10]. It is 114 kJ/mol (M) lower in energy
than the chain structure (Fig. 2(h)), and consequently water addition to the Si@O bond in
OSiO2 Si…OH†2 becomes exothermic by 265 kJ/mol
(M). This tells of a somewhat lower reactivity of
60
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
the second Si@O group, as compared to the ®rst,
which is in agreement with the results on the
monomeric systems using the (L) basis set. Interestingly, if the ring cluster is formed from two
SiO…OH†2 molecules (Fig. 2(j)), 386 kJ/mol (M) is
released, whereas the formation of the chain
structure only releases 272 kJ/mol (M).
Addition of a third water molecule, allows the
reaction routes to converge to the single-bridged
…HO†3 SiOSi…OH†3 molecule (Figs. 2(k) and (l)).
This molecule is the silica dimer, and it is of great
importance for understanding the chemistry of
silicates. Consequently, several investigations have
been conducted to establish structures and stability properties. The computational problem evolves
mainly around the issues how to achieve a correct
balance between ionic and covalent contributions
to the Si±O bonds, in conjunction with a correct
description of the intramolecular hydrogen bonding. Depending on the magnitude of each of these
e€ects, di€erent structures, and in particular different Si±O±Si bond angles, are obtained for the
global energy minimum. In the study by Teppen et
al. [21], three conformations, di€ering in the
number of hydrogen bonds (1, 1.5 or 2), were investigated by employing HF and MP2 methods. A
structure possessing two hydrogen bonds and C2
symmetry appeared to be the global energy minimum at the MP2 level. However, this structure
was found to be a transition state at the HF level,
whereas the two other structures came out as true
minima. An optimal structure with C2 symmetry
were
and two intramolecular H bonds (2.08 A)
also found for the Ge2 O7 H6 system [10]. Only little
help in deciding on the global minimum on the Si
system is obtained from this observation, since the
strengths of such H bonds are signi®cantly smaller
for the Si systems than for the Ge compounds. The
Si±O±Si bond angles are also in general wider than
the Ge±O±Ge angles (118° for Ge2 O7 H6 ). In the
present study, the C2 structure of …HO†3 SiOSi
…OH†3 (Fig. 2(k)), with a 134° Si±O±Si angle and
is found to
two very long O H bonds (2.60 A),
be a transition state with a small symmetry
breaking frequency using B3LYP and the (M)
basis set. An energy minimum for the (M) basis set
is obtained for a symmetry broken structure (Fig.
2(l)), which just has one long O H bond (2.22
Interestingly, the greater Si±O±Si bond angle
A).
(141°) is in good agreement with what is found in
a-quartz (144°) [1].
The ®nding that the C2 structure is a TS on the
B3LYP PES is in contradiction to a recent report
by Pereira et al. [27] on silicate clusters. That work
reports BLYP calculations, which have the C2
structure with a 132° Si±O±Si angle as the global
minimum. As their structure seems quite similar to
the TS with C2 symmetry obtained in the present
work, it seems reasonable to doubt their conclusion. With the BLYP functional, we obtain two
minima when employing the (S) basis set: one resembling the C2 , and another the C1 structure. The
symmetry broken structure becomes the global
minimum by 2 kJ/mol. Improvement of the basis
set to (M) results in the C2 solution becoming a
transition state also for the BLYP method. Thus,
the C1 solutions produced by the B3LYP functional and HF cannot be deemed as artifacts due
to HF exchange, as BLYP does not contain the
HF exchange component. When ®nally the basis
set in the B3LYP calculations is increased to (L),
both structures come out as true energy minima.
They are now equally stable, but still display two
distinctly di€erent Si±O±Si bond angles (134° and
140°, respectively). The H bonds in both systems
are still very long, so it becomes obvious that the
two conformers are the result of two equally important arrangements of SiO4 -tetrahedra in the
silica dimer. In bulk silicates, it is the connectivity
to the counter-cations that determines which type
of chain, twisted (C1 ) or straight (C2 ), will form the
material. It is interesting to note that a-quartz is
built up by helical chains of SiO4 -tetrahedra, an
arrangement based on the above C1 structure, and
that it is the handedness of the chains that renders
quartz its optical activity [1].
There are two ways to introduce the fourth
water molecule to the Si2 O4 …g† system, starting
from the single-bridged …HO†3 SiOSi…OH†3 molecule (Fig. 2(l)). One route involves the bridging of
two Si±OH groups e.g., as indicated in Fig. 2(n),
while the second possibility comprises hydrolysis
of the remaining Si±O±Si bridge. While hydration
is trivially exothermic (42 kJ/mol (M)), the formation of two Si…OH†4 …g† (Fig. 2(m)) from
…HO†3 SiOSi…OH†3 …g† ‡ H2 O…g† is endothermic by
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
24 kJ/mol (M) and 19 kJ/mol (L). The relevance of
this value for fully solvated species can though be
questioned. However, the energy gain in
Si2 O7 H6 H2 O…g† is to a large extent cancelled by
hydrogen bonding between the two Si…OH†4 …g†
fragments, although the water ligand renders the
chain species some extra stability. The e€ect of
further solvation is also expected to be quite similar both for Si2 O7 H6 H2 O…g† and the two fragments, as both systems have eight OH groups
available for hydrogen bonding to surrounding
H2 O. The remaining argument pro or con bridge
cleavage is the shape of the space in water occupied by the solvated species. The ellipsoid that
encloses the elongated Si2 O7 H6 H2 O…g† chain
might be a smaller distortion to the structure of
61
water than the two spheres around the Si…OH†4 …g†
fragments. In that case, the polymer gains additional stability. It can be noted that the formation
of Si2 O7 H6 H2 O…g† is much too exothermic (81
kJ/mol) using the (S) basis set, despite a quite good
structure. The origin of this e€ect lies in the two
short H bonds that are formed in Si2 O7 H6 H2 O…g†, which require polarization functions on O
for correct energetics. It can also be noted that the
assymetric Si2 O7 H6 H2 O…g† molecule has a wide
Si±O±Si bond angle (140°).
3.3. PO2 …OH †…g† ‡ nH2 O
The structure of PO2 …OH†…g†, metaphosphoric
acid, is planar (Fig. 3(a)). The O@P@O bond angle
Fig. 3. Structures in the PO2 …OH† ‡ 3H2 O system: (a) PO2 …OH†…g† …Cs †, (b) and (c) PO2 …OH† H2 O…g† …C1 †, (d) PO…OH†3 …g† …C3 †,
(e) P…OH†3 H2 O2 …g† …C1 †, (f) P…OH†5 …g† …C1 †,(g) and (h) PO…OH†3 H2 O…g† …C1 †, (i) and (j) PO…OH†3 2H2 O…g† …C1 †,
(k) PO…OH†3 3H2 O…g† …C3 †, (l) and (m) …C1 † together with relative stabilities and energetics for some hydrolysis reactions.
62
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
of 134±135° (M) and (L) is signi®cantly greater
than that of the puckered vanadium analogue
VO2 …OH† (112°) [5], which tells of the greater
¯exibility in accommodating electron pairs of local
p symmetry (in M@O), when 3d orbitals on M are
available for bonding. Similar to the O@Si…OH†2
system, two kinds of complexes can be formed
with water. A slightly smaller exothermicity (42 kJ/
mol (M) and 43 kJ/mol (L)) is observed when
forming the four-coordinated PO2 …OH† H2 O…g†
complex (Fig. 3(b)). The P OH2 bond is though
(M) and 2.12 A
(L)), despite
rather long (2.18 A
that no hydrogen bonds are observed. This long
bond and the reduced reactivity are both results of
the better covalent bonding in the two P@O
groups, as compared to an Si@O unit. The threecoordinated complex (Fig. 3(c)) formally contains
two hydrogen bonds, but the bond to the P@O
(M)). The good
unit is long (O H: 1.69±2.20 A
H bonding to the P±OH group gives this complex
a stability that is marginally (3 kJ/mol (M) and 4
kJ/mol (L)) below the complex in Fig. 3(b).
Water addition to one of the P@O bonds of the
PO2 …OH† H2 O…g† complex in Fig. 3(c), forming
orthophosphoric acid OP…OH†3 (Fig. 3(d)), results
in a further 108 kJ/mol (M) and 118 kJ/mol (L)
stabilization. Thus the total addition reaction from
meta- to orthophosphoric acid becomes exothermic by 153 kJ/mol (M) and 165 kJ/mol (L). This is
about 100 kJ/mol less than what was found in the
corresponding vanadium system [5]. This di€erence is probably due to the lower stability of the
V@O bonds in VO2 …OH†…g†, as compared to P@O
in PO2 …OH†…g†, which generates the higher water
anity for the former system. While the latter
system displays a close to tetrahedral oxygen coordination, the PO…OH†3 …g† molecule displays
signi®cant symmetry breaking, i.e., 116° and 102°
(M)/(L) for the O@P±O and O±P±O bond angles,
respectively. This observation is in accord with the
proposed e€ect from 3d orbitals on ligand coordination, i.e., symmetry broken coordination in
the 3p systems Si…OH†4 …g† and OP…OH†3 …g†,
whereas the 3d systems Ti…OH†4 …g† and
OV…OH†3 …g† both display close to tetrahedral coordination around the central atom. The overall
symmetry of PO…OH†3 …g† is C3 , which also is
lower than for the V system.
The remaining P@O bond in PO…OH†3 …g† can
react further with water. Two reactions are envisaged, one where water acts as reducing agent to
form P…OH†3 H2 O2 …g† (Fig. 3(e)) and a second
where P…OH†5 (Fig. 3(f)) is produced. The water
induced reduction is endothermic by as much as
429 kJ/mol (M), re¯ecting the stability of P(V) as
compared to P(III). In contrast, the formation of
P…OH†5 is endothermic only by 42 kJ/mol (M) and
34 kJ/mol (L), which can be directly translated to
an activation energy for oxygen exchange on
phosphates in water. Furthermore, in as much as
water can be understood to model a more general
nucleophile with hydroxyl groups, this energy estimates the barrier height for activating phosphate
transfer between two nucleophiles.
Employing the second H2 O in hydrogen bonding produces PO…OH†3 H2 O…g† complexes, which
are all more stable than forming the P…OH†5 …g†
molecule. There are two structures for this complex, due to that there are two possible sites for
binding water in PO…OH†3 …g†. The water molecule
can either form a bridge between two P±OH
groups (Fig. 3(g)) or between the P@O unit and
one P±OH group (Fig. 3(h)). Despite that one of
the hydrogen bonds in the former complex is rather long, it is 71 kJ/mol (M) more stable than
P…OH†5 …g†. If water addition to PO…OH†3 …g† is
considered, the reaction to form the PO…OH†3 H2 O…g† complex in Fig. 3(g) becomes exothermic
by 29 kJ/mol (M). This value is very similar to the
reaction that gives Si…OH†4 H2 O…g†, which displays a similar bonding situation. An additional 13
kJ/mol (M) energy gain can be obtained for
PO…OH†3 H2 O…g† if the complex in Fig. 3(h) is
allowed to form. The higher stability results from
the function of the bridging water molecule as an
equilizing agent between the P@O and P±OH
units. This works as water partially provides a
proton to the former and partially removes the
proton from the latter. This tendency for local
water mediated P±OH to P@O proton delocalization, which is seen already when employing a single H2 O…g† as bridge, is typical for Brùnsted acids.
This type of local proton delocalization is most
pronounced in the strong acids H2 SO4 …g† and
HClO4 …g†, and is treated further in the same context [4].
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
Allowing a second water molecule to bridge
between two P±OH groups, and forming the
PO…OH†3 2H2 O…g† complex depicted in Fig. 3(i),
is found to release an additional 39 kJ/mol (M).
However, an even more stable structure is achieved
by the formation of a water dimer ligand. This is
consistent with what was observed for the Si system, and the dimer complex (Fig. 3(j)) is an additional 10 kJ/mol (M) lower, thus resulting in a net
49 kJ/mol (M) exothermicity for the addition of
the second water molecule. Here, it is gratifying to
note the signi®cant shortenings of the O H
bond distances and how these are accompanied by
the corresponding elongations of the O±H bond
distances (see Table 3).
Finally, some representatives for the addition of
a third water ligand to PO…OH†3 …g† are included in
63
the discussion. The PO…OH†3 3H2 O…g† complex
in Fig. 3(k) preserves the C3 symmetry of the
parent molecule by using each water ligands to
bridge between the P@O group and one P±OH
unit. However, water monomers are not optimal
ligands. Equally stable to the structure in Fig. 3(k)
is the complex in Fig. 3(l), which has the same
con®guration of H bonds between the core molecule and ligands as does SO2 …OH†3 3H2 O…g†
complexes that display deprotonation [4]. Using
the (S) basis set, proton transfer is indeed observed
for this structure. However, at the improved and
more reliable (M) level the PO±H bond distance
but stays atbecomes rather elongated (1.04 A),
tached to the PO…OH†3 kernel. The energy release
on binding the third water is only 27 kJ/mol (M),
which indicates that this position represents a
Fig. 4. Structures in the P2 O5 ‡ 3H2 O system: P2 O5 : (a) OPO3 PO …D3h †, (b) O2 POPO2 …C2 †; P2 O6 H2 : (c) 2 PO2 …OH† …Cs †,
(d) O2 POPO…OH†2 …C1 †, (e) …HO†OPO2 PO…OH† …C2v †, (f) …HO†OPO2 PO…OH† …C2h †; P2 O7 H4 :(g) …HO†2 OPOPO…OH†2 …C2 †, (h) …C1 †,
(i) …C2 † and (j) …C1 †; P2 O8 H6 : (k) 2 PO…OH†3 …C3 † and (l) …HO†2 OPOPO…OH†2 H2 O …C1 † together with relative stabilities and energetics for some hydrolysis reactions.
64
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
sub-optimal site in PO…OH†3 2H2 O…g†. The global energy minimum for PO…OH†3 3H2 O…g† is
shown in Fig. 3(m), and it contains one water dimer and one monomer as ligands, each bridging
between the P@O and one P±OH group. This
structure is 14 kJ/mol (M) below the complex in
Fig. 3(l), an e€ect that is caused by the favorable
combination of two water bridges to P@O in
conjunction with a …H2 O†2 ligand. The fact that all
PO…OH†3 3H2 O…g† complexes do not form ion
pairs suggests that PO…OH†3 is a weaker acid than
SO2 …OH†2 , even in the nano-scale clusters.
3.4. P2 O5 …g† ‡ nH2 O
There are two important structures for P2 O5 …g†
of which the least stable is a triple-bridged
O@PfO3 gP@O cluster of D3h symmetry (Fig.
4(a)). The molecule is structurally related to similar molecules with three oxygen bridges that have
been determined for the Sc, Ti, V, Al, Si and Ge
systems [3,6,10]. In the majority of cases, this
structure lies somewhat above the global energy
minimum, as is also the case for P2 O5 …g†. Hence,
the single-bridged O2 POPO2 molecule (Fig. 4(b)) is
97 kJ/mol (M) more stable than the D3h cluster.
Interestingly, this ordering is opposite to what was
found for V2 O5 …g†. Repeatedly, the origin of this
di€erence is most likely found in the greater capacity of the early 3d elements, as compared to 3p,
to accommodate electron rich ligands.
Hydrolytic cleavage of the P2 O5 chain, with its
rather open P±O±P bond angle (134°), can be
employed to model the general cleavage of such
single bridges, as was done in case of the oxygen
bridged binuclear transition metal oxyhydroxides
[10]. Here, hydrolysis results in the formation of
two
of metaphosphoric
acid
molecules,
PO2 …OH†…g† (Fig. 4(c)), and the reaction is exothermic by 48 kJ/mol (M). This comparatively
large value is caused by the general instability of
the two P@O groups in each metaphosphate unit
Fig. 5. Structures related to …P2 O5 †2 : (a) P4 …g† …Td †, (b) P4 O6 …g† …Td † and P4 O10 …g† …Td † together with the energetics for oxidation
processes, dimerization of P2 O5 …g† and hydrolysis of P4 O10 …g†.
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
toward reaction, which result in elongated P±O
bonds in the P±O±P bridge. Indeed, molecular
P2 O5 …g† is generally known to dimerize, forming
P4 O10 …g† (Fig. 5(c)) with Td symmetry [1]. This
molecule has a P4 O6 core (i.e., the P(III) oxide
shown in Fig. 5(b), which also has Td symmetry),
in which each P atom has three P±O bonds, completed by one P@O on each P. This dimerization
reaction reduces the number of P@O groups, and
is consequently highly exothermic (491 kJ/mol (M)
and 536 kJ/mol (L)). However, the P4 O10 …g† molecule contains six P±O±P bridges that can be hydrolyzed. This results in the formation of four
PO…OH†3 …g† molecules, a process that is associated with rather small reaction energies. Due to
the repulsion between the individual P units in the
P4 O10 …g† cluster, does the reaction though come
out quite exothermic (215 kJ/mol (M) and 244 kJ/
mol (L)). From the fact that P4 O10 …g† does not
represent a ®nal product of hydrolysis, it can be
concluded that a discussion concerning binuclear
clusters is just as informative on hydrolysis. The
P4 O10 …g† molecule still serves as a good test on the
quality of the computational results. A comparison with experimental data shows very close
agreement with results obtained using the large (L)
(M) and 1.43 A
(L) vs. 1.43
basis set (P@O: 1.45 A
exp.; P±O: 1.63 A
(M) and 1.61 A
(L) vs. 1.60 A
A
exp.; P±O±P: 125° (M) and 124° (L) vs. 123° exp.)
[28]. Similar agreement is also found for the
P4 O6 …g† molecule, as well as for the P4 …g† molecule
(Fig. 5(a)). By looking at the energetics for the
oxidation P4 …g† and P4 O6 …g†, the stability of the
P(V) oxides becomes apparent (cf. Fig. 5).
As a consequence of the reactivity of the P@O
groups, the energetically favored alternative to
dissociative water addition comprises reaction
with one of the P@O bonds. This process is exothermic by 186 kJ/mol (M) for formation of the
chain structure O2 ˜P±O±PO…OH†2 (Fig. 4(d)). The
central P±O±P bond angle (131°) is quite insensitive to this addition, but the two P±O bond distances are a€ected in an unsymmetrical fashion
as an intramolecular H bond is
(1.59 and 1.69 A),
formed (O H: 2.00 A).
Despite the extra stabilization, clusters based on
hydrated P2 O2 rings are more stable than the hydrated chains. There exists two isomers for the
65
…HO†O˜P—O2 ˜P—O…OH† cluster. The C2v structure (Fig. 4(e)) is 42 kJ/mol (M) more stable than
the chain, and it can be viewed as the product of
water addition to one of the P±O±P bridges in
OPO3 PO…g†. The latter reaction comes out exothermic by 131 kJ/mol (M). The C2h structure (Fig.
4(f)), which displays inverted ligand arrangements
on the P atoms, is found to be 1 kJ/mol (M) more
stable than the C2v cluster. Dimerization of two
PO2 …OH†…g† molecules, forming the P2 O6 H2 …g†
structure in Fig. 4(f), is exothermic by 181 kJ/mol
(M), which repeatedly re¯ects the instability of the
P@O units in metaphosphoric acid.
Addition of a second water molecule yields the
pyrophosphoric acid, P2 O7 H4 . Similar to the silica
system, this species is of great importance. In this
case it is due to the fact that it is the primary
condensation product of orthophosphoric acid.
This reaction has been the topic of several studies
during recent years [29±31]. However, all investigations so far have failed to describe the full
structural complexity of the pyrophosphoric acid
system. In the present work, we ®nd four unique
energy minima, which di€er in the orientations of
the OH groups with respect to the P±O±P bridges.
All structures di€er in the P±O±P bond angles, and
their reactivity towards hydrolysis di€er. The least
stable structure (Fig. 4(g)) displays one
P±OH OH±P alignment and no symmetry ele is too
ments. The H O bond distance (2.30 A)
long for it to be classi®ed as a hydrogen bond. The
structure is quite similar to the symmetry broken
form of Si2 O7 H2 …g†, and the P±O±P bond angle is
consequently quite open (139°). 2 kJ/mol (M) is
gained if another pair of P±OH groups are allowed
to interact. This gives the structure (Fig. 4(h)) C2
symmetry with two long hydrogen bonds (2.06 A).
The P±O±P bridge is slightly more acute (133°),
due to the changed bonding. Again, the structure
has similarity to the Si2 O7 H2 …g† system, and more
precisely its symmetric form. If the ligands on one
P atom are rotated so that an P±OH O@P
bridge is allowed to form, then an additional 14 kJ/
mol (M) is gained. In this structure (Fig. 4(i)), a
is formed, while
proper hydrogen bond (1.95 A)
negligible interaction remains between the pair of
As a result, the
P±OH groups (O H: 2.38 A).
P±O±P bond angle becomes somewhat more bent
66
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
(125°). The unsymmetrical arrangement of the ligands with respect to the bridge gives the structure
no overall symmetry. An additional 5 kJ/mol (M)
is gained if two P±OH O@P bridges are formed
(Fig. 4(j)). The two hydrogen bonds come out ra despite the fact that the P±O±P
ther long (2.16 A),
bond angle is reduced even further (117°). Thus,
the bond angle is close to the previously reported
range of values (113±119°) [30,31]. In contrast to
the present study, signi®cantly longer hydrogen
were found in these
bond distances (2.28±2.39 A)
investigations.
Formation of the fourth and most stable
…HO†2 OPOPO…OH†2 structure in Fig. 4(j) from the
P2 O6 H2 …g† cluster in Fig. 4(f) is exothermic by
132 kJ/mol (M). It is noted that continued polymerization of this P2 O7 H4 …g† structure through
condensation of the terminal P±OH groups is
straight-forward, as there is one such non-hydrogen bonded group available on each P atom.
Naturally, polymerization can occur starting from
any of the four structures, but these processes are
expected to result in lower stability for those
polymers.
A main ®nding of this investigation comprises
the window of energies associated with the hydrolysis reaction for the four isomers (Figs. 4(g)±
(j)). While hydrolysis of the P±O±P bridge comes
out exothermic by 15 kJ/mol (M) in case of the ®rst
P2 O7 H4 structure (Fig. 4(g)), the reaction turns
endothermic by 7 kJ/mol (M) when considering the
most stable binuclear isomer (Fig. 4(j)). This span
in energy values re¯ects the values previously
published in the literature, as obtained using a
variety of methods and basis sets. One straightforward conclusion, which can be drawn from this
observation, is that the relative stability of pyrophosphate molecule as compared to the mononuclear H3 PO4 molecules entirely determined by the
amount of water available.
The ®nding that the condensation±hydrolysis
processes are determined by the reaction conditions on a nanometer length scale is not unique to
the phosphorous system, but was also found for
several transition metal systems [6]. Indeed, the
energetics for the water chemistry of the phosphate
system is not very di€erent from the silica system,
although the latter system displayed a somewhat
higher endothermicity upon hydrolysis of the
corresponding Si±O±Si bridge. In contrast, it is
noted in bypass that hydrolytic cleavage of the
oxygen bridge in disulfuric acid was found to be
exothermic [4]. Finally, all four isomers of pyrophosphoric acid have enantiomeric forms, and are
consequently optically active. The possible importance of the handedness of phosphoric acid
chemistry to biochemistry remains to elucidate.
4. Conclusions
The water chemistry of the mononuclear species
SiO2 …g† and PO2 …OH†…g†, as well as the binuclear
systems Si2 O4 …g† and P2 O5 …g†, has been investigated. The stabilities and reactivities of Si@O and
P@O groups, as well as Si±O±Si and P±O±P
bridges toward hydrolysis were studied. Systematic
investigation of structures and stabilities of hydrolysis products was performed by means of a
consecutive addition of molecular water, starting
with anhydrous forms the binuclear compounds,
and ending up with the corresponding mononuclear hydroxides. The formal oxidation states +IV
and +V were maintained throughout this study, as
neither the Si nor the P systems were found prone
to reduction by water.
The most stable monomeric products were
concluded to be the four-coordinate Si…OH†4 …g†
and PO…OH†3 …g† molecules or hydrated forms of
these. Higher coordination numbers were also
studied, as these could be of fundamental importance as reaction intermediates in e.g., phosphorylation processes. In particular P…OH†5 …g†, which
has a trigonal bipyramid structure, was found to
be 42 kJ/mol (M) above the H3 PO4 …g† ‡ H2 O…g†
asymptote. Again, local conditions are expected to
in¯uence these relative stabilities signi®cantly.
Particularly stable compounds of Si…OH†4 …g†
and OP…OH†3 …g† with water is obtained for water
dimer ligands. Interestingly, a tendency toward
intramolecular proton delocalization could be
noted for PO…OH†3 if the ligand bridges between
the P±OH and P@O groups. This tendency for
delocalization is hardly seen for the …H2 O†2
bridging between two Si±OH. The use of a trimer
water ligand increased the degree of proton
J.R.T. Johnson, I. Panas / Chemical Physics 276 (2002) 45±68
transfer in the PO…OH†3 system, although complete deprotonation did not occur. A much smaller
e€ect was noted for the Si…OH†4 system. This difference between the Si and P systems is taken to
relate to the relative micro-acidity of the two core
compounds. It is implied that this drive for water
mediated intramolecular proton delocalization
occurs according to a common mechanism for the
acids H3 PO4 , H2 SO4 , and HClO4 . The cause for
this is an e€ort to reduce the potential di€erence
between the acidic M±OH and the electron rich
M@O groups. By using this functionality, the
phosphates can provide nano-scale bu€ering systems, and thus allow for an ecient control of
proton activity.
The structures of the binuclear systems …HO†3
Si±O±Si…OH†3 …g† and …HO†2 OP±O±PO…OH†2 …g†
were addressed in detail, and the ordering of isomer stabilities were discussed based on intramolecular interactions. Both systems were global
minima along the water addition reaction coordinate. Thus cleavage of the oxygen bridges through
hydrolysis were found to be endothermic for both
systems, and reversely the condensation of two
Si…OH†4 …g† or PO…OH†3 …g† exothermic. The
P±O±P bridge displayed close to 17 kJ/mol lower
stability toward hydrolysis than the Si±O±Si
bridge, which renders the former near zero reactivity.
The understanding that the P±O±P bridge in the
biphosphates does not display particular exothermicity upon hydrolysis has been around for
several years in the context of biosynthetic chemistry [30]. This is further emphasized here as gas
phase hydrolysis of the four most stable isomers of
…OH†2 OP±O±PO…OH†2 were found to display energetics that vary in the range )14 to +7 kJ/mol.
This indeed implies that water activity and the
relative hygroscopicity of reactants versus products comprise decisive factors for the equilibrium
concentrations of the two. Thus, extreme constraints must be imposed on the nano-scale reaction conditions for hydrolysis of the P±O±P
bridges in ATP, if these bridges were to be the
``energy currency'' of the cell. Having said this, one
possible function of the ATP hydrolysis mechanism, which would be consistent with the above
®ndings, is the precise control of local water ac-
67
tivity e.g., in the vicinity of an active site in an
enzyme. Indeed, condensation reactions are central in biosynthetic processes, and the removal of
the released water must be considered vital to the
function of the enzyme.
In conclusion, the results of the present study
cannot be employed to support the simplistic understanding of the P±O±P bridge in ATP as a
carrier of an exact energy quantum for release at a
particular reactive site. More profoundly, quantum chemical calculations suggest the pyrophosphate and phosphate pairs to be decisive in
providing a nano-scale bu€er for both water and
proton activity. Indeed, it is strongly suggested
that consumption of ATP during biosynthesis
re¯ects precisely this micro-bu€ering function,
and that this role of ATP and its hydrolysis
products can be translated into a Gibbs free energy
equivalent.
Acknowledgements
This work was supported by the Swedish Natural Sciences Research Council (NFR). The National Supercomputer Center (NSC) in Link
oping
is acknowledged for allotment of computer time.
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