Stereochemistry of uranium in oxygen-containing compoundsappssc.me/wp-content/uploads/2018/12/2018-2-1.pdf · Stereochemistry of uranium in oxygen-containing compounds V.N. Serezhkin,

Applied solid state chemistry2

Crystal chemistry and structural studies

Stereochemistry of uranium in oxygen-containing compounds

V.N. Serezhkin, A.V. Savchenkov, D.V. Pushkin, L.B. SerezhkinaSamara University, Moskovskoye shosse 34, 443086 Samara, RussiaE-mail: [email protected] (V.N. Serezhkin)

Using the Voronoi-Dirichlet polyhedra (VDP), an analysis of the coordination of 3664 crystallographically nonequivalent U atoms (III, IV, V, or VI) in the structures of crystals of oxygen-containing compounds character-ized with an R-factor <0.05 was performed. It was found that with a fi xed degree of oxidation of uranium atoms, the volume of their VDP practically does not depend on the coordination number n in the UOn complexes, which varies from 3 to 12. It was found that in the sublattices containing only uranium atoms (U-sublattices) faces ((p, f ) distribution) depends on the number (kA) of crystallographically nonequivalent U atoms in the cell. It was estab-lished that for kA> 20, the distribution (p, f ) for the U-sublattices has the form similar to the (p, f ) distributions for the H-sublattices and the “ideal gas” model system. Th is fact suggests that for kA>20, the short-range (or crystal-chemical) order in the mutual arrangement of atoms U is absent and only long-range order is maintained (transla-tional symmetry). It has been suggested that crystalline substances that contain sublattices of chemically identical atoms with kA>20 can formally be considered as antipodes of quasicrystals, in whose structures there is a short-range order, although there is no translational symmetry.

Keywords: uranium, oxygen-containing compounds, stereochemistry, coordination polyhedra, Voronoi-Dirichlet polyhedra.

DOI : 1.18572/2619-141-218-2-3-2-16

1. Introduct ionTh e signifi cance of oxygen-containing uranium

compounds, about three hundred of which are nat-ural minerals, is due to several reasons, the most important of which is the need to improve the ura-nium nuclear fuel cycle. Since the radioact ive decay of 238U and 235U (together with 232Th and 4K) is the main source of energy that maintains the tempera-ture of the globe, a number of quest ions arise about the composition, st ruct ure and possible transfor-mations of uranium-containing minerals that ex-ist at high pressure and temperature in the upper and lower mantle of the Earth [1-3]. Underst and-ing the charact erist ics of cryst al chemist ry of ura-nium is also necessary to predict the relationship between the composition, st ruct ure and properties of organic uranium coordination polymers, which have been act ively st udied in recent decades [4-6], which was one of the reasons for the avalanche-like growth of cryst al st ruct ure information about ura-nium compounds st ored in databases [7 , 8] (Fig. 1). Th e revealed features of act inide compression indi-cate the participation of 5f elect rons in the binding of atoms of “light” act inides from Th to Pu [9–12] and allow us to take a new look at the already avail-able data on the st ruct ure of their compounds. Th e cryst al st ruct ure of about eleven thousand uranium compounds, two thirds of which contain oxygen, has now been est ablished [7, 8]. Th e purpose of this work was to analyze the st ereochemist ry of urani-um in the st ruct ures of cryst als st udied to date, con-taining coordination polyhedra (CP) or “complexes”

of the UOn composition, where n is the CN of the uranium atom.

2. Object s of research and methods of crys-tal chemical analysis

Cryst al chemical analysis was performed from the st andpoint of the st ereoatomic model of the cryst al st ruct ure (SMCS) developed by us, which is based on the charact erist ics of the Voronoi – Dirichlet polyhedra (VDP) [13–16]. Th e object s of

Figure 1. Th e total number (N) of st ruct urally charact erized uranium compounds in the databases [7, 8], depending on the year of publication.

№ 2 / 2018 3


the st udy were all oxygen-containing uranium com-pounds, information about which satisfi es three conditions: a) the st ruct ure of the cryst al, in which all uranium atoms form UOn complexes, is charac-terized with a divergence fact or <R <.5; b) there is no disorder in the arrangement of the U or O at-oms; c) all uranium atoms have integer oxidation st ate. Information for 2292 compounds containing 3664 cryst allographically nonequivalent UOn com-plexes in the databases of cryst al st ruct ure data [7, 8] corresp onded to these requirements. Based on information about the parameters of the elemen-tary cells of the cryst als, their symmetries and the coordinates of the basic atoms for all compounds, the charact erist ics of the VDPs of the atoms were calculated, and using the method of intersect ing sp heres [14] we calculated their CNs. In the gener-al case, the VDP of a uranium atom has the compo-sition UOnZm, where n is the CN of the uranium at-om, the sum n + m is equal to the total number of VDP faces (Nf). Th e Z atoms involved in the VDP, cut of the uranium atom, form the second coordi-nation sp here, and the U/Z contact s (the slash in-dicates the presence of a common face of the VDPs of the U and Z atoms) are not chemical bonds [13 - 16]. Th e method of intersect ing sp heres [14] allows unambiguously separating all interatomic contact s of uranium atoms into U – O bonds and non-va-lent U/Z interact ions. When classifying the identi-fi ed UOn complexes to a sp ecifi c geometric type, as before [15, 16], “simplifi ed” VDP, which do not take into account the U / Z interact ions, were used. Th e combinatorial-topological type (CTT) of the VDP, which corresp onds to each detect ed type of the UOn complexes, is given in Table. 1. In the CTT sym-bols, the lower-case numbers indicate the number of vertices at the face, and the superscripts indicate the total number of such faces. For each UOn com-plex, the topological type of vertices (TTV) of the corresp onding VDP is also presented in curly brack-ets. In the notation of TTV, the fi rst number indi-cates the rank of the vertex v (the number of VDP edges intersect ing at the vertex), and the second (af-ter the slash) indicates the total number of such ver-tices. For example, the entry {3/ 4 4/2} means that the VDP has four vertices of the third rank and two - of the fourth.

In order to avoid misunderst anding, we note that the simplifi ed VDP is a polyhedron, dual to CP, since the number of vertices of one polyhe-dron is equal to the number of faces of another, and vice versa. For example, if the UO6 complex has the shape of an oct ahedron (8 faces, 6 vertices), then the corresp onding VDP of the uranium atom has the shape of a cube (6 faces, 8 vertices) and there-fore CTT 46 corresp onds to it. Since there are three edges in each vertex of the cube, then TTV has the

following view: {3/ 8}. If the CP UO8 has the shape of a cube, then the corresp onding VDP of the ura-nium atom has the shape of an oct ahedron and the CTT 38 corresp onds to it. Since there are four edg-es intersect ing at each vertex of the oct ahedron, the TTV of the polyhedron has the form {4/6}.

3. Charact erist ics of VDP of uranium atomsAccording to the obtained results, in the con-

sidered compounds there are U (III), U (IV), U (V) and U (VI) atoms, which form 18 diff erent in shape CP UOn where n varies in the range from 3 to 12 (Table 1). Two types of CP — the oct ahe-dron and the pentagonal bipyramid (they corre-sp ond to VDP in the form of a cube and a pentago-nal prism with CTT 46 and 4552, Table 1) are found for all four degrees of oxidation of uranium, and the oct ahedra are the most charact erist ic CP for U (V) atoms, and pentagonal bipyramids for U (VI). U (IV) atoms most often realize CPs in the form of trigonal dodecahedrons (corresponding VDP have CTT 4454), which in isolated cases were also found for U (V) atoms (for example, the st ruct ure C56H52N9O11UZn2 {TEXSUL} [17]) or U (VI) (st ruc-ture Ba[(UO2)4(UO4)2(OH)2(NO3)4](H2O)2 {248232} [18] and C42H66N29O35ReU {NUDFEY} [19]). Here-inafter, in the curly brackets the numeric or alpha-betic collect ion code in the databases [7] or [8] is indicated. Most often, U atoms have VDP, in which the rank of all vertices is equal to three. VDP with vertices of the fourth rank (Table 1) are rare and make up less than 1% of the sample size. Some VDP with vertices of the third rank are also found in iso-lated cases. An example is the nine-vertex UVIO9 in the C16H32N4O11U {ROCGEW} st ruct ure [2], which can be viewed as a hexagonal bipyramid with one equatorial vertex sp lit into two Y positions. As a result of the “sp litting”, the complex composition (UO8 →UO7Y2) changes and the CTT of the corre-sp onding VDP of the uranium atom (4662 → 455262) also changes, since the YY segment does not lie in the equatorial plane (in such a hypothetical case, the complex would take the form of a heptagonal bipyr-amid, and the VDP of uranium would have CTT 4772), but is perpendicular to it.

In the st ruct ures of compounds, one oxygen at-om can be simultaneously bound to 1, 2, 3, or 4 ura-nium atoms. Depending on CN in relation to ura-nium, such oxygen atoms are hereinafter referred to as O1, O2, O3 and O4, resp ect ively. Th e diff er-ent cryst al chemical role of oxygen atoms is one of the reasons for causing a signifi cant variation in the length of the U – O bonds (Table 1) and, as a result, a dist ortion of the UOn complexes. For example, in numerous U (VI) compounds, as a rule, there are pract ically linear uranyl ions UO2

2 +, in which multi-ple bonds O1 = U = O1 with d (U = O1) = 1.78(4) Å



are realized. However, as is well known, due to cat-ion-cation interact ions, uranyl ions of the type O2 = U = O2 or O3 = U = O3 are also found in the st ruc-tures of cryst als, in which d (U = O2) and d (U = O3) are 1.84(4) and 1.93(5) Å [21]. Th e interatomic dis-tances in the UOn CP also depend on the oxidation st ate and CN of the uranium atoms. With a fi xed degree of oxidation of uranium, the average dis-tance between the atoms of uranium and oxygen as a whole quite regularly increases with an increase in the CN of U atoms, and with a fi xed CN - decreases with an increase in the degree of oxidation of ura-nium. For example, in the series U (III) - U (IV) - U (V) - U (VI) with an oct ahedral coordination of ura-nium d (U-O) equals to 2.32, 2.23, 2.15 and 2.11 Å in average, and with pentagonal-bipyramidal - 2.45, 2.32, 2.24 and 2.21 Å resp ect ively (Table 1).

Th e available data show that the VDP volume (Vvdp) of uranium atoms in the UOn complexes de-creases with an increase in the degree of oxidation in the series U (III) - U (IV) - U (V) - U (VI), aver-aging 13.8(1.4), 11.2(4), 1.(4) and 9.2(2) Å3. It is signifi cant that at a fi xed degree of oxidation, Vvdp is pract ically independent of the CN and the shape of the CP of uranium atoms (Table 1). It is this fact that gives grounds for considering the conditional-ly isolated atoms as “soft” (capable of easily deform-ing) sp heres of a fi xed volume with a radius Rsd, the volume of which coincides with Vvdp. Due to the set of interatomic interact ions, such sp heres are de-formed in the st ruct ures of cryst als and, acquiring a “cut”, turn into certain VDP with Vvdp = 4π(Rsd)3/3, which have common faces and form a Voronoi-Dirichlet partition. As can be seen from the table. 1, with the unchanged degree of oxidation of urani-um, the values Rsd (1.49(5), 1.388(16), 1.337(16) and 1.31(1) Å resp ect ively for U (III), U (IV), U (V) and U (VI )) pract ically do not depend on CN, de-sp ite the fact that the length of the U-O bonds in the UOn complexes varies in signifi cant ranges (≈.5, .8, .8, and 1.3Å, Table 1).

One of the exceptions to this pattern are the U (VI) atoms with CN = 8, which form a CP in the form of a dist orted cube (Table 1). Two vertices of such cube, lying on the same solid diagonal, are oc-cupied by the oxygen atoms of the uranyl ion, and in the six others there are equatorial oxygen atoms. Th e VDP volume of such atoms increased to 1 Å3 due to the peculiarities of the mutual sp atial dist ri-bution of 6 oxygen atoms, which are contained in a single hexadentate ligand (st ruct ures C45H69NO9U {IDITUK} [22] and C42H5N8O13SU {IBEROY} [23]). Both a significant variation in the length of the equatorial U – O bonds in the formed complexes, as well as a sp ecifi c deformation of the VDPs of the uranium atoms is a result of the st ruct ural rigidity of the ligands.

Th e other exceptions are the U (III), U (IV) and U (V) atoms with CN = 4. Th ey all have the same quasitetrahedral coordination, and the Vvdp for them is increased by about 1 Å3 compared to sim-ilar atoms with alternative CN (Table 1). A com-mon feature of atoms with CN = 4 is the presence of numerous (from 8 to 12 per atom) non-bonded U/H contact s, which corresp ond to small solid an-gles. According to the available data, the U/H con-tact s are approximately 1. Å longer than the U – O bonds. For example, in the recently charact erized complex O = UV(O-R)3 {ISEKEY} [24], on average, d (U-O) = 2.3 Å, and d (U/H) = 3. Å. Th erefore, numerous VDP faces, equivalent to U/H contact s, are approximately .5 Å further from the U-nucle-us than U-O faces, which causes an increase in Vvdp.

As is known [15, 16], the dimensionless second moment of inertia (G3) is the parameter charact er-izing the degree of deformation of the “soft” sp here of radius Rsd when it is transformed into a certain VDP of the same volume. The minimum possi-ble value of G3 (.77) corresp onds to a sp here, and for any polyhedron G3 increases the more, the more st rongly the shape of the VDP diff ers from the sp herical one. For VDP of 3664 uranium atoms in the discussed compounds G3 varies from .781 to .915 (the average is .84(1)). With an increase in the CN of uranium atoms from 4 to 12, the aver-age value of G3 as a whole regularly decreases from .86 to .78 (Table 1). Note that the atoms with CN = 4 and VDP in the form of an ideal tetrahedron theoretically corresp ond to G3 = .14. Th erefore, the G3 values for uranium atoms with CN = 4 low-ered to .85 - .86, as well as G3 = .84 for U (III) atoms with CN = 3, are due to numerous non-va-lent U/H contact s (their number is equal to the dif-ference [Nf –CN]) since the highest Nf values have exact ly the VDP of atoms with CN = 3 or 4 (Table 1).

Parameter G3 sensitively react s to any dist or-tions of the coordination sp here of atoms. For ex-ample, for a CP in the form of an ideal oct ahedron, the VDP has the shape of a cube, for which the theo-retical G3 = .833. Due to linear and/or angular dis-tortions caused by the presence of multiple U = O bonds or non-valent U/Z contact s, in 452 real UO6 oct ahedra, the G3 parameter varies from .826 to .915 and is on average .854(12). Frequent im-plementation in the st ruct ures of cryst als dist orted to one degree or another by the CP is not surpris-ing, since the symmetry of the CP (and their du-al VDP) depends on the symmetry of the position occupied by the central atom of the polyhedron. A clear example is the 2292 discussed compounds, in the st ruct ures of cryst als of which the U atoms most often occupy positions with C1 symmetry (≈73% of cases), Ci, СS, C2, and C3 (≈1, 8, 4, and 1%, resp ect ively). Th e frequency of occurrence of each

№ 2 / 2018 5

Crystal chemistry and structural studiesTa

ble 1

. Cha

ract

erist

ics o

f VD

P of

ura

nium

ato

ms s

urro

unde

d by

oxy

gen

atom

s *

Atom

CN

CP

**C

TT

VDP

TTV

VDP

Num

ber

of at

-om

sN

fV vd

p (Å3 )

R sd (Å

)D

A (Å

)G

3

d(U

-O),

Å **

rang

eav

erag

eμ

U(II

I)3

Trig

onal

pyra

mid

--

218

(1)

12.9

(2)

1.45

6(8)

.4

(3)

.8

42(1

)2.

15-2

.16

2.15

8(5)

6

4Te

trahe

dron

34{3

/ 4}

515

(2)

14.6

(1.7

)1.

52(6

).

52(

21)

.8

6(4

2)2.

15-2

.47

2.24

(6)

2

6O

ct ah

edro

n46

{3/ 8

}1

1312

.58

1.44

3.

53

.8

522.

11-2

.62

2.32

(24)

6

7PB

45 52{3

/1}

112

13.5

41.

479

.11

.

835

2.35

-2.6

52.

45(1

3)7

9Th

TP43 56

{3/1

4}1

912

.8

1.45

1

.7

972.

5-2

.6

2.54

(4)

9

3-9

allall

all1

14(3

)13

.8(1

.4)

1.49

(5)

.5

(32

).

847

(34)

2.11

-2.6

52.

33(1

7)48

U(IV

)4

Tetra

hedr

on34

{3/ 4

}3

16(

)12

.3(8

) 1.

43(3

).

7(6

).

849

(5)

2.1

-2.1

52.

12(2

)12

6O

ct ah

edro

n46

{3/ 8

}21

8(3)

11.2

(7)

1.39

(3)

.3

(5)

.8

38(8

)2.

6-2

.56

2.23

(8)

126

TP #

36

{3/2

4/3

}3

1(

)11

.3(6

)1.

39(2

).

14(

2).

82

(4)

2.18

-2.6

12.

3(1

5)18

7PB

45 52{3

/1}

168(

1)11

.4(3

)1.

4(1

).

5(3

).

835

(13)

2.5

-2.8

52.

32(1

2)11

2

STP

#32 45

{3/

6 4/

2}11

9(1)

11.5

(1)

1.39

8(4)

.7

(2)

.8

34(8

)2.

22-2

.79

2.32

(1)

77

8Tr

igon

al do

deca

hedr

on44 54

{3/1

2}64

9(1)

11.1

(3)

1.38

4(11

).

3(3

).

813

(5)

2.14

-2.7

12.

37(9

)51

2

Cube

#38

{4/6

} 5

9(1)

11.9

(4)

1.41

(2)

.

827

(3)

2.25

-2.8

22.

4(1

1)4

TwTP

#

46 52{3

/1

4/1}

2 11

(1)

1.9

(1)

1.37

4(6)

.2

(1)

.8

17(2

)2,

26-2

.5

2.35

(7)

16

Squa

re an

tipris

m #

48{3

/ 8 4

/2}

29(

1)11

.1(1

)1.

382(

5).

3(4

).

818

(5)

2,35

-2.3

72.

355(

8)16

HB

46 62{3

/12}

1 8

11.

1.

38

.

18.

815

2.6

-2.4

92.

38(1

9)8

9Th

TP43 56

{3/1

4}16

1(1

)11

.(2

)1.

38(

7).

3(2

).

8

(3)

1.99

-2.7

92.

42(1

)14

4

SSA

#45 54

{3/1

2 4/

1}3

9()

11.2

(7)

1.39

(3)

.3

(3)

.8

(1

)2.

32-2

.66

2.43

(7)

27

Hul

a-ho

op44 54 61

{3/1

4}2

1(

)11

.3(

5)1.

392(

2).

37(

2).

86

(1)

2.28

-2.6

2.

42(7

)18

1TS

A42 58

{3/1

622

11(1

)11

.18(

9)1.

387(

4).

12(

6).

793

(2)

2.35

-2.6

42.

46(5

)22

Foxh

oron

43 56 61{3

/16}

11

11.

61.

382

.3

6.

794

2.37

-2.5

82.

45(7

)1

12Ic

osah

edro

n512

{3/2

}1

12(

)11

.(2

)1.

378(

8).

2

(7)

.7

82(1

)2.

46-2

.55

2.51

(2)

12

4-12

allall

all18

29(

2)11

.2(4

)1.

388(

16)

.3

(3)

.8

15(1

8)1.

99-2

.85

2.38

(11)

1476



U(V

)4

Tetr

ahed

ron

34{3

/ 4}

113

1.8

1.

371

.14

4.

852

1.82

-2.1

12.

3(1

4)4

6O

ct ah

edro

n46

{3/ 8

}33

8(2)

1.

(4)

1,34

(2)

.3

(3)

.8

4(8

)1.

83-2

.63

2.15

(9)

198

7PB

45 52{3

/1}

118(

1)9.

9(3)

1,33

4(12

).

3(1

).

827

(6)

1.85

-2.6

52.

24(1

8)77

8Tr

igon

al do

deca

hedr

on44 54

{3/1

2}1

89.

961,

334

.

6.

89

2.17

-2.4

22.

29(1

1)8

4-8

allall

all46

8(2)

1.

(4)

1,33

7(16

).

3(3

).

836

(11)

1.82

-2.6

52.

18(1

3)28

7

U(V

I)6

Oct

ahed

ron

46{3

/ 8}

397

7(1)

9.3(

3)1.

35(

13)

.2

(3)

.8

55(1

1)1.

71-2

.85

2.11

(21)

2382

TP #

36

{3/2

4/3

}3

9()

9.7

(9)

1,32

3(4)

.

881

(2)

2.7

-2.

82.

75(

6)18

7PB

45 52{3

/1}

1937

8(1)

9.2(

2)1.

299(

8).

2(2

).

839

(5)

1.61

-2,9

32.

21(2

8)13

559

8H

B46 62

{3/1

2}1

829(

1)9.

3(2)

1.3

5(9)

.1

(1)

.8

36(4

)1.

63-2

.84

2.28

(3)

8656

Trig

onal

dode

cahe

dron

44 54{3

/12}

39(

1)9.

4(1)

1.31

(5)

.4

(3)

.8

37(3

)1.

76-2

.77

2.3

(33)

24

Dist

orte

d cu

be #

31 43 53 61

{3/1

2}3

9(1)

1.

(4)

1.33

5(18

).

3(4

).

875

(29)

1.78

-3.2

92.

38(4

8)24

9N

ine-

top

poly

hedr

on45 52 62

{3/1

4}1

99.

471.

312

.3

4.

838

1.75

-2.9

62.

38(3

9)9

6-9

allall

all34

268(

1)9.

2(2)

1.3

1(1

).

2(2

).

84

(8)

1.61

-2.9

62.

22(2

9)24

672

* CN

is th

e co

ordi

natio

n nu

mbe

r of u

rani

um w

ith re

sp ect

to

oxyg

en a

tom

s; C

P - c

oord

inat

ion

poly

hedr

on; C

TT -

com

bina

toria

l-top

olog

ical

type

of s

impl

i-fi e

d VD

P; Т

ТV -

topo

logi

cal t

ype

of v

ertic

es o

f sim

plifi

ed V

DP;

Nf is

the

aver

age

num

ber o

f VD

P fa

ces.

V vdp -

VDP

volu

me;

R sd -

the

radi

us o

f the

sp h

ere,

whi

ch

volu

me

is eq

ual t

o V vd

p; DA is

the

disp

lacem

ent o

f the

nuc

leus

of t

he U

atom

from

the

geom

etric

cent

er o

f gra

vity

of i

ts V

DP;

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№ 2 / 2018 7


of the 15 other identifi ed types of site symmetry does not exceed .8%.

Th e parameter, which charact erizes the non-centrosymmetry of the UOn complexes, is the vect or DA, which indicates the magnitude of the disp lace-ment of the nucleus of the atom U from the center of gravity of its VDP. According to the available da-ta (Table 1) in the discussed sample, DA is on aver-age .2(2) Å and within σ equals at the same time. Moreover, the dist ribution curves for U atoms in the UOn complexes on the (d, φ) dist ribution [25] corre-sp ond to the U = O and U - O bonds and have the form of semicircles with radii ≈1.78 (2) and 2.4 (1) Å, resp ect ively, with the center at the beginning of the polar coordinate syst em (Fig. 2a), which contains the nuclei of all uranium atoms. In our opinion, this fact indicates the quasisp herical symmetry of the dist ri-bution of the elect ron density of uranium atoms sur-rounded by oxygen atoms. Th is opinion is also con-sist ent with the type of (d, φ) dist ribution for U / U contact s in a sublattice of the cryst al st ruct ure con-taining only uranium atoms (hereinafter U-sublat-tice). Th us, the contact curve corresp onding to the

Figure 2. Dist ribution (d, φ) for VDPs of uranium atoms, calculated taking into account all atoms in the st ruct ures of compounds (a), or in the U-sublattices of the same cryst als (b). Dependence of the number (N) of interatomic contact s in VDPs of U atoms depending on the length of the dist ance d(U–O) in the st ruct ures of the compounds (c) or the length of the dist ance d(U–U) in the U-sublattices of the same cryst als (d). His-tograms (c) and (d) are plotted with a st ep of .1 and .1 Å, resp ect ively. In fi gures (a, c), the data for 26862 U–O contact s are taken into account, and in fi gures (b, d) – it was 52662 contact s (VDP faces) of U / U.

shortest U / U contact s in the U sublattices of the cryst als under discussion also has the form of a semi-circle with a radius of ~ 4.(2) Å (Fig. 2b).

For atoms that are taken into account in the (d, φ) graphs (Fig. 2a, b), hist ograms were also const ruct -ed. They characterize the distribution of inter-atomic contact s depending on the dist ance d (UO) in the VDP of uranium atoms in the st ruct ures of compounds (Fig. 2c) or on the dist ance d (U / U) in the U-sublattices of the same cryst als (Fig. 2d). In fi g. 2 the fi rst peak in the region of ~ 1.7-1.9 Å corresp onds to the U = O bonds in the UO2

2+ or UO2

+ ions, and the second (~ 2.1 - 2.7 Å) corre-sp onds to the U-O bonds in the UOn polyhedra of U (III) and U (IV) atoms and to the equatorial U-O bonds of U (V) and U (VI) complexes. In fi g. 2d the left doublet peak with d (U / U) in the re-gion of ≈3.5–4.5 Å corresp onds to uranium atoms, which are part of the AOn coordination polyhedra, which are connect ed to each other by bridging ox-ygen atoms. Th e sp litting of the peak is caused by a diff erent way of articulation of polyhedra - shorter U / U contact s corresp ond to the presence of a com-



mon edge in two AOn CP, and longer ones - a com-mon vertex.

All contact s with d (U / U)> 5 Å in fi g. 2g corre-sp ond to uranium atoms that do not have common bridging oxygen atoms. Such uranium atoms form

mononuclear complex molecules (ions) or are con-nect ed to each other by bridging polydentate linkers in 1D, 2D or 3D coordination polymers. Since in the cryst al st ruct ures such uranium atoms are separat-ed from each other by bulk polyatomic ligands, the

Figure 3. Th e dependence of the solid angles Ω of the VDP faces of 3664 uranium atoms on the U – O interatomic dist ances in the st ruct ures of the compounds (a) or the U – U dist ances in the U-sublattices of the same cryst als (b). Dependence of the solid angles Ω of the VDP’s faces of 3325 oxygen atoms on the O – O interatomic dist ances in the O sublattices (c). In all cases, the data for the same 2292 uranium compounds are taken into account, Ω are expressed as a percentage of the total solid angle of 4π st eradians. Figures a, b, c show the data for 26862, 52662 and 451516 experimental points, resp ect ively.

№ 2 / 2018 9


realization of a certain interatomic dist ance with d (U / U)> 5 Å in the probabilist ic sense can be con-sidered a random event. Th erefore, it is not surpris-ing that the shape of the envelope curve for the d (U / U) sp ect rum in the range of 5–13 Å in Fig. 2g is close to normal dist ribution.

In the sample of VDPs of 3664 uranium atoms under discussion, which were calculated taking in-to account the positions of all atoms in the cryst al st ruct ures, there are a total of 2875 faces, 26483 of which corresp ond to U – O bonds. Most often H, O, and C atoms, which account for 157, 379 and 95 faces, resp ect ively, were in the role of Z atoms in-volved in non-valent U / Z interact ions, which cor-resp ond to 1592 faces. Figure 3a shows the (Ω, d) dist ribution for the 26862 VDP faces corresp ond-ing to the U = O, U – O bonds, or non-valent U / O contact s. According to the regression analysis da-ta, the dependence of dist ances d (U-O) ≤ 3 Å is de-scribed by the equation

Ω(U-O) = 51.48(4) – 16.88(2) d(U-O),(1) with accuracy of approximation R2 = .97. Note that equation (1) takes into account the charact erist ics of the VDP of all U atoms, regardless of their oxi-dation st ate or CN. In fi g. 3a U – O multiple bonds corresp ond to the VDP face, which corresp onds to solid angles in the range from ≈25 to 19% of 4 st e-radians. Th e U – O bonds corresp ond to a face with Ω in the range from ≈19 to 5%, and non-valent U / O interact ions, to a face with Ω <5%.

In contrast to the (Ω, d) dist ribution for the UOn complexes (Fig. 3a), the similar (Ω, d) dist ribution for the U / U faces of VDP atoms in the U sublattic-es of cryst als of the same compounds has the form of a “fl ying rocket tail” ( Fig. 3b). Th e (Ω, d) dist ri-bution for the O / O faces of the VDP of 3325 ox-ygen atoms in the O sublattices of the same sub-st ances has a similar form (Fig. 3c). Note that the shortest contact s (d (O – O) ≈ 1.5 Å and Ω in the region of 26–34% of the total solid angle 4π st eradi-ans) corresp ond to oxygen atoms of peroxide ions. Th e similarity of the dist ributions in Fig. 3b and 3b is caused by the fact that in sublattices containing chemically identical atoms there are no chemical bonds between uranium atoms (or oxygen, if we ig-nore the relatively small number of contact s corre-sp onding to O – O bonds in peroxide ions), and, as a result, there is no short-range order in their mu-tual arrangement, due to homoatomic chemical in-teract ions.

Recently, it was shown [11, 12] that the charac-terist ics of the U-sublattices can be used to identi-fy 5f-binding interact ions between uranium atoms in cryst al st ruct ures. According to [11, 12], such in-teract ions simultaneously satisfy three conditions. A necessary condition is the presence of an inter-atomic dist ance with d (U – U) <3.5 Å, which cor-

resp onds to the well-known Hill limit [1, 26]. Two suffi cient conditions are the values of DA> .2 Å and G3> .79 for VDP of U atoms that participate in 5f-binding.

An analysis of the U-sublattices in the st ruc-tures of 2992 compounds under discussion showed that at the same time only three subst ances meet the three indicated requirements. In one of them, K[UO2(L)2]·Q {QOSVIE} (L is 1,3-diphenyl-1,3-propanedionate, and Q is 18-crown-6) [27] - two pentagonal bipyramids UVO7 due to cation-cat-ion interact ions between UO2

+ ions are linked by a common axial edge into a dimer with d (U-U) = 3.46 Å. Th e two framework st ruct ures of the polyuran-ates CuU3O1 {73611} [28] and Sr3U11O36 {8599} [29] contain pentagonal bipyramids UO7, which are connect ed by an equatorial edge with one UO6 oc-tahedron, which has an uranium atom that has an-ti-uranyl coordination. In other words, the UO6 oc-tahedron has a “square UO4 core” [21] with four short (1.91 - 2.8 Å) U – O bonds, and two long(2.34 - 2.35 Å) bonds that pass perpendicular to the “core” plane. In both uranates, the “UO4 core” plane coincides with the equatorial plane of the UO7 bi-pyramid, the U – U dist ance in copper uranates (be-tween U1 and U2) and st rontium (between U5 and U6) is 3.48 and 3.45 Å, resp ect ively. We note that another oxygen-containing uranium compound, in which the reduct ion of U-U dist ances in the U sub-lattice to 3.37 - 3.47 Å is explained from the same positions by the presence of 5f-binding interact ions [11], is the orthorhombic modifi cation of uraninite UO2 at pressures above 33 GPa {16815 } [1], which did not fall into the sample under consideration due to the relatively large (≈.7) R-fact or.

4. Features of the topology of the U-sublat-tices in oxygen-containing uranium compounds

As it is known [3 - 33], from the st andpoint of the SMCS, when implementing the principle of maximum fi lling of sp ace in the case of sublattic-es of atoms of “heavy” elements in cryst als, rule of 14 neighbors should be fulfi lled, rather than rule of 12 neighbors, as it is considered according to clas-sical concepts. Th e analysis showed that in the U-sublattices of the compounds under consideration the number of VDP faces (equals to the number of atoms surrounding the base U atom) varies from 5 to 27, and these polyhedra belong to 1134 diff erent CTTs. As can be seen from fi gure 4b, which shows the dist ribution of 3664 VDPs of uranium atoms de-pending on the number of their faces (hereinafter the dist ribution (p, f )), in the U-sublattices of the compounds under consideration 14-facets, const i-tuting ≈46% of the sample size, are the most char-act erist ic. In terms of frequency, dodecahedrons occupy only fourth place (≈7% of atoms), yielding to polyhedra with 16 and 15 faces. As in the over-



Figure 4. Dist ribution of VDP of uranium atoms depending on the number of faces (f ) of polyhedra in the U-sublattices of the st ruct ure of cryst als of oxygen-containing compounds: (a) - 1533 compounds with kA = 1; (b) - 2292 compounds with an average kA ≈ 1.6; (c) - 2 compounds with an average kA ≈ 38.

№ 2 / 2018 11


whelming majority of other homoatomic sublattices [33], the most common is CTT [4668], which corre-sp onds to the Fedorov cuboct ahedron, which oc-curs for 23% of uranium atoms. Th e second most abundant (≈8% of atoms) are 14-faceted polyhe-dra with CTT [445466], which, as was recently est ab-lished [34], turn into Fedorov cuboct ahedra due to the one-st ep procedure of “pinning-and-sp litting” of one VDP edge.

Th e polymodal (p, f ) dist ribution for the U-sub-lattices (Figure 4b) agrees well with the rule of 14 neighbors, which is not surprising, since the crys-tals of the discussed compounds in one unit cell contain on average less than two (≈1.6) cryst allo-graphically diff erent uranium atoms. It was recently discovered [32, 33] that the average number of crys-tallographically diff erent A atoms (hereinafter kA) in a cell signifi cantly aff ect s the form of (p, f ) dist ribu-tions, since it aff ect s the ratio of the long-range and short-range order in the mutual arrangement of at-oms in the A sublattice. So, for kA = 1, all atoms A, surrounding the central one, are cryst allographi-cally equivalent with it and, even if atoms A have site-symmetry C1, their mutual spatial distribu-tion cannot be random. Th e positions of such crys-tallographically equivalent atoms in the A sublat-tice are necessarily mutually consist ent, since even a slight disp lacement of the central atom inevitably leads to a similarly large disp lacement of all atoms of the A environment without exception, taking in-to account the requirements of the sp ace symme-try of the cryst al. Th us, for kA = 1, in the mutual ar-rangement of atoms in the A sublattices, there is at the same time both short-range (cryst al chemi-cal) and long-range (translational) order. For com-parison in Figure 4a there is the (p, f ) dist ribution for the VDP of U atoms in 1533 compounds with kA = 1, which are contained in the analyzed sample (Fig. 4b). When kA = 1 there are VDPs, which be-long to 11 diff erent CTTs. As expect ed, VDPs with 14 faces are most often implemented (they make up 65% of the sample size). Th e most charact erist ic of them are the Fedorov cuboct ahedra and related polyhedra with CTT [445466], which are found for ≈4 and 14% of uranium atoms, resp ect ively.

If kA >> 1 (according to [31, 32], with kA> 2), then any atom A, taken as a base one, has pract i-cally no cryst allographically equivalent atoms A in its nearest environment. Th erefore, a small dis-placement of the central atom of VDP no longer af-fect s the positions of neighboring A atoms, since from the cryst allographic point of view they are not obliged to coordinate placement relative to each other (their mutual position is determined by a large number of fact ors and is essentially ran-dom). Th erefore, for kA> 2, the short-range (or cryst al-chemical) order in the mutual arrangement

of atoms A is absent and only long-range order is preserved (translational symmetry). Taking in-to account this feature, cryst alline subst ances con-taining A-sublattices with kA> 2, in our opinion, can be formally considered as “antiquasicryst als”, that is, antipodes of quasicryst als, in st ruct ures of which, as is known [35], there is a short-range co-ordination order, although there is no translation-al symmetry.

Note that, according to [32, 33], for kA> 2, the form of the (p, f ) dist ribution for the A sublattic-es should change fundamentally. First , the dist ri-bution should become monomodal, and second-ly, the dist ribution maximum should corresp ond to VDP not with 14, but with 15 (if there are no homo-atomic bonds between A atoms) or 16 faces (if at-oms have the ability to form chemical bonds AA). As part of this work, it was interest ing to verify the exist ence of these changes, esp ecially since due to the eff orts of Burns P.C. and other researchers [36–48] in recent years, the st ruct ure of 2 oxygen-con-taining uranium compounds with kA> 2 has been est ablished (Table 2). Note, that only one of them(II in Table 2) fell into the st udied sample of 2292 compounds, since for 19 other subst ances the R fact or did not satisfy the requirements. Th erefore, the rest rict ion on the R fact or for compounds I-XX was not taken into account, because the calcula-tions used only the coordinates of uranium atoms, the accuracy of determination of which, as is well known, is signifi cantly higher than for the “light” at-oms O, H, etc.

Th e obtained results show that the assumed changes in the type of (p, f ) dist ribution are gener-ally confi rmed. So, in U-sublattices of compounds with kA> 2, VDPs are most often found with 15 (Fig. 4c), and not 14 faces, as in the sublattices with kA <2 (Fig. 4a, b). Due to a sharp increase in the number of VDPs with an odd number of faces (11, 13, 15, 17, and 19), the polymodal (p,f ) dist ri-bution with maxima at even values of f = 12, 14, and 16 with kA <2 (Fig. 4a , b) approached the monomo-dal, if we ignore the minimum at f = 16 in fi g. 4c, which, apparently, is due to the small sample size or the sp ecifi city of the st ruct ure of compounds I - XX. In the U-sublattices of compounds with kA> 2, VDPs with 654 diff erent CTTs are pres-ent, to which only 769 atoms corresp ond. In this case, most often (18 atoms) there are VDPs with 15faces and CTT [445467]. Th e Fedorov cuboct ahe-dra with 14 faces and CTT [4668], which dominat-ed in (p, f ) dist ributions with kA <2 (Fig. 4a, b), in a similar dist ribution with kA> 2 (Fig. 4c) are found only for 6 atoms. At the same time, related 14-fac-eted polyhedron with CTT [445466], implemented in 12 cases, occupy the second place in the sample for prevalence.



Table 2. Some charact erist ics of uranium compounds with kA > 2 *

№ Состав kA CN of U Vvdp (Å3) RefcodeRef-er-

ence

I (Mg.53Fe.47)Mg.3Pb8.74 [(UO2)18O18(OH)12]241H2O 36 6, 7 9.2(3) 8557 [36]

II Li6Na8[UO2(O2)(OH)]4442H2O 22 8 9.(2) 168974 [37]

III Na14(SO4)[UO2(O2)(OH)]2856H2O 28 8 9.1(2) 168977 [37]

IV (NH4)44[(UO2)44(O2)66)(H2O)2 23 8 8.9(3) 23913 [38]

V K35(UO2)31Sm9(O2)51(H2O)28 31 8 9.(3) 239443 [39]

VI Li12Na 32.67O523.33P48U48 24 8 9.2(6) 243893 [4]

VII Li6Na22O453P48U48 24 8 9.4(7) 243894 [4]

VIII U28Mo4P12O211 28 8 9.1(2) 251578 [41]

IX U28W4P12O18 28 8 9.(2) 251579 [41]

X U44Mo2P16O266 23 8 9.1(2) 25158 [41]

XI U5W6P21O331 5 8 8.7(4) 251582 [41]

XII U16O35 128 7, 8, 9, 1 11.4(1.1) 261647 [42]

XIII K6Li3[UO2(O2)(OH)]4289H2O 21 8 9.(7) 261667 [43]

XIV K17[(UO2)3(O2)3(P2O7)12(PO4)(H2O)4] 3 7, 8 9.(2) 26167 [43]

XV H91Li48O427U48 48 8, 9, 1 9.1(2) 41464 [44]

XVI H944O1752U256 64 7, 8 9.1(5) 414643 [44]

XVII [UO2(O2)(OH)]5 5 8 9.1(4) 41952 [45]

XVIII Li36[(UO2)36(O2)41(OH)26]42H2O 36 8 8.9(2) 42185 [46]

XIX Na22P46U45O342 45 7, 8 9.2(2) 42249 [47]

XX C1H74K22Li18O242P2U3 3 8 8.9(1) FEBLEF [48]

* Vvdp values are calculated taking into account all atoms in the cryst al st ruct ure. For IV, data for U (23) was not taken into account because of the presence of nitrogen atoms in its coordination sp here. For XII, in-creased Vvdp and σ (Vvdp) are caused by the simultaneous presence of uranium atoms with diff erent degrees of oxidation.

Th e results obtained indicate that the increase in the number of cryst allographically nonequiv-alent uranium atoms in the unit cell is accompa-nied by a signifi cant increase in the topological

diversity of VDPs in the U-sublattices. Th us, forkA = 1, ≈1.6, and ≈38, on average, one topological type of VDP is 14, 3.2, and 1.2 atoms, resp ect ively. Additional analysis shows that the eff ect of kA on

№ 2 / 2018 13


the form of (p, f ) dist ributions is associated with a change in the number of vertices of the most fre-quently occurring VDP faces. As can be seen from fi g. 5, an increase in kA from 1 to ≈ 38 leads to a regular and signifi cant increase (by ≈ 6 -1%) in the number of VDP faces with an odd number of vertices (Nv = 3, 5 or 7) due to a sharp decrease in the number of faces with 4 or 6 vertices (≈11 and 22 % resp ect ively). We also note that only forkA> 2 in the U sublattices, desp ite the relatively small sample size (769 atoms in total), the frequen-cy of occurrence in VDP faces with 3, 4, 5, and 6 vertices (resp ect ively ≈15, 26, 22, and 18 %, Fig. 5) almost coincides with that est ablished for H-sub-lattices (resp ect ively, ≈13, 23, 24, and 2% [32]), which contain more than 4 million cryst allograph-ically diff erent H atoms with an average of kA ≈ 27. It is because of the absence of the short-range or-der in the mutual arrangement of chemically iden-tical atoms (U or H) with kA> 2, these sublattic-es have the same type of (p, f ) dist ributions with maxima of VDP faces at 15. For the same reason, the (p, f ) dist ributions of the U and H sublattices are similar to the monomodal (p, f ) dist ribution with a

maximum at f = 15 for the well-known “ideal gas” model syst em, which can be considered as a solid body devoid of short-range order in the arrangement atoms [32, 33].

5. ConclusionTh e use of VDP in cryst al chemical analysis al-

lows to solve a number of previously inaccessi-ble problems. One of them, essentially similar to “searching for a needle in a hayst ack,” is to identi-fy errors that for various reasons appear in crys-tal-st ruct ural databases that are const antly increas-ing in volume. As our experience shows, a number of VDP parameters that are absent in the arsenal of classical cryst al chemist ry can serve as descriptors that make it possible to detect errors relatively eas-ily, even if they go unnoticed when depositing “cif ” fi les into the database [7, 8].

In the process of preparing this article, we found several errors, however, let us dwell on only one example - uranyl succinate monohydrate. Un-til recently, the st ruct ure of its two modifi cations, rhombic {SUCCUR} [49] (hereinafter α-SU) and monoclinic {SUCCUR1} [5] (hereinafter β-SU), was known, reliable data for which were taken

Figure 5. Dist ribution of the VDP faces of uranium atoms depending on the number of vertices at the face (Nv) in the U-sublattices of the cryst al st ruct ure of: (a) - 1533 compounds with kA = 1; (b) - 2292 com-pounds with an average kA ≈ 1.6 (contain 3664 VDP of U atoms); (c) - 2 compounds with an average kA ≈ 38 (769 VDP of U atoms).



into account in a sample of 2292 compounds . However, in 215, information appeared for the third modifi cation (hereafter x-SU) {SUCCUR2} [51]. Th e abnormally large volume of VDP for the U (VI) atom in this st ruct ure (11.8 Å3) is unam-biguous evidence of gross errors, esp ecially since for α- and β-SU the volume of VDP is 9.12 and 9.13 Å3 and agrees well with the average value of 9.2(2)Å3 for more than 34 U(VI) atoms in the UOn complexes with any n from 6 to 9 (Table 1). Anomalies are also observed for a number of oth-er VDP parameters of the U atom in x-SU (for ex-ample, the value of DA is almost 2 times greater than the average value for U (VI)). The inaccura-cy of the data for x-SU is easily detected on the basis of the VDP characteristics of oxygen at-oms. Thus, in the structures of any U (VI) car-boxylates, the shortest O – O distance is ≈2.2 Å and corresponds to the contact between the oxy-gen atoms of one carboxyl group. In the case of x-SU, the shortest O-O distance is 1.43 Å and corre-sponds to the contact between the oxygen atoms of two different succinate ions coordinated by the same uranium atom. Since this distance is shorter than the single O – O bond in the peroxide ion, there are no succinate ions in x-SU, since they are connected to an infinite polymer chain with d (O – O) = 1.43 Å bonds. However, the researchers [51] did not even notice this circumstance, focus-ing on another feature of the structure, the bent up to 115° uranyl ion. The authors did not explain the reasons for such an anomalous structure of the uranyl ion in x-SU and, limiting themselves to mentioning the existence of the polymorphs α- and β-SU, in the structures of which the uranyl ion has the usual almost linear structure, called the results of their work “a milestone in the histo-ry of actinide chemistry” [51].

Since the volumes of rhombic α -SU and x-SU unit cells almost coincided (783.76 and 783.69 Å3), and the equivalent cell parameters differ on-ly in the second or third digits, most likely, the authors [46] made a mist ake in determining the sp ace group of cryst als (Brave lattice type is set in-correct ly). Th erefore, the anomalous result of x-SU researchers [51], in our opinion, is not a “mile-st one”, but evidence of the insuffi cient competence of the authors. It remains to be regretted that such “milest ones” that litter the scientifi c information obtained by several generations of researchers sometimes break into the pages of peer-reviewed journals and enter the st ruct ural database. It would be desirable to hope that the future “Heracles”, who will be able to clean the computer cryst al-st ruc-tural bases from the accumulated various “mile-st ones” like x-SU, will use the VDP parameters of atoms as useful tools.

AcknowledgementTh e work was performed with the fi nancial sup-

port of the Russian Foundation for Basic Research (Project Number № 16-3-2а).

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