Ab initio modelling of calcium phosphate clusters and their vibrational spectra
Calcium phosphate and hydroxylcalcium phosphate clusters that model amorphous phase elementary unit cells as well as their vibrational spectra were calculated by ab initio quantum chemical method using GAMESS code. Normal coordinate analysis was accomplished for phosphate anion, tricalcium phospha...
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irk-123456789-1214432017-06-15T03:03:48Z Ab initio modelling of calcium phosphate clusters and their vibrational spectra Boldeskul, I.E. Sukhodub, L.F. Kalinkevich, A.N. Khavryutchenko, V.D. Calcium phosphate and hydroxylcalcium phosphate clusters that model amorphous phase elementary unit cells as well as their vibrational spectra were calculated by ab initio quantum chemical method using GAMESS code. Normal coordinate analysis was accomplished for phosphate anion, tricalcium phosphate and hydroxylapatite. Calculated IR-spectra and spectra of inelastic neutron scattering were defined in comparison with experimental data. It was shown that within the suggested approach, vibrational spectroscopy appears to be a reliable method of verifying the quantum chemical calculated structure versus the experimental data. Кластери кальцiй-фосфату та гiдроксикальцiй-фосфату, якi моделюють елементарнi одиницi аморфної фази, а також їх вiбрацiйнi спектри були розрахованi за допомогою ab initio квантово-хiмiчного методу з використанням програмного коду GAMESS. Було проведено нормально-координатний аналiз для фосфатного анiону, трикальцiйфосфату та гiдроксилапатиту. Розрахованi IЧ-спектри та спектри непружного розсiювання нейтронiв були спiвставленi з експериментальними даними. Показано, що у рамках запропонованого пiдходу вiбрацiйна спектроскопiя є надiйним методом для верифiкацiї структур, що знайденi методом квантово-хiмiчних розрахункiв. 2006 Article Ab initio modelling of calcium phosphate clusters and their vibrational spectra / I.E. Boldeskul, L.F. Sukhodub, A.N. Kalinkevich, V.D. Khavryutchenko // Condensed Matter Physics. — 2006. — Т. 9, № 4(48). — С. 669–679. — Бібліогр.: 15 назв. — англ. 1607-324X PACS: 31.15.Ar, 61.46.Bc, 87.68.+z, 87.15.-v DOI:10.5488/CMP.9.4.669 http://dspace.nbuv.gov.ua/handle/123456789/121443 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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Calcium phosphate and hydroxylcalcium phosphate clusters that model amorphous phase elementary unit
cells as well as their vibrational spectra were calculated by ab initio quantum chemical method using GAMESS
code. Normal coordinate analysis was accomplished for phosphate anion, tricalcium phosphate and hydroxylapatite.
Calculated IR-spectra and spectra of inelastic neutron scattering were defined in comparison with
experimental data. It was shown that within the suggested approach, vibrational spectroscopy appears to be
a reliable method of verifying the quantum chemical calculated structure versus the experimental data. |
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Article |
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Boldeskul, I.E. Sukhodub, L.F. Kalinkevich, A.N. Khavryutchenko, V.D. |
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Boldeskul, I.E. Sukhodub, L.F. Kalinkevich, A.N. Khavryutchenko, V.D. Ab initio modelling of calcium phosphate clusters and their vibrational spectra Condensed Matter Physics |
| author_facet |
Boldeskul, I.E. Sukhodub, L.F. Kalinkevich, A.N. Khavryutchenko, V.D. |
| author_sort |
Boldeskul, I.E. |
| title |
Ab initio modelling of calcium phosphate clusters and their vibrational spectra |
| title_short |
Ab initio modelling of calcium phosphate clusters and their vibrational spectra |
| title_full |
Ab initio modelling of calcium phosphate clusters and their vibrational spectra |
| title_fullStr |
Ab initio modelling of calcium phosphate clusters and their vibrational spectra |
| title_full_unstemmed |
Ab initio modelling of calcium phosphate clusters and their vibrational spectra |
| title_sort |
ab initio modelling of calcium phosphate clusters and their vibrational spectra |
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Інститут фізики конденсованих систем НАН України |
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2006 |
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http://dspace.nbuv.gov.ua/handle/123456789/121443 |
| citation_txt |
Ab initio modelling of calcium phosphate clusters and
their vibrational spectra / I.E. Boldeskul, L.F. Sukhodub, A.N. Kalinkevich, V.D. Khavryutchenko // Condensed Matter Physics. — 2006. — Т. 9, № 4(48). — С. 669–679. — Бібліогр.: 15 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT boldeskulie abinitiomodellingofcalciumphosphateclustersandtheirvibrationalspectra AT sukhodublf abinitiomodellingofcalciumphosphateclustersandtheirvibrationalspectra AT kalinkevichan abinitiomodellingofcalciumphosphateclustersandtheirvibrationalspectra AT khavryutchenkovd abinitiomodellingofcalciumphosphateclustersandtheirvibrationalspectra |
| first_indexed |
2025-07-08T19:54:36Z |
| last_indexed |
2025-07-08T19:54:36Z |
| _version_ |
1837109847302078464 |
| fulltext |
Condensed Matter Physics 2006, Vol. 9, No 4(48), pp. 669–679
Ab initio modelling of calcium phosphate clusters and
their vibrational spectra
I.E.Boldeskul1, L.F.Sukhodub1, A.N.Kalinkevich1, V.D.Khavryutchenko2
1 Institute of Applied Physics, National Academy of Sciences of Ukraine,
58 Petropavlovskaya Str., 40030 Sumy, Ukraine
2 Institute of Sorption and Problems of Endoecology, National Academy of Sciences of Ukraine,
13 General Naumov Str., 03164 Kiev, Ukraine
Received March 29, 2006, in final form June 20, 2006
Calcium phosphate and hydroxylcalcium phosphate clusters that model amorphous phase elementary unit
cells as well as their vibrational spectra were calculated by ab initio quantum chemical method using GAMESS
code. Normal coordinate analysis was accomplished for phosphate anion, tricalcium phosphate and hydrox-
ylapatite. Calculated IR-spectra and spectra of inelastic neutron scattering were defined in comparison with
experimental data. It was shown that within the suggested approach, vibrational spectroscopy appears to be
a reliable method of verifying the quantum chemical calculated structure versus the experimental data.
Key words: molecular simulation, cluster approximation, calcium phosphate, hydroxyapatite, normal
coordinate analysis
PACS: 31.15.Ar, 61.46.Bc, 87.68.+z, 87.15.-v
1. Introduction
Nonstochiometry of Ca/P ratio in synthetic calcium hydroxylapatite (Ca-HAP) used in bio-
medical materials is well known and is due to heterogeneous minor phases, such as polymorphic
tricalcium phosphate (TCP), TCP-hydroxide, oxide-, hydroxide- and carbonate-calcium: CaO,
2Ca(OH)2, CaHPO2, Ca3(PO4)2, 3[Ca3(PO4)2], Ca10(PO4)6(OH)2, etc. [1,2].
Complex phase composition and mutual transformation of components require a simultaneous
application of different physical techniques for correct structure formation in the synthesis and for
adequate description of the product. These phases can be identified using X-ray scattering and
spectroscopy analysis within its threshold range [3–5]. Mass spectrometry [6,7] and vibrational
spectroscopy used with the aim of an express control in chemical synthesis, as well as for the
analysis of native bone tissue [8,9] seem to be more sensitive techniques.
Characterization of vibrations and the peculiarities of spectral and structural behaviour of
phosphate- and calcium ions, including hydroxyl functional groups, as well as their sensitivity to
intra- and intermolecular interactions, crystal effects including, allow us to suggest an effective
application of vibrational spectroscopy for cluster formation analysis. Informativity of vibrational
FTIR- and Raman-spectra including microspectroscopy rises due to the application of new experi-
mental techniques, such as inelastic neutron scattering (INS) spectroscopy, increases the reliability
of the spectra band assignment, especially for all vibrations with high level of hydrogen atom
participation.
Modern computational chemistry permits the modelling of the above mentioned states and their
spectra. The aim of the present work is computer modelling of the mentioned molecular clusters
and vibrational spectra of such clusters in their relevance to experimental data.
c© I.E.Boldeskul, L.F.Sukhodub, A.N.Kalinkevich, V.D.Khavryutchenko 669
I.E.Boldeskul et al.
2. Methodology
Literature data on quantum chemical calculations of the calcium containing compounds are
not numerous. There are numerous methods of modelling the space structure at the atomic level.
Therefore it is difficult to choose the best quantum chemical method of computing a big set of
calcium-phosphate based compounds with different structure and their vibration spectra. The
main question that arises during the modelling process is how to verify the obtained structure.
This question becomes a big problem for small particles, amorphous or real surface under study,
when it is impossible to use standard structure methods such as X-ray or neutron diffraction. In
order to solve this problem we proposed to use vibration spectroscopy as a method of verifying
and comparing the calculated and real structures.
For quantum chemistry modelling we applied ab initio methodology with PC-GAMESS program
package [10]. All computations were performed up to a complete structure optimization, Cartesian
force field evaluation, dipole moment and polarizability derivatives calculation. Normal coordinate
analysis in internal dependant coordinate system was performed by means of methods, algorithms
and software used earlier [11], but we should remind the basic principles of this methodology and
utilization.
The force constant matrix in Cartesian coordinates after GAMESS program was converted to
internal dependant coordinate system. Inverted vibration task or force field fitting was solved using
a full-matrix method. Inelastic neutron spectra intensity was calculated using the known neutron
coherent and incoherent cross-section on atomic nucleus with their natural isotope ratio. For the
INS intensity calculation the form of normal vibrations was used. After solving a direct vibration
problem in internal dependant coordinate system, the form of normal vibrations was transformed
to Cartesian coordinates and gave us atom deviation amplitudes. Multiplying derivatives (of dipole
moments or polarizability) by the atom deviation amplitudes one can obtain the alteration of the
total dipole moment or polarizability for the current normal vibration. The square of this alteration
is proportional to the absolute intensity in IR- or Raman spectra. The intensity in INS spectra is
calculated similarly, but separately for coherent and incoherent parts of total neutron cross-section
of every normal vibration.
Therefore, the intensity calculation leads to the delta-function which shows the position and
intensity of normal vibration. Due to the lack of suitable theory of the vibration band shape,
the theoretical vibrational spectra were obtained as the sum of Gauss-like lines normalized to
100% with pre-exponential coefficient equal to the computed intensity, the position equal to the
computed normal vibration frequency and halfwidth being defined by the type of the spectrum and
after building the theoretical spectrum, the value of the halfwidth was slightly varied for better
agreement with the experiment.
For INS spectra the halfwidth was taken as the known apparatus function and for IR- and
Raman spectra the starting value was taken 10 cm−1. Experimental spectra, which were taken
from the literature, were scanned, digitized and used to compare with theoretical spectra and to
solve inverted vibration problems.
Table 1. Space and electronic structure data for phosphate anion.
Parameter MINI basis set MINI–d1 basis set STO–6–311 basis set
P–O bond length in Å 1.8095 1.5878 1.6409
P–O bond order 0.945 1.517 1.091
Charge on P 0.5560 0.4510 1.8463
Charge on O –0.8890 –0.8627 –1.2116
The results of quantum chemical calculation will be given in table 1. We used some basis sets
(MINI without polarization d-function, MINI-d1 with one polarization d-function and STO–6–311)
for the ab initio calculation, which is introduced into GAMESS–PC program. They are well known
and therefore we shall not discuss them. At first, we should discuss the building “brick” for all
670
Ab initio modelling of calcium phosphate clusters
phosphate compounds – phosphate anion PO−3
4 . To test methodology and to obtain scaling factors
for the phosphate anion, we performed the calculation for the ideal tetrahedral anion PO−3
4 . The
space and electronic structure data for phosphate anion are presented below.
After data evaluation for the normal coordinate analysis in internal dependant coordinate
system inverted vibrational problem was solved for these three data sets, using literature data [12].
Experimental frequencies for the ideal tetrahedral anion PO−3
4 are: ν1=938 cm−1, ν2=420 cm−1,
ν3=1017 cm−1, ν4=567 cm−1.
After force field fitting the calculated and experimental frequencies are congruent with high
accuracy (deviation is less than 0.1 cm−1). Force constants are listed in table 2.
Table 2. Force constants.
Force constant MINI MINI–d1 STO
6–311
Fitted
MINI
Fitted
MINI–
d1
Fitted
6–311
K(P–O) 3.3965 11.0926 8.1674 9.6522 9.7085 9.6877
K(P–O/P–O) –0.2680 0.6651 0.2806 1.0954 1.0766 1.0835
K(O–P–O) 1.4063 2.4303 2.1032 2.9504 1.9326 2.2458
K(P–O/O–P–O) 0.0576 0.2957 0.2110 0.2402 0.2211 0.2267
K(P–O′/O–P–O) –0.0547 –0.2957 –0.2110 –0.2373 –0.2211 –0.2267
K(O–P–O/O–P–O) –0.2008 –0.3194 –0.2729 –0.1562 –0.3651 –0.3021
K(O’–P–O’/O–P–O) –0.5979 –1.1528 –1.0117 –0.8796 –0.8930 –0.8904
These data show that in all cases the quantum force field needs to be scaled and/or it is
necessary to solve the inverted vibration problem. For the fitted force fields the difference between
the same force constant is small. It means that the method of fitting the force field is applicable and
produces a good quality force field independently of the starting points. These force constants sizes
are presented in 106 cm−2. To convert the bond-bond force constant to mdin/Å the value should
be multiplied by factor of 0.6409891, the bond-angle force constant being converted to mdin, the
value should be multiplied by a factor of 0.6986781 and the angle -angle force constant converted
to mdin/Å, the value should be multiplied by a factor of 0.7615592. This result shows that ab initio
method produces force constants with various accuracy depending on the basis set. However, in all
cases the force field should be fitted using experimental frequencies or, better. At first it is needed
to scale the field and then to fit it. Our experience shows that we can transfer the scaling factors
for the same vibrational coordinate and for the same basis set to the row of the compounds with
similar structure fragments.
3. Results and discussion. Cluster models
Calcium-phosphate based materials under our interest are usually manufactured by plasma
spray or other chemical vapour deposition (CVD) process, which produces amorphous and/or
nonstochiometric compounds. Since we started from the gas-phase, the crystal structure as an
initial structure for simulation should be rejected [12].
As a starting point for space structure optimization one can start from the “free” ions Ca+2
and PO−3
4 . If necessary, the hydroxyl ion was added to the initial ion gas phase mixture. We
understand that this way of building the initial structure may lead to different minima on the
potential energy surface (PES), but this way is free from a strict dictate of the crystal structure
and is more preferable for amorphous solid simulation.
In a mathematical sense, no criterion guarantees that the global minimum has been found on
the PES. Nonetheless, using chemical restriction that any of the considered isomers conserves two
PO4-groups in which the phosphorous atom is surrounded by four oxygen atoms, we can perform
a systematic search on the PES by enumerating all the different topologies, that is, the different
ways of connecting calcium and oxygen atoms, encountered in Ca3(PO4)2 clusters [13].
671
I.E.Boldeskul et al.
To investigate many minima energy hypersurfaces we developed a simple, but effective method,
which was successfully tested on typical amorphous solid like high dispersed silica and silica glasses
[11]. These results will be presented in the article to follow [14].
Therefore, hereinafter, we describe the simplest calcium-phosphate clusters, which can become
building blocks for amorphous and glass-like apatites and their derivatives.
Simplest calcium-phosphate clusters with formula Ca3(PO4)2 are shown in figures 1 and 2 of
table 3. At this stage the mentioned cluster was taken as a reference model, because this system is
commonly considered to be an elementary unit cell of amorphous phase and is known in literature
[13]. This work discusses 89 ab initio starting geometries corresponding to different topologies of
combining three calcium cations and two phosphate anions. The calculated and experimental IR-,
Raman and INS-spectra of the clusters are presented in tables 4 and 5.
Table 3. Spatial structure of some calcium-phosphate clusters.
1
2
3
4
The most stable structure, Ca3(PO4)2 cluster (table 3, figure 2), is also known. Our results for
two clusters (table 3, figures 1–2) are in good agreement with the literature results [13]. Symmetrical
structure was calculated using two basis sets: clusters 2 with basis set MINI and cluster 3 with
basis set MINI d1 (one additional polarization d-function for every atom). More stable structure
D3h symmetry with all three calcium atoms bridging two PO4 groups is shown in figure 2 of
table 3. It is 92.93 kcal/mol (basis set MINI) which is more preferable than structure figure 1.
The bond length between calcium ions and the oxygens nearest to PO−3
4 is close to the sum of
Wan-der-Waals radii of these atoms. These distances are in between the limits 2.18− 2.36 Å while
bond orders are within 0.129 − 0.235. It is interesting to note that there is no linear relationship
between bond length and bond order for Ca–O bonds. Detailed data for these two clusters (2 and
3) are presented in table 6.
All bonds in the clusters are usual ones. These data show that the chemical bond between
calcium ions and the nearest oxygen is mainly ionic. It leads to a very important conclusion that
calcium phosphate structure should be very sensitive to the environment and should form an
amorphous phase very easily.
672
Ab initio modelling of calcium phosphate clusters
Table 4. Vibrational spectra (INS, IR- and Raman) of the some calcium-phosphate clusters.
1. Cluster 1. Theoretical INS spectrum. 2. Cluster 1. Theoretical IR spectrum.
3. Cluster 1. Theoretical Raman spectrum. 4. Cluster 2. Theoretical INS spectrum.
5. Cluster 2. Theoretical IR spectrum. 6. Cluster 2. Theoretical Raman spectrum.
7. Cluster 3. Theoretical INS spectrum. 8. Cluster 3. Theoretical IR spectrum.
The vibrational spectra calculated for these structures in the phosphate ion vibration region are
presented in figure 3 of table 4. It is evident that vibration frequencies ν(PO) are under 1000 cm−1
(except basis set MINI d1) and together with the calculated quantum chemical parameters, such
as interatomic distance and their charges show ionic character of the bond. For a less symmetrical
structure (2) as well as for the calculated inelastic neutron scattering spectra (INS) the calculations
demonstrate more peaks due to the elimination of the prohibition by symmetry rules.
Similarly, more complex 3D model of 3[Ca3(PO4)2] cluster was built from three clusters (2).
Complete optimization of geometry leads to the structure whose main difference from the initial
structure is the increase of calcium-oxygen distance. It leads to the non-bonding of the calcium ions
673
I.E.Boldeskul et al.
Table 5. Vibrational spectra (INS, IR- and Raman) of some calcium-phosphate clusters.
(Continue.)
9. Cluster 3. Theoretical Raman spectrum. 10. Cluster 4. Theoretical (1) and experimen-
tal (2) [15] INS spectrum.
11. Cluster 4. Theoretical (1) and experimen-
tal (2) [15] IR spectrum.
12. Cluster 4. Theoretical (1) and experimen-
tal (2) [15] IR spectrum.
13. Cluster 4. Theoretical (blue and black)
and experimental [15] (red) Raman spectrum.
with the nearest oxygenes since this distance is larger than the sum of Van-der-Waals radii of these
atoms. Bond orders between calcium ions and the nearest oxygenes are less than 0.170, but their
numbers are large. This means that the bond orders decrease, while the number of contacts to cal-
cium increases. Total bond order for every calcium ion is between 0.537 and 0.576. This corresponds
to calcium coordination number 4 to 5, that is not typical of calcium ions, which may be up to
12-fold coordinated. These data show that covalent part of calcium-phosphate ion interaction is not
big enough and non-directional and unsaturable electrostatic ionic bonds should play an important
role in calcium phosphate interactions. It means that these kinds of compounds should easily turn
into amorphous phase. Vibrational spectra of such a system are being calculated at the moment.
Finally cluster 4 shows the simplest HAP system with formula unit Ca5(PO4)3(OH) and its
calculated vibrational spectra. Literature data [15] on IR and INS spectra make it possible to
specify the calculated spectrum up to a full agreement with the experiment by solving a re-
verse spectral task. Normally coordinated analysis makes up for assigning vibrational frequencies
(table 7) and shows characteristic properties of HAP structure. Despite the smallest cluster size
this system can reproduce the main features of experimental spectra: INS, IR and Raman. Experi-
mental data utilization enables us to make a correct vibration spectra assignment based on the
674
Ab initio modelling of calcium phosphate clusters
Table 6. Structure and electronic characteristics for clusters 2 and 3.
Parameter Basis set MINI Basis set MINI d1
P–O bond length (Å)/ bond order 1.730 / 0.902 1.609 / 1.270
P=O bond length (Å)/ bond order 1.696 / 1.103 1.472 / 1.925
Ca–O bond length (Å)/ bond order 2.312 / 0.150 2.311 / 0.273
∠ O=P–O angle (degree) 120.8 116.9
∠ O–P–O angle (degree) 96.12 101.14
QCa 1.593 1.348
QP 0.945 0.717
QO− –0.901 –0.709
QO= –0.631 –0.610
intensity calculations. Using the big difference between the nature of the band intensity for these
three kinds of experimental vibrational spectra and their identity with normal vibration forms we
can divide the vibrational spectra into two groups: below 800 cm−1 and above. Between 800 cm−1
and 1300 cm−1 one can observe the vibrations and a corresponding band, which can be assigned
to the phosphate ion internal vibrations – P–O bond stretch symmetrical and antisymmetrical
vibrations. Due to the decrease of the phosphate ion local symmetry in the real solids from ideal
Td, strong selection rules (for IR- and Raman spectroscopy) are broken and one can observe all
bands and their splitting due to the disappearance of degeneration. As a result, the experimental
spectrum after removing all the faults turns out to be an envelope curve or the sum of all normal
vibration bands. Therefore, one can use this spectral region to detect the phosphate ion status.
The spectral region between 400 cm−1 and 800 cm−1 can be used to detect the O–P–O angle
bending vibrations. These kinds of vibrations are more sensitive to the chemical environment
and space structure transformation due to Ca–O bonds and their force constants involve more
participants in these vibrations. Therefore, this region can be used in investigating the calcium
ion position and in coordinating the polyhedron transformation. However, this requires additional
cluster investigations.
Also the spectral region below 400 cm−1 can be used in investigating the cluster packing and
the bonding between phosphate-calcium aggregates. However, we need good quality INS, IR- and
Raman spectra for this region in order to build spectra-structure relationships and understand
their nature. Without quantum chemical calculation and a complete normal-coordinate analysis
these relations and rules, which are used in the industrial quality control, should be empirical
speculations only.
It means that vibration spectroscopy should be a beneficial method of controlling and testing
in calcium-phosphate systems. We hope that further elaborate investigations in this field will lead
us to a deep comprehension of how to control and manage the structure and properties of calcium-
phosphate systems.
4. Conclusions
Calculations of vibrational frequencies in IR-, Raman- and INS-spectra supplemented by inten-
sity computation within one force field and structure under investigation ensure better assignment
of experimental data.
The modelling of the calcium-phosphate cluster properties, first of all their vibrational spectra,
with GAMESS code followed by comparison with experiment shows that MINI basis set appears
to be a good compromise between computational time and costs and accuracy of calculations.
The results of this study suggest that direct quantum chemical calculations and comprehensive
assignment of wave numbers in vibrational spectra of the simple hydroxyapatite clusters can be
helpful in analysing amorphous or microcrystalline nano-size calcium-phosphate systems.
675
I.E.Boldeskul et al.
Table 7. Calculated normal vibration for the cluster Ca5(PO4)3(OH) – hydroxyapatite. Normal
vibration notation: ν – stretch vibration, δ – angle deformation, ρ – out-of-plane vibration, χ –
torsion vibration, P.E.D. – potential energy distribution.
No Freq. cm−1 INS int. rela-
tive.
IR int. rela-
tive.
P.E.D. % Assignment
148 3735.00 100.00 14.45 99.94 ν O-H
147 1112.66 2.24 34.34 77.67
11.18
ν P–O
ν P–O
146 1092.71 0.50 25.84 9.17
83.47
ν P–O
ν P–O
145 1073.64 96.00 35.77 51.34 δ Ca–O-H
144 1056.95 4.53 45.68 45.15 ν P–O
143 1035.60 4.63 100.00 56.84 ν P–O
142 1014.36 5.53 48.66 67.32
5.97
8.42
ν P–O
δ O–P–O
δ Ca–O–P
141 957.74 5.04 56.75 58.59 ν P–O
140 934.53 1.34 55.70 49.97 ν P–O
139 913.40 2.99 42.16 67.68
7.11
ν P–O
δ O–P–O
138 892.09 4.35 37.32 16.24
50.39
ν P–O
ν P–O
137 869.26 1.03 19.21 54.66
6.68
ν P–O
δ Ca–O–P
136 656.59 32.15 30.92 15.00 ν P–O
135 637.96 60.29 15.73 38.50 ρ Ca–O-Ca
134 636.54 37.98 23.88 19.79 ν P–O
133 629.42 43.55 1.74 21.55 ρ Ca–O-Ca
132 604.94 12.28 54.31 14.74
5.65
32.66
13.63
ν Ca–O
ν Ca–O
ν P–O
ν P–O
131 590.28 16.85 28.73 12.46
12.29
5.28
19.11
6.55
ν Ca–O
ν Ca–O
ν Ca–O
ν P–O
δ O–P–O
130 579.71 14.74 7.23 5.57
19.75
33.94
ν Ca–O
ν Ca–O
ν P–O
129 568.31 4.62 34.69 7.26
7.42
14.87
ν Ca–O
ν P–O
ν P–O
128 565.47 7.70 10.69 17.19
14.98
9.66
ν P–O
ν P–O
δ O–P–O
127 564.58 4.50 23.39 6.41
9.79
5.77
14.16
6.24
ν Ca–O
ν Ca–O
ν Ca–O
ν P–O
ν P–O
676
Ab initio modelling of calcium phosphate clusters
126 547.03 11.52 53.15 13.44
13.33
15.11
5.52
13.04
7.86
ν Ca–O
ν Ca–O
ν P–O
δ O–P–O
δ O–P–O
δ Ca–O–P
125 526.66 15.02 20.24 20.41 ν Ca–O
124 517.61 13.37 2.41 13.59 ν Ca–O
123 513.70 6.55 9.35 5.08
22.28
ν Ca–O
ν Ca–O
122 496.60 6.42 10.63 11.99
6.78
ν Ca–O
ν Ca–O
121 474.24 14.84 5.75 10.20
5.53
23.40
5.86
ν Ca–O
ν P–O
δ O–P–O
δ Ca–O–P
120 462.53 9.14 7.38 10.18
6.74
10.34
6.33
ν Ca–O
ν Ca–O
ν P–O
δ O–P–O
119 450.38 11.29 15.47 14.52 ν Ca–O
118 424.41 3.86 3.81 23.81
16.93
16.33
6.27
ν Ca–O
ν P–O
δ O–P–O
δ O–P–O
117 423.17 11.09 5.12 5.65
5.12
11.51
6.40
ν Ca–O
ν Ca–O
ν P–O
δ O–P–O
116 421.99 8.66 2.61 9.59
11.12
9.06
ν Ca–O
ν P–O
δ O–P–O
115 369.66 15.06 5.53 11.15 ν Ca–O
114 355.73 11.52 0.82 9.59
5.95
11.57
ν Ca–O
ν P–O
δ O–P–O
113 340.98 7.19 23.89 6.66
8.06
ν Ca–O
ν Ca–O
112 317.66 6.80 15.69 10.76 ν Ca–O
111 304.05 3.52 8.33 5.03
11.97
7.77
ν Ca–O
ν Ca–O
ν Ca–O
110 292.33 9.41 8.59 11.06
7.94
ν Ca–O
ν Ca–O
109 286.40 5.74 5.70 6.80
14.72
5.16
5.76
ν Ca–O
ν Ca–O
ν Ca–O
δ O–P–O
108 272.61 2.05 5.95 7.47
7.25
15.90
ν Ca–O
ν Ca–O
ν P–O
107 255.65 13.24 8.95 19.79
9.60
10.74
10.00
5.35
ν Ca–O
ν Ca–O
ν P–O
δ O–P–O
δ Ca–O–P
677
I.E.Boldeskul et al.
106 241.07 7.20 8.21 14.14
12.51
6.30
ν Ca–O
ν Ca–O
δ O–P–O
105 235.74 10.58 3.14 6.80
7.49
ν Ca–O
δ O–P–O
104 225.17 16.02 0.14 13.08
9.48
22.76
6.19
ν Ca–O
ν Ca–O
δ O–P–O
δ O–P–O
103 209.83 8.97 5.44 5.10
5.86
9.23
11.57
ν Ca–O
ν Ca–O
δ O–P–O
δ O–P–O
102 194.48 13.04 0.62 12.52 ν Ca–O
101 181.53 9.78 1.31 9.69 ν Ca–O
100 171.95 9.28 6.12 16.25
5.14
ν Ca–O
ν P–O
99 169.68 5.02 0.80 10.10
19.33
6.06
ν Ca–O
δ O–P–O
δ Ca–O–P
98 151.80 10.92 2.32 8.94
7.00
8.09
7.01
9.02
5.84
ν Ca–O
ν Ca–O
δ O–P–O
δ O–P–O
δ Ca–O–P
δ Ca–O–P
97 145.94 12.65 7.40 15.08 δ O–P–O
96 139.23 11.06 4.32 7.07
5.93
9.22
ν Ca–O
ν Ca–O
δ O–P–O
95 130.43 11.11 6.66 6.46
10.63
6.72
δ O–P–O
δ Ca–O–P
δ Ca–O–P
94 124.67 7.17 2.19 7.79
13.80
ν Ca–O
ν Ca–O
93 110.53 16.91 7.36 10.70 ν Ca–O
92 107.36 11.57 6.86 20.61
5.03
10.72
ν Ca–O
δ O–P–O
δ Ca–O–P
91 98.72 2.40 2.49 6.78
7.99
7.09
9.77
ν Ca–O
ν P–O
δ O–P–O
δ Ca–O–P
90 92.58 9.77 3.39 18.34 ν Ca–O
89 82.11 7.89 2.26 10.22 χ Ca–O
88 11.92 8.00 0.57 24.46 χ P–O
678
Ab initio modelling of calcium phosphate clusters
References
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Ab initio моделювання кальцiй-фосфатних кластерiв i їх
вiбрацiйних спектрiв
I.Є.Болдескул1, Л.Ф.Суходуб1, О.М.Калiнкевич1, В.Д.Хаврюченко2
1 Iнститут прикладної фiзики НАНУ, вул. Петропавлiвська, 58, м. Суми, Україна, 40030
2 Iнститут сорбцiї та проблем ендоекологiї НАНУ, вул. генерала Наумова, 13, м. Київ, Україна, 03164
Отримано 29 березня 2006 р., в остаточному виглядi – 20 червня 2006 р.
Кластери кальцiй-фосфату та гiдроксикальцiй-фосфату, якi моделюють елементарнi одиницi амор-
фної фази, а також їх вiбрацiйнi спектри були розрахованi за допомогою ab initio квантово-хiмiчного
методу з використанням програмного коду GAMESS. Було проведено нормально-координатний
аналiз для фосфатного анiону, трикальцiйфосфату та гiдроксилапатиту. Розрахованi IЧ-спектри та
спектри непружного розсiювання нейтронiв були спiвставленi з експериментальними даними. По-
казано, що у рамках запропонованого пiдходу вiбрацiйна спектроскопiя є надiйним методом для
верифiкацiї структур, що знайденi методом квантово-хiмiчних розрахункiв.
Ключовi слова: молекулярна симуляцiя, кластерне наближення, фосфат кальцiя, гiдроксилапатит,
нормально-координатний аналiз
PACS: 31.15.Ar, 61.46.Bc, 87.68.+z, 87.15.-v
679
680
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