Документ взят из кэша поисковой машины. Адрес оригинального документа : http://beams.chem.msu.ru/sotrudniki/larin/CC_EF1f.doc Дата изменения: Wed Jan 5 02:00:22 2000 Дата индексирования: Mon Oct 1 20:30:54 2012 Кодировка:

Original paper submitted for publication in
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY






EVALUATION OF ELECTRIC FIELD WITHIN PORES OF ALUMINOPHOSPHATE SIEVES

A.V. LARINa, C. HANSENNEb, D.N. TRUBNIKOVa, D.P. VERCAUTERENb*

aDepartment of Chemistry, Moscow State University, Leninskie Gory,
Moscow, B-234, 119899, Russia
bLaboratoire de Physico-Chimie Informatique, FacultИs Universitaires
Notre Dame de la Paix, Rue de Bruxelles 61, B-5000 Namur, Belgium







TOTAL PAGES 22

TABLES 3

FIGURES 6




*) Corresponding author
ABSTRACT

A new way of evaluation of the electric field (EF) in aluminophosphate
(ALPO) sieves is illustrated based on the propagation of multipole moments
distributed over atomic sites for arbitrary ALPOs of ratio Al/P = 1. The
atomic multipole moments (AMMs) are evaluated for all crystallographic
independent atomic types of ten ALPO structures within the scheme developed
by Saunders et al. considering the electron density computed with the
CRYSTAL98 code at the periodic density functional theory (PDFT) level and
different basis sets. The method uses calculated AMMs to calibrate
approximate dependencies and allows the construction of molecular charge
distribution for any sieve in two steps. First, atomic charges are
evaluated using analytical expressions of the charges fitted as functions
of the framework geometry. Second, high AMMs up to hexadecapole are
approximated for all atomic positions using a cumulative coordinate scheme.
Differences between calculated and approximated EF values within the porous
space available for adsorbed molecules are discussed.

Keywords : periodic density functional theory, atomic multipole moments,
aluminophosphate sieve, electric field, electrostatic potential

INTRODUCTION

Modern selection of porous crystalline materials appropriate for studying
adsorption or chemical processes should ideally be done on the basis of the
wider list of candidates and thus would require a quick screening method.
Theoretical hybrid quantum mechanics / molecular mechanics (QM/MM)
approaches are only in their infancy for the study of microporous materials
and even more for mesoporous due to the problem of long range electrostatic
interactions [1, 2]. The two main hindrances are the correct modeling of
the MM part and the boundary domain of the QM/MM part. Additionally, with
the fundamental importance of electrostatic terms in QM/MM approaches [3],
its knowledge is often extremely useful to predict the favored location of
physisorbed molecules to develop more general adsorption models or to
initialize molecular dynamics simulations [4]. Therefore, together with the
calculation of the electrostatic potential (EP), it is crucial to touch the
question of the electrostatic field (EF) evaluation whose correct solution
is absolutely necessary to reveal the most occupied adsorption sites and
assign them with a particular framework structure. So, the aim of our study
is to use data obtained by periodic ab initio computation with the CRYSTAL
code [5] and to be able to transfer them in a correct way for the EF
simulation from several frameworks to other similar materials. In this
sense, with the exception of all-siliceous mordenite where nearly constant
EP values were used to conclude on small EF values in the centre of the
cylindrical mordenite channel [6], we do not know any work devoted to EF
analyses with periodic HF (PHF) or DFT (PDFT) in porous materials. The EF
at the atomic equilibrium positions in an isolated crystal or molecule
should be zero. Non zero EF value obtained in the SCF type calculations is
mainly created by artificial wave function forces [7]. The analyses at the
EF values at the atomic sites of the adsorbate are justified being non zero
even if these values are also perturbed by the same wave function forces.
Aluminophosphate (ALPOs) present a perspective class of microporous
materials which have been already widely applied as catalysts at industrial
level. In earlier publications, we proposed the application of a cumulative
coordinate (CC) method to evaluate the atomic multipole moments (AMMs) and
subsequent EP within such materials [8-10]. A precision of 30 % was
achieved for the EP approximation in AlPO4-31 (ATO) at the B3LYP/3-21G
level, which was considered as a good qualitative picture [10]. A first
reason which limited a more quantitative EP construction was the
insufficient correlation \r\ ( 0.9 with respect to the CC proposed for the
atomic O dipole due to a very important EP contribution of the O dipoles
[8]. A higher EP accuracy, around 17 %, was however achieved when we used
the same AMM approximations for all T atoms (Al and P) and O quadrupoles
and calculated O dipolar moments [10]. The second reason of the
insufficient EP precision was the consideration of limited types of
approximated AMMs [8-10], more precisely, considering only the octupoles at
the T atoms and dipole and quadrupole at the oxygens. Other AMMs were
indeed assumed as zero in our previous works [8-10]. We also remind that
the T octupoles are the lowest AMMs allowed by strict Td group point
symmetry of the atomic position TO4. The third reason was the consideration
of the nearest atomic neighbors only in the analytical expressions used as
approximations. Finally, the choice of basis set in ref.10 deserves more
discussion. It was indeed shown that the role of the high order AMMs in the
total EP value is of minor importance as compared to the contributions from
the atomic charges [10], and we demonstrated that the difference between
the total EP and the one created by the charges only at the 6-21G** level
is around 100 % for the MeAPO-39 (ATN) sieve [8]. It was finally shown that
the 3-21G basis is the most "ionic" one throughout the STO-3G, 3-21G, 6-
21G**, and 8-511G*(Al)/8-521G*(P)/8-411G*(O) series [9], which is in
contradiction with the known estimates of atomic charges, for example, from
fine structure X-ray spectroscopy [11]. In this work, we thus will consider
two basis sets STO-3G, 6-21G**, which result in less ionic charge
distributions relative to the one with 3-21G and for which the role of the
contributions from the high order AMMs to the EP and EF are larger relative
to the one of the atomic charges. The EF will then be simulated in two
sieves, which are either used or not in the ALPO series to calibrate the
AMM approximations. This will give a qualitative figure of the EF
distribution in the pores which is useful for discussion of any adsorption
process and which, to our knowledge, was never presented at the ab initio
level for these types of sieves.
In the next part, we shortly present the theory summarising ref. [8-
10] followed by explanations on the computational aspects as well as on the
models of the considered ALPOs. In the main part of the paper, we discuss
the CC approximations obtained with B3LYP and different basis set levels.




THEORY OF THE AMMs APPROXIMATION


Distributed multipole analyses as used herein were developed [13] as a
continuation of the Mulliken partition scheme of the electron density. As
explained in ref. [8], Stone's expression allows the development of simple
analytical approximations for the atomic multipole moments (AMMs) of a
given crystallographic independent atom QLm(A) (L and m being the order and
component, m = -(2L+1), ., 2L+1, of the AMM, respectively) with respect to
the charge and geometry of respective fragments including N neighbours of A
[8, 9]. The coordinates for the charge and geometry dependences of the AMMs
are deduced as:

QLm(A) = aLRLm(A) + bL
(1)

where aL and bL will be fitting parameters, and the RLm(A) functions
correspond to the unnormalized functions XLm(A,i) as considered in
CRYSTAL [5]:


As we discussed already [8-10], we also decided to consider, instead of
the coordinate form (equation 2), a modified or "scaled" form:

which includes a term inversely proportional to the distance diA between
atom A and its i neighbour, diA = ((Xi - XA)2 + (Yi - YA)2 + (Zi -
ZA)2)1/2 with an exponent K which could be 0 or (G(L + 1), G being an
empirical value which choice should be discussed. As will be shown below,
the choice of G is important for the precision of the fitting of the
AMMs. Previous results [8-10] were obtained at either G = 2, or with a K
= 0 (that is equivalent to equation 2). Expressions for XLm can be found
in ref. [14].


APPROXIMATION OF THE MULLIKEN CHARGES


COMPUTATIONAL ASPECTS

The electron densities of ten aluminophosphate models (ALPOs,
Table 1) were computed via the CRYSTAL98 code [5] with the hybrid B3LYP
functional and the STO-3G and 6-21G** basis set levels. The ALPO sieves
were chosen owing to their relatively small size elementary unit cell (UC)
and hence with a small number of AO per UC. The X-ray diffraction (XRD)
structures were optimized with the GULP code [17] and Catlow force field
[18]. The Mulliken atomic multipole moments (AMMs) up to the 4th order were
calculated within the scheme developed by Saunders et al. [13].
All the cumulative coordinate (CC) equations above require the
estimation of the Mulliken or other type Q00(i) charges (i = Al, P, and O).
As first estimation, we applied simple analytical charge dependences for
each atomic type [12, 15] combined to an iterative procedure to achieve a
"neutral" UC. As no particular influence of the ALPO topology on the
charges was observed between the sieve types, the charge dependences were
fitted over all ALPOs (with exception of AlPO4-C in Table 1). At the first
iteration, the charge approximations were considered in the shortened forms
while taking into account only the geometrical parameters, i.e., average T-
O distance, tetrahedral distortion for the T atom, thus without considering
the charges of the neighbour atoms, i.e., the O charges for the Al or P
atoms. Starting from the second iteration, the charge values of the
neighbour atoms calculated at the first step were also taken into account.
When the remaining charge of the UC is minimal (usually some 10-2 e), it is
partitioned between all the atoms to get a neutrality of 10-8 e. The
procedure was applied below in this work to the AlPO4-5 and AlPO4-C types
to evaluate the simulated EF values.
Two new steps were undertaken to increase the precision achieved
earlier for the AMM approximations [8, 9]. First, we varied G in the
shortened series (3) of the AMM decomposition with respect to the charges
of the neighbors. The higher the G value, the more local ED distribution.
The K dependent power (eq. 3) scales the contributions from the remote
charges to the AMMs under study. Second, we analyzed more remote shells,
i.e., secondary order atoms for both T and O atoms as compared to only the
nearest shell in the previous works [8-10]. More precisely, 8 neighbors for
each atom were taken into account. Eight neighbors for O denote the two
nearest TO4 units, while 8 atoms for each T atom mean the fragment T(-O-
T')4.


RESULTS AND DISCUSSIONS


Accuracy of the AMM approximation and atomic geometry

Our first task was to define the list of the sieves used for the AMM
fitting and named below as training set. Advantage of geometry parameters
(T-O distances, T-O-T' angles, etc.) is that they can be measured
experimentally is the sieves. For most of the ALPOs optimized as described
above, the usual maximal deflections of the O-T-O' tetrahedral angles and T-
O distances relative to the average values were limited to 3-4( and 0.05 е,
respectively. Only for the AlPO4-H2 (AHT), one O-Al-O angle is 118.1њ
(deflection 8.7() even after optimization. Without optimization, the Al-O
distances at one Al site of this sieve are strongly overestimated, i.e.,
all are larger than 1.85 е, while usual values are around 1.7 е. Comparing
the calculated atomic multipole moments (AMMs) between AHT and the other
sieves, we observed that the accuracy of the geometry optimization can
influence the results of the CC approximation (Figure 1). Hence the AHT
structure which we consider as distorted will be excluded from the training
set.

Accuracy of the AMM approximation and framework parameters

For the choice of the rest of the training set, the framework density
(FD) was found to be important for the accuracy of the CC approximation. In
order to explain the choice of the sieves for the AMM fitting we addressed
to the behaviour of the low order AMMs for the Al and P atoms (Figures 1a
and b). Namely these AMMs, e.g., T dipoles and quadrupoles (T = Al, P), as
well as the O octupoles vary the most with the structure of the sieves.
Some calculated AMMs (closed circles in Figure 1) do not obey to the linear
CC approximation (lines in Figures 1a and b).
To illustrate this, we present the most emphasized influence of the
choice of sieve type on the fitting. The inclusion of the dense ones and
ATN in the fitting of the P quadrupoles (Figure 1b) lowers drastically the
correlation |r| value from 0.967 to 0.503 and the a2 values from -0.00204
to -0.00105 au. For comparison, the same fitting for P quadrupole at the
B3LYP/6-21G** level without or with dense structures varies in the |r|
values between 0.894 and 0.834. This last variation in |r| is much less
than the one with the P quadrupoles shown in Figure 1b.
The other AMMs already discussed earlier [8-10], e.g., T octupoles, O
dipoles and quadrupoles as well as the Mulliken charges, vary less with the
sieve types taking or not into account geometry optimization of the
framework. One should remind that in our first treatment [8], we did not
find an essential difference between the respective AMM fitting for the XRD
models and the models optimized with the BKS force fields (FF). But later
when using the more accurate Catlow FF, we showed an importance of more
accurate ALPO models for the most precise fittings of the AMMs [9] and
hence for quantitative simulations of the EP. Namely, the precision of the
fitting achieved with the training set only including GULP models falls
while adding to the set a less accurate XRD model of berlinite [9].
As it follows from Table 1, the FD value will be the main separation
criterion between the sieves which AMMs can be accurately approximated
versus the CC (open types shown by open symbols in Figure 1) and the ones
which AMMs cannot be (dense types and ATN shown by closed symbols in Figure
1). We conclude that sieves with a framework density higher than 19.2
T/1000 е3 cannot be recommended within the training set for the CC
approximation of the O octupoles, and T dipoles and quadrupoles. There is
however one exception, i.e., ATN with a FD of 18.0 T/1000 е3 which suggests
that the FD parameter is not a strict criterion. Irrespective of the lower
FD value, the Al quadrupoles (Figure 1a) and P quadrupoles (Figure 1b) in
ATN do not satisfy to the CC approximations as compared to the T
quadrupoles in other "open" types (AEI, AEL, AFI, and CHA). It would thus
require more work to light the reasons of this deflection of the AMMs from
the ones calculated for the other open structures. At the moment, the final
choice of the ALPOs for the training set is thus limited to AEI, AEL, AFI,
and CHA.
We showed the "open", i.e., with small FD, ALPO structures which
finally allow to approximate the AMMs of all L orders which are necessary
for a quantitative EP simulation (Figure 2). Their internal spaces are
diversified enough. Only the CHA type is not shown from the set of the open
structures because its skeleton is better known. It is worth to mention
that another framework parameter was tested to do not influence on the AMM
approximation. The loop configurations of the T atoms, i.e., the connection
types between their secondary neighbors, are the same for the AFI (AlPO4-5)
and ATO types and for the AlPO4-18 (AEI) and AlPO4-34 (CHA) ones [19]. The
first two sieves belong to the different groups, i.e., ATO is dense and AFI
is open (Figure 1), while the second, AEI) and CHA, are both the open
types. The first connection (one cycle between the secondary neighbors) is
included into the AHT and AEL (AlPO4-11) structures which are both open.
But the respective FDs of the sieves with the same connections differ as
much as 19.2 (ATO) and 17.3 (AFI) T/1000 е3 strongly (Table 1) in the first
case. Hence, we suppose that the loop configurations do not correlate with
the accuracy of the AMM fitting.

G optimization

An optimal G value in K = GL + 1 of eq. (3) corresponds to the
maximal |r| correlation of the respective fit for each AMM and type of
atom. The selection of the best G values is explained for the first for
AMMs of Al at the B3LYP/6-21G** level in Figure 3. Examples of thus
determined aL and G values are presented for STO-3G in Table 2. The free
term bL of equation (1) is usually near zero and smaller than its
uncertainty. Hence it can be taken as zero in all cases.
We observed different optimal G values in the K powers (3) for the
AMMs of different atoms (Table 2). It is instructive to compare them. Two
groups of the AMMs could be separated. The main group of the AMMs is
determined based on their higher electrostatic potential (EP) contribution
produced at the point X of internal porous space. The EP contribution is
roughly determined by the ratio of the absolute range of the AMM variations
(QLm(i))max = maxi |QLm(i)|, i running over all atoms of the same type (Al,
P, or O), to the distance diX in the 2L + 1 power, i.e., finally as
(QLm(i))max/diX2L+1. Such a comparison was once done in ref. [9]. The AMMs
of the main group, i.e., O dipoles and quadrupoles, T octupoles, reveal
the same or very close G values with both STO-3G and 6-21G** [15], i.e., 4
for the O dipoles, 6 for the O quadrupoles, 2 or 3 for the T octupoles. The
G values corresponding to the AMMs of the second group of a lower
importance regarding their EP contributions, i.e., T dipoles and
quadrupoles, O octupoles, vary with the basis set.
At the STO-3G level (Table 2), the G difference between the lower AMMs
(L = 1, 2) for the O and T atoms (Table 2) correlates with already known
results [19, 20]. Namely, the sharp difference is observed herein between
the small optimal G values for the QLm(T) atoms and large ones for the
QLm(O), L = 1, 2, m = -2L+1, ..., 2L+1. As shown in Table 3, the high G
value (G = 5) provides a domination of the CC contributions from the
charges of the nearest atoms only. It is exactly the case of the lower AMMs
for oxygen atoms. Its lower order AMMs do not depend on the parameters of
the O atoms in the second shell and the O dipoles are described accurately
by the only angular ((Al-O-P) function at the PHF level and different basis
sets [19]. On the contrary, the T' atoms of the second shell of the T atom
influence its lower order AMMs which are forbidden for a straight
tetrahedral symmetry of the T site. Relevance of a coordinate corresponding
to a tetrahedral distortion of AlO4 to approximate quadrupole quadrupole
coupling Cqq constants (proportional to the electrostatic field gradient at
the nuclei) of 27Al [20] shows that the positions of the four nearest PO4
tetrahedra influence on the resulting field gradient at the Al atom. In
this sense, it is worth to mention the different chemical shifts of 29Si at
various nSi(4-n)Al positions in the aluminosilicates [21] that indirectly
proves the importance of second shell for the Si atom in relevant porous
materials. Examples of thus determined aL and G values will be discussed in
details for 6-21G** elsewhere [15]. One can add that 6-21G** does not
reveal any approximation for the P dipole and worse correlation for the Al
dipole as compared to STO-3G.
The same G ratio for lower order AMMs, i.e., high G values for O and
low G values for T atoms, is justified for 6-21G** basis set with the
exclusion of the Al quadrupoles for which we obtained very high G = 6
(Figure 3). The shift to the larger G values for the Al quadrupoles with
the less "ionic" 6-21G** basis set can be clearly seen in Figure 3 and
could suggest an independence of the remote P charges. An appreciable
change of the AMM values and their contributions relative to the others
upon replacement of a basis set was shown in a previous paper [9]. This
large G = 6 value for the Al quadrupoles coincides with the G value for the
O quadrupoles with both 6-21G** [15] and STO-3G (Table 2) basis sets
relative to the AMM of the P atom. Another example of the Al and O
similarity compared to the P atom was recently observed while fitting the
ALPO charges [10, 12]. This procedure (see "Approximation of the Mulliken
charges") is a part of our technique applied below in order to evaluate the
charges for APC and AFI types. The consideration of the average charge of
the neighbour atoms was extremely important for P and not for Al and O
during an iteration fitting procedure based on the geometrical and charge
characterization of the atomic positions.

Comparison of the approximated and calculated electrostatic field within
the sieve of the training set (AFI)

In this paper we compare the approximated and calculated
electrostatic field (EF) values EF = (Fx2 + Fy2 + Fz2)1/2 , where Fi is
the i cartesian field component, i = x, y, z, using the CC method [8-10].
As a measure of such difference, we use the ratio between approximated
EFapp and calculated EFcal values:

( = (1 - EFapp/EFcal)(100 %
(4)

If one uses the analogous equation (4) for electrostatic potential (EP),
the localized region of the EP error can be easily controlled. As we have
illustrated already [8-10], the line EP = 0 (the bound between the white
and black zones in Figure 4a) where the larger EP errors are observed, can
be traced along the "border" of the ALPO channel or cavity. Similarly, the
ratio (eq. 4) or the deviations between the calculated and approximated EF
can be large around the points named below as the "poles" where EFcal
equals to zero or is small even if the EF approximation is relatively
accurate. As it is illustrated below, an absolute EF value does not
decrease up to zero in any point of the internal space of the APC sieve
considered below. Here, we mean that at the pole the EF satisfies to the
condition d(EF)/dR = 0 (that is generally a minimum) and not to EF = 0. For
a nearly symmetric sphere or a channel inside a sieve, a zero EF value is
obtained in the center due to a reciprocal compensation. Hence, the EF
poles are located in the internal space available for adsorbates and the EF
ratio (eq. 4) is less convenient for an illustration versus (1 -
EPapp/EPcal) [8-10] owing to the more complex positions of the poles. But
the drawback of Eq. (4) is partly compensated by the weaker influence of
the EF approximated at the poles compared to the total interaction energy
(IE) value of adsorbate with the sieve (see next part).
First, we compared the calculated and approximated EF with 6-21G**
for AFI which was used to fit the AMMs. It is a difficult task to determine
the closest position of an adsorbate relative to the framework atoms. The
part of internal space available for adsorbed molecules crudely given via
EP iso-lines by the white zone where EP < 0. This criterion is justified
for cations but leads to a rather overestimated space of the domain
available for a neutral adsorbate if one analyzes the distances from the
white zone to the framework atoms. All the black domain is considered as
forbidden for adsorbate. The EP iso-contours (Figure 4a) were done in the
plane passing through three atoms located in the low right corner, i.e.,
P1, O2, and Al1 with the atomic angle of 176.5њ. The atoms are denoted by
black arrows in Figure 2b and the P1 - O2 - Al1 "branch" is nearly
perpendicular to the plane of 12R window. Respective part of the EF section
is shown in Figure 4a. We observe seven "poles" of the calculated EF whose
(x, y) coordinates can be approximately evaluated as: the central (6, 12)
and two satellites on the top and the bottom adjacent as (6, 14.5), and (6,
7.5), two symmetric ones on the left at (2.5, 19) and (2.5, 3) and the
similar ones on the right at (9, 19) and (9, 3). Within the white zone of
the lowest EF, the deviation of approximated EFapp from calculated EFcal is
maximal at the poles noted but they are lower than 30 % in all the cases.
Using the same order of the poles as numerated above the deviations are 13,
26, 13, 20, 20, 26, and 26 % for all seven minimum (the poles with largest
differences are shown by the arrows in Figure 4b). Hence, we can prove that
the EF is satisfactorily reproduced at the same ALPO which is used for the
AMM fitting.

Electrostatic field prediction within the sieve not included in the
training set (APC)

Secondly, after AFI we tested the EF approximation with STO-3G for the
APC sieve not involved into the fitting of the AMMs using eqs. (1-3). It
was indeed important to evaluate the possibility to apply the EF
approximation to any ALPO structure. Hence both non optimized (XRD [16])
and optimized (GULP [17, 18])) forms of APC were considered. The models
optimized with GULP and Catlow FF are the most accurate or stable (at the
PHF or PDFT levels) ones as we compared [22] over six FF types also
including the FFs available for ALPOs within Cerius 2.0 shell [23].
Meanwhile the XRD models are the most distorted ones, f. e., the XRD model
of APC includes T site with overestimated P-O bond length of 1.59 е and Al-
O bond lengths of 1.77 and 1.79 е. After optimization the distances are
reduced to 1.53, 1.74, and 1.72 е, respectively. Hence, if the
approximation is accurate for the XRD model, it should be more precise for
GULP one. Let consider here the EF approximation in the XRD model of the
APC sieve.
The EF and EP as calculated by CRYSTAL98 are shown in two different
planes (Figures 5 and 6) passing through any three atoms for the XRD model
of the APC form. The atoms which serve as the basic ones for the planes are
shown by white (O2-O5-O5) and black (Al1-O2-P1) arrows in Figure 2c. For
simplicity, the dashed line connects the O5 and O5 type atoms which have
the numbers O66 and O72 in the total numeration. The upper O5 atom is in
the one 4R ring with the third O2 basic atom which is located in opposite
to O5. Respective planes are nearly perpendicular. The first section passes
the internal space under the mentioned 4R window while the second passes
through the space of neighbor channel. The planes cross the two neighbor
channels thus giving more wide comparison of the fitted EF values. As
before, the space available for adsorbed molecules is crudely accepted
within EP < 0 and shown by the white zone (the EP contours are shown in
more details in Figures 5a and 6a). Upper EF value shown in the space
available for adsorbates (white zone) is 0.012 au (Figure 5b) and 0.02
(Figure 6b) that result in non negligible contributions to the interaction
energy (IE) of both the polar (with a non zero dipole) and non polar probe
molecule (see below in this Part). The pole coordinates (X, Y) can be
crudely done as (9, 3), (17, 10), (22, 5), (3, 19) and (9, 10), (7, 17),
(6.2, 1.5), (3, 12), (7.5, 4.5) in the O2-O5-O5 (Figure 5b) and Al1-O2-P1
(Figure 6b) sections, respectively. Respective errors in the EF values at
the pole positions are near -97, -97, -110, -50 % (Figure 5b) and -160,
-140, -140, -87, -160 % (Figure 6b). The respective domains are small for
the GULP optimized and larger for non optimized XRD models. As one can
verify the smaller EF difference between the calculated and approximated
values is obtained for the APC model optimized with GULP. Omitting very
similar illustrations one could compare the smaller differences in the O2-
O5-O5 plane as -48, -54, -48, -24 % at nearly the similar pole positions
shown in Figure 5b. Hence, a badly optimized model as the XRD model of APC
can result in a problem for the EF prediction.
In some cases we however observe the large differences within both XRD
and GULP models, f. e., -160 and -160 % at the (9, 19) and (6, 6) points
(shown by grey arrows in Figure 5b), in the area formally allowed for
adsorbate with our criterion (EP < 0). These points do not correspond to
any EF pole (Figure 5c) and located near EP = 0 line. We can however
propose that the problem of the large EF difference near the EP = 0 line or
at the bound of the allowed domain comes from a worse approximation of the
higher AMMs (such as the O hexadecapoles) which are only important within
short range distances. This cannot create a problem for the QM/MM methods
which consider accurately this EF and EP part from nearest atoms.
We sought the reasons of the deviations at the pole positions by
comparing the (1 - EFapp(L 0)/EFcal(L)) ratio at different upper L. The
large deviation for all the EF poles in Figures 5 is found to be due to
this inaccuracy of the approximation of the charges for APC. Using (1 -
EFapp(L = 0)/EFcal(L = 0)) ratio calculated with the charges (L = 0) only,
the EF difference results already in -61, -43, -43, -52 % at the same pole
positions shown in Figure 5b. These inaccuracies are the consequence of the
larger interatomic bond distances and angles than the ones in the optimized
models used for the fitting of the atomic charge functions [10, 12]. These
large deviations already at L = 0 provide increased EP and EF errors while
applying the CC approximations for the AMMs. It is worth to mention that
these inaccuracies from the charge approximations influence less the EP
values which are very similar with L = 0 and 4, i.e., less than 25 %, in
the same two sections for the XRD model (the cases L = 4 in Figure 7a and L
= 0 in Figure 7b).
If the problem of large differences between approximated and
calculated EF would be related to the pole positions only as for the
optimized APC model (Figure 5), then the CC method should be accepted as
satisfactory one for the EF simulations. It is easy to prove that 100 %
error around the pole's domain is not crucial for the total IE value of
adsorbed probe. As we can confirm a wide part of the space is characterized
by a nearly zero EF value being less than 10-3 au. For comparison
respective contribution of the inductive energy for the N2 molecule with
parallel polarizability ((( of 14.774 a.u. [24] will result crudely in Uind
= Ѕ((((F2 ( Ѕ(15((10-3)2 = 7.5(10-6 au or 4.7(10-3 kcal/mol that can be
considered as a negligible one even for this maximal EF value. For a polar
water molecule, dipole-field term will give more essential (( = 0.729 au
[25]) but nevertheless rather minor value Udipole = (F = 0.729(10-3 =
7.29(10-4 au or 0.46 kcal/mol (to compare with adsorption heats of 5.2-6.9
and 4.9-5.7 kcal/mol for N2 [26, 27] and H2O [28], respectively, over
different zeolites). In the part of the cavity with EF > 10-3 au, the ratio
(1 - (EFapp/EFcal)) (100 % has a reasonable values below 30 %.

CONCLUSIONS

In this work we applied the cumulative coordinate (CC) method to
approximate the atomic multipole moments (AMMs) for a series of ALPO sieves
at the periodic B3LYP level and different basis sets. The constants of
proposed linear equations (slope aL only in eq. 1) are evaluated on a basis
of preliminary computations over a training set of optimized sieves
considered of reasonable quantity of atoms per elementary unit cell or UC
of AEI, AEL, AFI, CHA type ALPOs. To increase the precision achieved in
earlier works [8-10] we analyzed the influence of secondary order remote
shells for both T (Al, P) and O atoms as compared to only nearest ones as
previously. The inclusion of the secondary neighbors (in total eight atoms)
denotes the two nearest TO4 units for O atom and the fragment T(-O-T')4 for
T atom. Moreover, the distance dependences of CC was optimized by choosing
the G power in eq. (3).
We showed that the choice of the sieves for the training set is
important to accurately approximate the T dipoles and quadrupoles, and O
octupoles, i.e., the AMMs with a lower EP and EF contributions. The
behavior of these AMMs varies between the ALPOs and the choice of the
training set requires a care even if the ALPO geometries are optimized.
Based on these results, ALPO frameworks with the density higher than 19.2
T/1000 е3 cannot be preliminary recommended to use within a training set
for the CC approximation. This requirement is not relevant to the AMMs
which are the most important for the EP and EF evaluations, i.e., O dipoles
and quadrupoles, T octupoles, as studied earlier in the works [8-10]. The
later reveal the same or very close G values fitted with both basis sets.
Owing to the larger number of considered neighbours and the G variation
in the CC form we succeeded in this work to render a higher accuracy in the
approximation of the O dipole (Table 2) than r = 0.9 which was the problem
in our previous publication of the EP at the B3LYP/3-21G level [10]. Most
of the deviations are coming herein not from the CC fitting but from a less
accurate approximation of the APC atomic charges. Hence a further step for
the developing charge approximations should be done to improve the EF
prediction with the CC method and to reach a decrease of an EF error also
at the pole positions.
First, the CC approximations are applied to the AFI sieve which
served to fit the AMMs resulting in small deviations between calculated and
approximated EF. Then the CC approximations were applied to the APC sieve
for which the periodic B3LYP/STO-3G computations are feasible and which was
not included in the training set. As soon as a preference of the
empirically optimized ALPO models relative to XRD ones has been shown [9],
we mainly compared the accuracy of the CC approximations for the XRD models
which possess a worse optimized geometry as compared to an optimization
with any force field type. The XRD model of APC sieve includes too long Al-
O and P-O bonds while the model optimized with GULP code corresponds to a
more stable structure. The error in the EF values does not exceed 30 %
within domain where the EF has an appreciable value (crudely evaluated as
more than 4(10-3 au) in the total interaction energy with an adsorbed
molecule. The absolute approximated EF values are less accurate at the
limited "pole" domains where EF approaches to zero due to the symmetry of
internal space and the approximated EF deviates from calculated one more
drastically. However, we showed that the respective terms of the
interaction energy at the pole positions are usually small relative to the
total interaction energy and the larger EF errors at the pole positions
does not create a problem.
We thus showed that the EF values are represented within an internal
space in APC available for a small molecule adsorbed within 30 % error
without direct periodic B3LYP computation. The proposed approach allows the
possibility to develop non time consuming method of screening procedure for
a search of the most attractive site for a chosen molecule to evaluate the
most promising ALPO type. The AMM evaluation proposed for porous crystals
could become logical part of the QM/MM methods which provide description of
the EP simulation from inert (MM) crystalline part treated by molecular
mechanics in the QM/MM computations.

ACKNOWLEDGEMENTS

The authors acknowledge the FUNDP for the use of the Namur Scientific
Computing Facility (SCF) Centre. DPV thanks FNSR-FRFC and the Loterie
Nationale for the convention No 2.4578.02, the Interuniversity Research
Program on "Quantum Size Effects in Nanostructural Materials" (PAI/IUAP
5/01) for partial support.
REFERENCES

1. L.G.M. Pettersson, Theor. Chim. Acta, 1994, 87, 293.
2. J. Sauer, P. Ugliengo, E. Garrone and V. R. Saunders, Chem. Rev.,
1994, 94, 2095.
3. P.N. Daya, R. Pachter, M.S. Gordon, G.N. Merrill, J. Chem. Phys. ,
2000, 112, 2063.
4. P. Demontis, G.B. Sufritti, Chem. Rev. , 1997, 97, 2845.
5. V.R. Saunders, R. Dovesi, C. Roetti, M. CausЮ, N.M. Harrison, R.
Orlando, C.M. Zicovich-Wilson, CRYSTAL98 1.0, User's Manual, Torino,
1999.
6. J.C. White, A.C. Hess, J. Phys. Chem., 1993, 97, 6398.
7. P. Ugliengo, B. Civalleri, C.M. Zicovich-Wilson, R. Dovesi, Chem.
Phys. Lett., 2000, 318 247.
8. A.V. Larin, D.P. Vercauteren, Int. J. Quant. Chem., 2001, 83, 70.
9. A.V. Larin, V.S. Parbuzin, D.P. Vercauteren, Int. J. Quant. Chem. ,
2005, 101, 807.
10. A.V. Larin, D.N. Trubnikov, D.P. Vercauteren, Rus. J. Phys. Chem.,
2005, 79, 1138.
11. R.L. Barinskii, V.I. Nefedov, X-ray Spectral Determination of Atomic
Charges in Molecules, (Nauka, Moscow, 1966).
12. A.V. Larin, W.J. Mortier, D.P. Vercauteren, Chem. Phys. Lett.,
submitted.
13. V.R. Saunders, C. Freyria-Fava, R. Dovesi, L. Salasco, C. Roetti,
Mol. Phys., 1992, 77 629.
14. C. Pisani, R. Dovesi, and C. Roetti, Hartree-Fock Ab Initio Treatment
of Crystalline Systems, (Springer-Verlag, New York, 1988).
15. A.V. Larin, D.N. Trubnikov, D.P. Vercauteren, Rus. J. Phys. Chem.,
2005, accepted for publication.
16. "Atlas of Zeolite Framework Types", Eds. Ch. Baerlocher, W.M. Meier,
D.H. Olson, International Zeolite Association, Elsevier, Amsterdam,
2001.
17. J.D. Gale, GULP 1.3, Royal Institution/Imperial Colledge, UK,
1992/1994.
18. K.P. SchrЖder, J. Sauer, M. Leslie, C.R.A. Catlow, J.M. Thomas, Chem.
Phys. Lett., 1992, 188, 320.
19. A.V. Larin, D.P. Vercauteren, J. Mol. Cat. A, 2001, 166, 73.
20. A.V. Larin, D.P. Vercauteren, Int. J. Quant. Chem., 2001, 82, 182.
21. G. Engelhardt, D. Mitchel, High Resolution Solid State NMR of
Silicates and Zeolites (J. Wiley & Sons, Chichester, 1987).
22. Cerius 2, User's Guide, Version 4.0.0; MSI, San Diego (1997).
23. A.V. Larin, V.S. Parbuzin, D.P. Vercauteren, Chem. Phys. Lett.,
submitted for publication.
24. G. Maroulis and A. J. Thakkar, J. Chem. Phys., 1988, 88, 7623.
25. S.S. Xantheas, T.H. Dunning Jr., J. Chem. Phys., 1993, 99, 8774.
26. T. Masuda, K. Tsutsumi, H. Takahashi, J. Colloid Interface Sci.,
1980, 77, 238.
27. D. M. Ruthven, R. L. Derrah, J. Chem. Soc., Faraday Trans.1, 1975,
71, 2031.
28. A. Giaya, R.W. Thompson, Microporous Mesoporous Mater., 2002, 55
265.











TABLE 1. Symbols, number of atoms per unit cell (UC), of different Al, P
(nP = nAl), and O types, of atomic orbitals (AO) per UC, symmetry group and
framework density (FD, T/1000 е3) of the aluminophosphate (ALPOs) sievesa),
all of them corresponding to the Al/P = 1.

|Name |Symbol |Atoms/UC |nAl/nO |AO/UC |Symmetry|FD |
| | | | |(6-21G**) |group | |
|AlPO4-C |APC |90 |2/8 |1472 |Pbca |18.0 |
|AlPO4-18 |AEI |72 |3/12 |1040 |C2/c |14.8 |
|AlPO4-5 |AFI |72 |1/4 |1104 |P6cc |17.3 |
|AlPO4-11 |AEL |60 |3/11 |920 |Ibm2 |19.1 |
|AlPO4-H2 |AHT |36 |2/7 |552 |Cmc21 |18.4 |
|AlPO4-34 |CHA |36 |1/4 |552 |R3 |14.5 |
|AlPO4-31 |ATO |36 |1/4 |552 |R3 |19.2 |
|MeAPO-39 |ATN |24 |1/4 |432 |I4 |18.0 |
|Berlinite |BERb) |18 |1/2 |276 |P3121 |26.2 |
|Cristobalite |CRIb) |12 |1/2 |184 |C2221 |22.4 |


a) coordinates and FD from ref. [16]; b) symbols BER and CRI are used for
shortness



TABLE 2. The G orders, correlation r, aL coefficients in the non scaled (2)
and scaled (3) expressions for AMM of L-order with STO-3G basis set.

|Atom |Basis |L = 1 |L = 2 |L = 3 |L = 4 |
|Al |aL |-0.4727 |-0.00136 |-2042.07 |-1146.62 |
| |G |1 |NSa) |3 |2 |
| |r |-0.984 |-0.821 |-0.997 |-0.926 |
|P |aL |-0.093 |-0.0119 |-93.136 |-91318.7 |
| |G |0 |NSa) |2 |3 |
| |r |-0.996 |-0.965 |-0.998 |-0.991 |
|O |aL |13.816 |13596.01 |-0.00161 |- |
| |G |4 |6 |NSa) |- |
| |r |0.999 |0.984 |-0.871 |- |


a) non scaled CC (eq. 2)
TABLE 3. The CC contributions (3) at the B3LYP/6-21G** level for the P1
atom of the AEL sieve from the atoms located at the diP1 distance from the
P1 varying G. The sums from the first (four atoms) and the second (four
atoms) surrounding shells are shown by bold for the Р atom.

|(L, m) |i-ato|diP1, аu |The CC contributions (6) from atoms |
| |m | |G = 1 G|
| | | |= 5 |
|(1,-1) |O4 |2.847 |0.0295 |4.494(10-4 |
| |O1 |2.857 |0.0220 |3.298(10-4 |
| |O5 |2.867 |0.0478 |7.078(10-4 |
| |O7 |2.894 |-0.1052 |-1.499(10-3 |
| |1st shell |-0.0058 |-1.245(10-5 |
| |Al2 |5.771 |0.0564 |5.086(10-5 |
| |Al1 |5.876 |-8.768(10-4 |-7.386(10-7 |
| |Al2 |5.890 |-0.0240 |-1.982(10-5 |
| |Al1 |5.950 |-8.536(10-4 |-6.313(10-7 |
| |1st and 2nd shell |0.0249 |1.717(10-5 |
|(2,-2) |O4 |2.847 |0.1613 |3.733(10-5 |
| |O1 |2.857 |-0.0180 |-4.054(10-6 |
| |O5 |2.867 |-0.1996 |-4.369(10-5 |
| |O7 |2.894 |0.0682 |1.276(10-5 |
| |1st shell |0.0065 |2.348(10-6 |
| |Al2 |5.771 |-0.1392 |-1.131(10-7 |
| |Al1 |5.876 |-4.948(10-3 |-3.510(10-9 |
| |Al2 |5.890 |0.1248 |8.506(10-8 |
| |Al1 |5.950 |2.100(10-4 |1.338(10-10 |
| |1st and 2nd shell |-0.0127 |2.317(10-6 |
|(3,-3) |O4 |2.847 |1.0605 |3.735(10-6 |
| |O1 |2.857 |1.886(10-3 |3.298(10-4 |
| |O5 |2.867 |0.8830 |2.860(10-6 |
| |O7 |2.894 |1.4778 |4.283(10-6 |
| |1st shell |3.4321 |1.088(10-5 |
| |Al2 |5.771 |-0.1729 |-1.266(10-10 |
| |Al1 |5.876 |-0.0349 |-2.085(10-11 |
| |Al2 |5.890 |-0.7629 |-4.291(10-10 |
| |Al1 |5.950 |-6.246(10-5 |-3.175(10-14 |
| |1st and 2nd shell |2.4523 |1.088(10-5 |
|(4,-4) |O4 |2.847 |8.3249 |4.461(10-7 |
| |O1 |2.857 |0.0397 |2.017(10-9 |
| |O5 |2.867 |-3.6784 |-1.762(10-7 |
| |O7 |2.894 |-4.2048 |-1.737(10-7 |
| |1st shell |0.4813 |9.818(10-8 |
| |Al2 |5.771 |5.2854 |3.488(10-12 |
| |Al1 |5.876 |-0.3062 |-1.541(10-13 |
| |Al2 |5.890 |5.3875 |2.501(10-12 |
| |Al1 |5.950 |2.227(10-5 |9.036(10-18 |
| |1st and 2nd shell |10.8480 |9.818(10-8 |

Figure captions

Figure 1. Quadrupole moments of Al (a) and P (b) for ATN and dense (closed
symbols, BER, CRI, and ATO), open (open symbols, AFI, AEI, AEL, and CHA),
and distorted (closed symbols, AHT) ALPO types or training set at the
B3LYP/STO-3G level. Approximated quadrupole values for APC atoms are shown
by triangles down (a).

Figure 2. Unit cells of AEI (a), AFI (b), APC (c), AEL (d) structures. The
Al (light), P(dark), O (grey) atoms are depicted by light, dark, and grey
spheres, respectively. The atoms used for the choice of the EP and EF
sections are depicted by errors (b, c). Dashed line (c) is passed through
the O5 and O5 atoms of the APC sieve.

Figure 3. Choice of the G values for the Al multipole moments AMMs of order
L at the B3LYP/6-21G** level. Optimal values (at maximal correlation
coefficient r) are in the circles, 0, 6, 3, and 2 for L = 1 - 4,
respectively.


Figure 4. (a) Electrostatic potential values (EP, au) with respect to the
Al1-O2-P1 plane (the three atoms far on the right in the low right corner)
of AFI calculated with the 6-21G** basis sets; (b) electrostatic field
values (EF, au); (c) EF evaluation errors presented as (1 - EFapp(L =
4)/EFcal(L = 4))(100 (%). Negative and positive EP are shown by the white
and black zones.

Figure 5. (a) Electrostatic potential values (EP, au) with respect to the
O2-O5-O5 plane (the three atoms are shown in the low right corner) of the
XRD non optimized model of APC calculated with the STO-3G basis set; (b)
electrostatic field values (EF, au); (c) EF evaluation errors presented as
(1 - EFapp(L = 4)/EFcal(L = 4))(100 (%). Negative and positive EP are shown
by the white and black zones.

Figure 6. (a) Electrostatic potential values (EP, au) with respect to the
Al1-O2-P1 plane (the three atoms are shown in the low right corner) of the
XRD non optimized model of APC calculated with the STO-3G basis set; (b)
electrostatic field values (EF, au); (c) EF evaluation errors presented as
(1 - EFapp(L = 4)/EFcal(L = 4))(100 (%).Negative and positive EP are shown
by the white and black zones.

Figure 7. Electrostatic potential (EP, au) errors presented as (1 -
EFapp(L)/EFcal(L))(100 (%) values in the (a, L = 4) Al1-O2-P1 and (b, L =
0) O2-O5-O5 planes (respective EP values are given in Figures 6a and 5a,
respectively) of the XRD non optimized model of APC calculated with the STO-
3G basis set.




Figure 1, a-b





























Figure 2
a) AEI b)
AFI























c) APC
d) AEL


Figure 3
































Figure 4, a-c

































Figure 7a, b











Figure 5





Figure 6
[pic]
-----------------------
[pic]

[pic]

b)

a)

a)

b)

c)

(c)