J. Phys. Chem. 1987, 91, 4675-4681 has also been used with some success in the calculation of exciton ~ p l i t t i n g . ~Our ~?~ calculation ~ on DHA (with 30 lowest configurations) predicts a splitting of 14 cm-' between the pair of excitonic states-with the lower energy one being not accessible by electric dipole transition. This is in agreement with our experimental observation that the forbidden one is lying low. The CI wave functions indicate that the states originate dominantly from the coupling of the lowest energy r a * transition localized on the two benzene rings with a small admixture of a transition essentially localized on the >CHz fragments. Spectra in Fluid Solution. The spectra of DHA in fluid MCH-IP and n-heptane solution are depicted in Figure 2 and Figure 5, respectively. Unlike those in rigid media, the excitation and emission spectra in these two media are identical (as far as the peak positions are concerned). Interestingly, the emission spectra in fluid media are diffuse and that in MCH-IP medium is red-shifted compared to that in rigid medium. However, the excitation and the absorption spectra resemble those in MCH-IP glass. It is observed that when the rigid glass melts, the structured emission switches to the diffuse red-shifted one. This switching of emission occurs at 110 K in MCH-IP and 170 K for n-heptane; the temperatures closely correspond to the melting points of the media. This indicates that the blurring of emission is a viscosity effect and caused by some molecular motion in the softened media. It is knownz3that in the ground state DHA has a planar conformation which is only 135 cm-' (0.4 kcal/mol) above the puckered form, and hence interconversion from one to the other
-
-
(32) Sadlej, J. In Semiempirical Methods of Quantum Chemisfry;Ellis Horwood: Warsaw, 1979. (33) Tiberghien, A.; Delacote, G. Chem. Phys. Lett. 1972, 14, 184. (34) Fave, J. L.; Delacote, G.; Tiberghien, A.; Schott, M. Mol. Phys. 1973, 26, 17.
4675
takes place readily a t room temperature. However, such interconversion in the ground state is possibly not the reason for the blurring, since had it been so, the excitation and the absorption should also become blurred. Since the excitation and the absorption spectra in MCH-IP remain unaffected when the glass melts, we believe that the blurring is due to a change in geometry in the excited state. The question then arises whether or not the molecule approaches toward more coplanarity (Le., dihedral angle increases). We are in favor of a nearly coplanar relaxed excited state in the fluid media because the planar form is relatively free from strain and because the profile of the blurred emission resembles the outline of the structured emission in n-heptane at 77 K, which we interpret as due to a coplanar form.
Conclusion 1. We have shown that the lBzustate of benzene splits by 140 cm-' in DHA with the lower state relatively more forbidden than the other. 2. In rigid n-heptane matrix the molecule is forced to take up a planar conformation in the ground state. 3. In fluid media the excited state relaxes to a planar or nearly planar conformation.
-
Acknowledgment. We gratefully acknowledge the support of the Department of Science and Technology, Government of India (Project No. 23 (IP-2)/81-STP II), and the National Science Foundation (Project No. 83-19310). We thank Dr. D. S. Roy and Mr. B. Karmakar for assistance with the measurement of two-photon spectrum and Dr. S. P. Bhattacharyya and Mr. K. Das for computational assistance. We also thank one of the referees for helpful comments. Registry No. DHA, 613-31-0; MCH, 108-87-2; IP, 78-78-4; n-heptane, 142-82-5.
Framework Topology of Tectosilicates and Its Characterization in Terms of Coordination Degree Sequence Mitsuo Sat0 Department of Chemistry, Gunma University, Kiryu, Gunma, Japan (Received: August 20, 1986)
Any kind of 3-dimensional tectosilicate framework can be completely covered with the concentric cluster (CCL) ranging from topological distance 0 to infinity, and the CCL can be numerically represented in terms of coordination degree sequence (CDS). The CDS, which is defined as the consecutive degree sequence of the front nodes, reflects the connectivity relations of the front nodes of the CCL, and its mathematical meaning can be clarified by introducing two fundamental operations, point coalescence and edge addition. These operations serve not only for clarifying the relationship between the CDSs but also for systematic derivation of them. Characterization and classification of tectosilicate frameworks are discussed.
Introduction Along with an increasing interest in zeolite chemistry, attention has been given to the framework topology not only in the relation between their functional properties and their structures but also in synthesizing new zeolites with properties to meet particular needs. One of the approaches is Meiser's SBU criterion.' Based on this criterion, characterization and classification of various kinds of zeolite frameworks have been carried out.'S2 The SBU criterion can be highly appreciated in the sense that it is a simple and effective geometrical means of characterizing the complicated frameworks of zeolites, but there is no distinct evidence that these SBU's are topologically unique ones constructing those frame(1) Meier, W. M. Molecular Sieues; Society of Chemical Industry: London, 1968;p 10. (2) Breck, D. W. Zeolite Molecular Sieues; Wiley: New York, 1974; p 45.
0022-3654/87/2091-4675$01.50/0
works. In 1979, Brunner3 and Meier and Moeck4 presented an alternative concept of coordination sequence (CS), which is defined as a sequence of the total number of points at each topological distance from 0 to n. They suggested the number sequences reflect the topological feature of frameworks. Soon after, Sat0 and Ogura5 and Sato6 presented a similar concept and tried to characterize various frameworks. In this paper, the latter concept is further extended not only for characterization but also for numerical representation of the frameworks.
Concentric Cluster (CCL) Tectosilicate frameworks involving the majority of zeolite frameworks are simply represented by the points (Si or A1 atoms) (3) Brunner, G. 0. J . Solid Slate Chem. 1979, 29, 41. (4) Meier, W. M.; Moeck, H. J. J . Solid State Chem. 1979, 27, 349. (5) Sato, M.; Ogura, T. Chem. Letl. 1980, 1381. ( 6 ) Sato, M. Proc. 6th Inl. Zeolite Conf. 1983, 851.
0 1987 American Chemical Society
4616 0th
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987 1st
2nd
3rd
Sato TABLE I: Examples of Degree Sepuence and Their Total Front Valencies (in Brackets) for Known Tectosilicate Frameworks“
type code ANA BREl BRE2 BRE3 BRE4 CAN ERIl ERI2 ED1 1 ED12 FAU GME LAU 1 LAU2
topological distance 2
3
4
LAU3
LAU4 LAU5
Figure 1. Oth, Ist, 2nd, and 3rd concentric clusters covering the frameworks of analcime (a), laumontite (I), and faujasite (0. 0 indicates a centering point of the CCL.
and the lines connecting adjacent. points, in which oxygen atoms surrounding Si or AI atoms are usually ignored. Every point has four incident lines, so the frameworks are graphically 4-connected 3-dimensional networks extending to infinite space. In order to characterize these networks, the concept of a concentric cluster around a given point is introduced here. An nth concentric cluster (CCL) is defined as a set of all the points ranging from topological distance 0 to n and all the lines responsible for the connections between them. Every point in a given framework serves as a center of the CCL. It is obvious that the 0th CCL comprises a point itself, and the 1st one a set of one centering point, four adjacent points, and four connecting lines. The 0th and 1st CCLs cannot be any criteria for characterization, because they can be found quite commonly through the framework. In the 2nd or much higher distance, it is possible to form various kinds of CCLs. Figure 1 shows the CCLs which are found in the frameworks of analcime (a), laumontite (I), and faujasite (0. Here, it must be noted that whatever point is chosen as a starting point, a given framework can be completely covered with these CCLs by extending its topological distance 0 to infinity. The framework may be covered with only one kind or with several different kinds of CCLs. According to Meier et al.,4 the former may be of “topological homogeneity”, while the latter of ”topological heterogeneity”. As can be seen in Figure 1 , their graphical representations are straightforward, but in the 3rd or much higher CCLs it becomes very difficult to grasp their topological features or differences visually. In this case, it is simple and useful for their characterization to check the connectivity relation of front nodes.
Coordination Degree Sequence (CDS) For a given nth CCL, we define the front nodes as all the points at the distance n and the inner nodes as those at a lesser distance. Valencies of the inner nodes are all 4, while those of the front ones are either 1, 2, 3, or 4. The number of front nodes and their valencies are determined by their connectivity relations, Le., topological featues as shown in Figure 2. In accordance with Brown and Mansinter,’ the degree sequence can be defined for the front nodes as (m1,m2,m3,m4), where mi means the number of front nodes with valency i. Obviously, the 2nd CCL is constructed on the basis of the 1st one and the (n + 1)th on the nth, so the sequence of these degree sequences ranging from distance 1 to (7) Brown, H.; Masinter, L. M. STAN-CS-73-361, May 1973
LAU6 LTL 1 LTL2 MOR 1 MOR2 MOR3 MOR4 PHI THO 1 THO2 THO3 YUGl
YUG2 type code ABW
full name Li-A(BW)
alb ANA
albite
BIK
bikitite
BRE CAN CHA coe cri CYM DAC ED1 EPI ERI FAU FER
brewsterite cancrinite chabazite coesite cordierite cristobalite cymrite dachiardite edingtonite epistilbite erionite faujasite ferrierite
GIS
gismondite
GME HEU KFI
gmelinite
cor
analcime
heulandite
ZK-5
type code LAU LEV LOS LTA LTL MAZ MER MFI MOR NAT OFF PAU PHI qua
RHO
sca
SOD STI THO tri YUG
full name
laumontite levynite losod zeolite A zeolite L mazzite merlinoite ZSM5 mordenite natrolite offretite paulingite phillipsite quartz
rho scapolite sodalite stilbite t homsonite tridymite yugawaralite
Numerical symbols of type codes are included to distinguish between crystallographically different sites. Capital letters represent zeolite species (IUPAC), while lower case represent nonzeolite species. infinity is expected to be a quantity which reflects the topological feature of a given CCL. We call this consecutive degree sequence a “coordination degree sequence (CDS)” after the coordination sequence (CS) defined by B r ~ n n e r .Table ~ I shows some of CDSs obtained. CAN (cancrinite) consists of only one type of CDS, while BRE (brewsterite) consists of four different types of CDS, all of which correspond to their different CCLs. It is practically impossible to have the CDSs up to infinity for a given framework. However, as far as the problem is concerned only with the discrimination of the frameworks, there is no need to follow the sequence up to much higher distances. It can be easily recognized that even up to this 4th distance most of them can be clearly discriminated. For example, the CDSs of both gmelinite and phillipsite are the same up to the 2nd distance, but at the 3rd distance they can be differentiated. Erionite consists of two kinds
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The Journal of Physical Chemistry, Vol. 91, No. 18, 1987
Framework Topology of Tectosilicates
(a)
- agi
( 16.6.0.0)
a-
r
+'
*
IW u
EA (12,0,0,0
)
0
( 11.7.1.0) \
( 10,2,0,0
e( 8.8.0.0)
( 6.3.0.0)
Figure 2. Front nodes and its degree sequence. Open circles show the
front nodes, while black ones show the inner nodes. A number sequence such as (8,2,0,0) means that the number of front nodes with valency 1 is 8, that with valency 2 is 2, that with valency 3 is 0, and that with valency 4 is 0
TABLE II: Characterization of Connective Relation in Terms of Fundamental Operations, Point Coalescence, and Edge Addition, and Their Front Node Valencies' type C e i V 1 2
3 4 5 6 7 8
n-1
9 10
--I-1
2
3
4
)
Figure 4. Three kinds of connective relations of front nodes: independence (i), coalescence (c), and edge sharing (e). Two fundamental operations: point coalescence (PC) and edge addition (EA).
+
+ ++ +++ +
+ + +
++ ++ +++
1 2
3 4 2 3 4
++
3
+
4 4
Oc, coalescence; e, edge addition; i, independence; v, front node valency. neighboring relations are obviously restricted to only these 10 types. In type 1, the node is connected to one node at the distance (n - 1) and three nodes at the distance (n 1). In type 6, the node is connected with two nodes at the distance (n - l ) , one node at the distance (n + l ) , and one node at the distance n. Neglecting the bonding to the (n 1)th neighbor, they can be characterized in terms of only three kinds of connections, independence (i), coalescence (c), and edge sharing (e) as shown in Figure 4. These connectivity relations can easily be recognized by introducing two simple operations, point coalescence (PC) and edge addition (EC) as shown in Figure 4. The point coalescence is an operation which coalesces any two front points to one point. The edge addition is the one which puts one edge between any two front points. The 10 types in Figure 3 are easily characterized in terms of these connectivity relations, which are summarized in Table I1 in association with their resulting valencies. Now, the relationship between the number of front nodes and the node valencies can be clearly realized by these fundamental operations. For instance, as shown in Figure 4, the point coalescence changes the degree sequences (12,0,0,0) to (10,1,0,0). This reduces the total number of front nodes from 12 to 11 but keeps the total valencies of 12 constant. Meanwhile, the edge addition between front nodes changes the sequence (12,0,0,0) to (10,2,0,0). This keeps the total number of front nodes 12 constant but increases the total valencies by 2. These relations can be simply expressed as follows
+
7
6
A -fi 8
9
__---
A 15
Figure 3. All the connectivity relations of a given node at nth distance with the neighboring ones.
of CDSs. One of them is the same as that of gmelinite up to the 3rd distance but differentiated at the 4th distance. This suggests that their topological similarities are kept up to the 3rd distance. The next problem is to find some mathematical relationship holding for those CDSs, both within the same distance and between neighboring distances. This will serve not only for clarifying the relationship between the degree sequences but also for predicting the possible ones. Relationship Holding for the CDS Within the Same Distance. Figure 3 shows all the connectivity relations permitted for a given node situated at the nth distance. Every node is 4-connected in the framework, so the nearest-
+
point coalescence: edge addition: edge addition:
C u m , = hf
(1)
Em, =p
(2)
Cum, = M
+ 2q
(3)
Expression 1 indicates that the total valencies of front nodes can be kept constant in the point coalescence, where v means valency, m, the number of nodes with valency u, and M the total valency of starting CCL. Expressions 2 and 3 indicate that the edge
4678
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987
Sat0
TABLE III: Number of Different Degree Seauences Counted for the 2nd CCLs“ ~~
4
p 12 11 10 9 8 7 6 5 4 3
0
total
34
1 2 3 4 5 6 7 8 2 4 7 IO 14 19 22 24 3 5 8 12 16 19 21 21 4 7 10 14 17 18 18 17 5 8 1 2 1 4 1 5 1 5 1 3 1 0 7 1 0 1 2 1 3 1 2 1 0 7 4 8 1 0 1 0 9 7 4 2 1 8 8 7 4 2 1 6 4 2 1 2 1
1 1
2 3 4 5 7 6 4
9 25 20 14 7 2
10 24 18 10 4 1
11 22 14 7 2
12 29 10 4
68
57
45
34
13 24 7 2
14 10 4
23
15
15 7 2
16 4 1
17 2
18
total
1
231 182 145 109 82 56 31 19 7 1
9
5
2
1
869
1
1
1
45
57
68
77
83
86
83
77
u p is the number of front nodes, and q is the number of edges added. TABLE IV: All the Degree Sequences Permissible for 9 = 0 and 9 = 1 in the 2nd CCLsO
@-
P
q=o
p
q=l
q=o
q=l
Figure 5. Construction of 3rd 1 valency CCL on the basis of a given 2nd CCL.
addition keeps the number of front nodes constant but increases the total valencies by 2q, where p indicates the total number of front nodes and q the number of edges added between front nodes. From these relations, all the possible CDSs within the same distance can be derived systematically. Table I11 shows the number of different degree sequences counted for the 2nd distance, which are classified according to the numbers p and q. Here, p means the number of front nodes E m , and q that of edges added. The total number of 34 in the first left column corresponds to that due to point coalescence only. Addition of one edge ( q = 1) produces 45 different degree sequences, and two edges (q = 2) 57. Thus, the total number of them amounts to 869. This is a total number permitted for the 2nd CCL. All the degree sequences derived for q = 0 and q = 1 are shown in Table IV. A similar procedure can be applied for the 3rd distance. The total number of them counted amounts to 43 519. Between Neighboring Distances. The next problem is to find some relationship holding for the degree sequences between nth and ( n 1)th neighboring distances. As any kind of ( n + 1)th CCLs can be derived by applying the fundamental operations on the starting (n 1)th CCL, the first problem is, therefore, to construct an (n + 1)th starting CCL on the basis of the nth CCL. In this procedure, it must be noted that the starting CCL should not contain any front nodes related to the fundamental operations. We call this CCL a “1 valency CCL”. The 1 valency CCL adopted here means the CCL in which all the front nodes are characterized by valency 1. This can be performed by adding the nodes with valency 1 onto the nodes at the distance n in accordance with their acceptable capacity. For instance, as shown in Figure 5, one node with valency 1 at the distance n can accept three nodes with valency 1 at the distance ( n l), and one node with valency 2 does accept two nodes with valency 1. This is trivial because every node is 4-connected. Now, starting with this 1 valency CCL and applying the fundamental operations, we can derive all the ( n I)th CCLs which are compatible with the given nth CCL. A mathematical relationship between their parameters can be shown as follows. If we set an nth degree sequence as (ml,mz,m3,mr) and (n + 1)th as (m,’,mz’,m3’,m4’) and use the previous equation (3), the following relation can be easily shown:
8
7
+
(7,0,1,1) 4 (2,6,0,0) (34,LO) (4,2,2,0) (5,0,3,0) 3 (4,3,0,1) (5,1,1,1) total (6,0,0,2)
(4,4,0,0) (5,2,1,0) (6,0,2,0) (6,1,0,1)
(2,5,0,0) (3,3,1,0) (4,1,2,0) (4,2,0,1) (5,0,i,i)
+
+
+
3ml
+ 2m2 + m3 + 2q‘
= m,’
+ 2m2’ + 3m3’ + 4m4’ (4)
The left-hand term indicates the total valency M of the starting 1 valency CCL plus the valency increment of 2q’, where q’means
(0,0,4,0) (0,0,2,2) (0,1,2,1) (0,1,0,3) (0,2,0,2) (1,0,1,2) (0,0,0,3) 34
45
(0,7,0,0) (1,5,1,0) (2,3,2,0) (3~~0) (2,4,0,1) (3,2,1,1) (4,0,2,1) (4,1,0,2)
“ p is the number of front nodes, and q is the number of edges added.
the number of edges added to the front nodes at the distance ( n + 1). The right-hand term indicates the total valency xvm,. The above equation can be arranged into a simple form
C(4 - v)m, + 2q’ = Em,‘ hence 4p
+ 2q’ = x v ( m , + m;)
(5)
where p means the total number of front nodes Cm, at the nth distance. This is a general equation holding for the degree sequences between nth and (n 1)th distances. By use of this equation, all the ( n 1)th degree sequences compatible with the nth ones can be systematically derived. Table V shows some of the compatible sequences. Starting with the degree sequence (4,0,0,0) at the 1st distance, sequences such as (12,0,0,0), (lO,l,O,O), (8,2,0,0) at the 2nd distance are all compatible with it. The degree sequence (12,0,0,0) at the 2nd distance is compatible with the sequence (36,0,0,0), (34,1,0,0), (32,2,0,0) at the 3rd distance but not with the sequence (32,0,0,0), (30,1,0,0). Therefore, a CDS such as (4,0,0,0), (12,0,0,0), (36,0,0,0), ... is
+
+
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987 4679
Framework Topology of Tectosilicates TABLE V Examples of Coordination Degree Sequences Which Are in Compatible Relation to Each Other
TABLE VI: Classification of Tectosilicate Frameworks in Terms of Total Front Valencies (TFV)"
topological distances 2
1
Total f r o n t valencies
3
10
eo
30
50
40
70
60
I....I....I....I....I....I....I
/
....
FER MOR DAC €PI MF I BIK
t t t t t t t t t t t t t t t t t + t t t
sca
BRE STI
HEU
YUG MAZ
\
PPPPr-
qua tri cri cor
alb coe ANA ABW SOD CAN
LOS LAU LTL OFF LEV ERI PHI
MER
GIS
P P P FFigure 6. Construction of 2nd CCLs permitted for a given degree se-
quence (7,1,1 ,O).
Pau GME KFI
CHA RHO ITA FAU CY M NAT THO ED1
t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t
Derivation of CCL Any kind of framework can be covered with the CCL by extending the topological distance to infinity. Therefore, it is in principle possible to derive all the frameworks by the construction of the CCLs with a given CDS. For this purpose, it is necessary to construct the CCL from lower to higher distance progressively. The 0th and 1st CCLs are trivial as shown in Figure 1. The 2nd CCL can be constructed on the basis of the 1st CCL. The degree sequence gives us the information about the parts of the materials with which the CCL should be constructed. For example, the sequence (7,1,1,0) at the 2nd distance supplies us with the four kinds of parts as shown in Figure 6: seven nodes with valency 1, one node with valency 2, one node with valency 3, and one 1st CCL. By use of these parts, all the CCLs which are topologically different must be constructed. In principle, it is possible to construct all the possible combinations of the given parts under the restriction of topological distance and then neglect the isomorphic ones. It is very difficult to perform this work by hand manipulation only. In order to avoid unexpected errors or mistakes, it is necessary to introduce any kind of constructing algorithm. The problem is the same as the generation of structural isomers in a chemical graph. Three methods are now available for this purpose: counting polynomial method: connectivity stack method in CHEMICS system: and numbering method in ISOGEN system.I0 These original algorithms are modified for the derivation of the CCL in this investigation. Application examples of the counting polynomial method have been presented in a previous paper. In the case of point coalescence, all these methods are equally effective, but in the case of edge addition, the third one is found to be superior to the first two. Figure 7 shows some ( 8 ) Polya, G . Acta Math. 1937, 68, 145. (9)Kudo. Y.:Sasaki. S . J . Chem. Inf. Comout. Sci. 1976. 16. 43. (10) Zhu, S. Y . ;Zhang, J. P. J . Chem. InJ'Comput. Sci. 1982, 22, 34.
t t
t t t t t
t t t t t
t
t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t
t t t t t t t t
t
t t
t t t t t t t t t t t t t
t t t t t t
t t t
t t t
t
t t t t
t t t t t
+
t t t
t
t t t t t t t t t t t t
t t t t t t
t t t t t t t t
t t t t
t t
t t t
t
t t
I....I....I....I....I....I....I 10
allowed to appear in a real 4-connected framework but a CDS such as (4,0,0,0), (12,0,0,0), (30,1,0,0), ... is not.
t t t t
t t t t t
20
30
40
50
60
70
For type codes see Table I.
of 2nd CCLs derived for q = 0. Alphabetical symbols in the figure show the CCLs which have been confirmed to exist in all the real frameworks ever reported. The 3rd CCLs can be constructed on these 2nd CCLs by applying a similar procedure. However, execution of this procedure requires much more computing time. An alternative procedure using their compatible relationship is needed. The details are not described here.
Total Front Valency (TFV) and Classification of Frameworks As stated above, any given framework can be characterized by its own CDSs. However, it is actually difficult to read the topological features of the frameworks from only the given 4-digit A simpler and more effective quantity symbols (ml,m2,m3,m4). which reflects the framework topology is needed. We will consider here the total valency of front nodes, V = xum,, which is already used in eq 1, 3, and 5 . The total front valency V has some interesting characteristics. For example, in the case of topological distance 2, V = 12 means that there are no edge additions, while Y > 12 means that there are some edge additions. If the information of the total number of nodes p = E m , is further added for examination, different combinations of various rings can be distinguished as shown in Figure 8. V = 12 and p = 12 indicate that there are not any combinations of four- and/or five-membered rings, Y = 12 a n d p < 12 only four-membered ones, V > 12 and p = 12 only five-membered ones, and V > 12 and p < 12 both four- and five-membered ones. In the case of topological distance 3, the combinations of six- and/or seven-membered rings are further added. The relationship between the constituting rings and the total front valency is not so simple as in the case of distance 2. However, it is fully expected that any important information about the kinds and combinations of constituting rings is contained in these values. Table I lists some of them, which are shown in parentheses next to the corresponding degree sequence. Using these values, we can arrange tectosilicate frameworks in descending
4680 The Journal of Physical Chemistry, Vol. 91, No. 18, 1987
Sat0
q.0 a
p = 12
b p = 11
d
C
*
T
*
p = 10
f
e
p.9
p = a
p - 7
p =-6
Figure 7. Examples of topologically different 2nd CCLs for q = 0.
v
= 12
"b"
p
12
"b"
0
only four-membered ones in the lower part (from cordierite to edingtonite). The ordering in the table is in fair accordance with that presented by Meier and Moeck based on the coordination ~ e q u e n c e . The ~ similarity between them could be reasonably explained as follows. In the listing from quartz to edingtonite in the table, their global arrangement is not obviously determined in terms of 2nd TFVs of 12, but 3rd ones with 20, 24, 28, 32, and 36. These are closely related to the number of 2nd front nodes p in the following equation
&m,'
This can be derived from eq 5 by setting q'= 0 (no edge addition). Thus, the global arrangement due to the 3rd TFVs agrees with that due to the number of 2nd front nodes p, the coordination number {Nk) in Meier and Moeck's definition. In the listing from ferrierite to mazzite, their arrangement is mainly determined with 2nd TFVs. These are related to the number of edges added q' in the following equation
&m,' Figure 8. Characterization of CCLs in terms of total front valencies V = xumu and total number of front nodes p = Emu.
order. Table VI shows the result of it, in which the TFV values are only taken up to 70. It is interesting to note in this table that grouping of various frameworks in terms of constituting rings is naturally realized. For example, the frameworks containing a t least five-membered rings are placed in the upper part (from ferrierite to mazzite), those containing six-membered ones in the middle part (from quartz to cristobalite), and those containing
= 4p - 12
= 12 + 2q'
An increase in the number of edges added conversely reduces that of coalesced nodes, thus increasing that of front nodes. This explains why the arrangement due to the TFVs is consistent with that due to the coordination number. Conclusion
The CCL presented here is a kind of molecular cluster which is characterized by concentricity around a given centering point. Topological characterization of a given framework in terms of
J . Phys. Chem. 1987, 91, 4681-4685 the constituent CCLs is useful for avoiding any introducting of subjective ambiguity in the framework recognition. The CDS, which is introduced as a numerical representation, serves for the discrimination and characterization of various CCLs and related frameworks. By use of the mathematical relationships and computer algorithms presented here, it is now possible to derive all the CDSs and their relevant CCLs systematically, although it takes enormous computing times for their complete execution. There appear to be a lot of CCLs which have not yet been confirmed in the real frameworks. However, systematic counting and listing all the topologically unique CCLs are necessary not only for understanding the structural relationship of known 4-connected
468 1
frameworks but also for prediction of unknown ones. Presently, there are no general criteria to justify the geometrical or chemical significance of these CCLs in the construction of the framework. A molecular dynamics approach is now planned for the problem.
Acknowledgment. The author expresses his gratitude to Drs. Y. Kudo, Yamagata University, Japan, and S.Y. Zhu, Nankai University, People’s Republic of China, for providing their useful computer programs. H e is also indebted to Prof. W. M. Meier, ETH, Zurich, for his critical reading of the manuscript. The research was supported by the Grant in Aid for Scientific Research of Ministry of Education in Japan.
Radiative and Nonradiative Transitions in the Eu( I I I) Hexaaza Macrocyclic Complex [Eu( C,,H,,N,) (CH,COO)]( CH,COO)CI.2H20 N. Sabbatini,* L. De Cola, Istituto Chimico “G. Ciamician” dell’Universit6, Bologna, Italy
L. M. Vallarino, Department of Chemistry, Virginia Commonwealth University, Richmond, Virginia 23284
and G . Blasse Physical Laboratory, State University Utrecht, Utrecht, The Netherlands (Received: December 8, 1986; In Final Form: March 9, 1987)
The photophysical properties of the hexaaza macrocyclic complex [Eu(C,H,N6)(CH3COO)] (CH3COO)C1.2H20are reported in water solution and in the solid state. The absorption spectrum and the luminescence spectrum and lifetime show that the Eu3+-macrocycle moiety remains unaltered in water solution, while the remaining coordination positions are occupied by the acetate anion or water molecules depending on the concentration of the complex. Luminescence decay measurements performed as a function of temperature (300 or 77 K) and solvent ( H 2 0 or D20) indicate that no low-lying charge-transfer level is present and only one water molecule is coordinated to the Eu” ion in the presence of added acetate anions. The Eu3+luminescence is quite efficient for f-f excitation (ae,,, 0.1) while it becomes very inefficient for excitation into the ligand (ae,,, 6 X The efficiency of the energy transfer from the ligand to Eu3+deduced from the emission quantum yields is compared to that calculated from the luminescence of the ligand (obtained for the Gd3+ complex at 4.2 K) and Eu3+ absorption, using the Forster-Dexter theory
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Introduction The effects of the second-sphere perturbations on the photochemical and photophysical properties of transition-metal complexes have been discussed by Balzani et al. in a recent review paper.’ In the frame of that study lanthanide complexes were also considered, assuming that an analogy could be seen between the effects produced by the second coordination sphere on the d-block metal complexes and the first coordination sphere on the f-block metal ions. That point of view was based on the observation that the first coordination sphere in lanthanide complexes is often ill-defined2*3 and several important properties of the system depend only slightly on the coordination environment. In ref 1 perturbations caused by the ligands on the f-electrons were examined by analyzing the properties of the luminescent excited states. The complexes of the Eu3+ ion are the most suitable ones in this respect because of the very peculiar spectral and decay characteristics of their luminescence e m i s s i ~ n . ~ * ~ ”
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To enlarge the knowledge of the effects of perturbations produced by new ligands on the excited-state properties of the Eu3+ ions we have studied in this paper the photophysics of the complex [ E U ( C ~ ~ H ~ ~ N ~ ) ( C H(CH3COO)C1.2H20, ~COO)] EuHAM, where C2&IZ6N6is the hexaaza macrocyclic ligand shown in Figure 1. The template synthesis of this complex has been very recently reported by Vallarino et al.’ The interest of this study lies also in the fact that many studies on Eu3+ complexes having new coordination environments are nowadays performed for applicative purposes,6g8-’zespecially on complexes with macrocyclic ligands because of their higher thermodynamic stability and kinetic inertness compared to complexes with monodentate and bidentate Also, the excited-state properties of Eu3+can be studied both in solution and the solid state and offer therefore a direct means to compare (6) Richardson, F. S.Chem. Rev. 1982, 82, 541. (7) De Cola, L.; Smailes, D. L.; Vallarino, L. M. Inorg. Chem. 1986, 25, 1729.
(1) Balzani, V.; Sabbatini, N.; Scandola, F. Chem. Reu. 1986, 86, 319. (2) Thompson, L. C. In Handbook on the Physics and Chemistry of Rare
Earths; Gschneidner, K. A.; Eyring, L., Eds.; North-Holland: Amsterdam, 1979; Vol. 3, p 209. (3) Jargensen, C. K.; Reisfeld, R. Top. Curr. Chem. 1982, 100, 127. (4) Blasse, G. In Handbook on the Physics and Chemistry of Rare Earths; Gschneidner, K. A.; Eyring, L., Eds.; North-Holland: Amsterdam, 1979; Vol. 4, p 237. (5) Horrocks, W. De W.; Sudnick, D. R. Acc. Chem. Res. 1981, 14, 384.
0022-3654/87/2091-4681$01.50/0
(8) Horrocks, W. De W.; Albin, M. Prog. Inorg. Chem. 1984, 31, 1. (9) Biinzli, J.-C.G.; Wessner, D. C w r d . Chem. Rev. 1984, 60, 191. (10) Bryden, C. C.; Reilley, C. N. Anal. Chem. 1982, 54, 610. (1 1) Ballardini, R.; Mulazzani, Q.G.; Venturi, M.; Bolletta, F.; Balzani, V. Inorg. Chem. 1984, 23, 300. (12) Kamoto, Y.; Ueba, Y.; Dzanibekov, N. F.; Banks, E. Macromolecules 1981, 14, 17. (13) Izatt, R. M.; Bradshaw, J. S.; Nielsen, S. A.; Lamb, J. D.; Christensen, J. J. Chem. Reu. 1985, 85, 271.
0 1987 American Chemical Society
