Национальной академии наук республики казахстан

Доклады Национальной академии наук Республики Казахстан  
 
 
   
16  
[3] M. Sowjanya, A. K. Sahoo and Sananda Kumar, “Distributed Incremental Leaky LMS,” International Conference on 
Communications and Signal Processing  (ICCSP),  2015,  pp. 1753-1757. 
[4]  Chen W. Y. and Haddad R. “A variable step size LMS algorithm,” IEEE Proceedings of the 33rd Midwest  Symposium 
on Circuits and Systems,  1990, vol. 1, Calgary, pp. 423-426 . 
[5]  Won Y. K., Park R. H., Park J. H. and Lee B. U. “Variable LMS algorithms using the time constant concept,” IEEE 
Transactions on Consumer Electronics, 1994, vol. 40, no. 4, pp. 1083-1087. 
[6]  Chen Y., Gu Y. and Hero A. O. “Sparse LMS For System Identification,”  IEEE  International  Conference Acoustic, 
Speech  and  Signal  Processing, 2009, pp. 3125-3128. 
[7]  Salman M. S. “Sparse leaky-LMS algorithm for system identification and its convergence analysis,” International 
Journal of Adaptive Control and Signal Processing, 2013, vol. 28, no. 10, pp. 1065-1072. 
[8] Turan C. and Salman M. S. “Zero-Attracting Function Controlled VSSLMS Algorithm with Analysis,” Circuits, 
Systems,  and  Signal  Processing,  Springer, 2015, DOI 10.1007/s00034-015-9996-5. 
[9]  Sing-Long C.A., Tejos C.A., Irarrazaval P. Evaluation of continuous approximation functions for the l
0
-norm for 
compressed sensing, Proc. Int. Soc. Mag. Reson. Med., 2009, vol. 17,  pp. 4585. 
 
МОДИФИКАЦИЯЛАНҒАН СИРЕК LMS-АҒАТЫН  
АЛГОРИТМНІҢ КӨМЕГІМЕН ЖҮЙЕЛЕРДІ СƏЙКЕСТЕНДІРУ 
 
Д. Туран, Р.Н. Сулиев, Е.Н. Əмірғалиев  
 
Тірек сөздер: адаптивті алгоритмдер, жүйелерді сəйкестендіру, сиректелген жүйелер. 
Аңдатпа. Бұл мақалада сиректелген жүйені сəйкестендіру үшін ZA-LLMS (Zero-Attracting Leaky-LMS) алгоритімін 
жақсартуда  қолданылатын  жаңа LMS-ағатын  алгоритмін  ұсынылады.  Ұсынылған  алгоритм  қадам  мөлшері  мен  l
0
-
нормалы айыппұлдың ауытқу артықшылықтарымен сиректелген жүйені қолданады. Өнімділігін салыстыру мақсатында 
ұсынылып отырған алгоритмді LLMS-пен жəне ZA-LLMS-пен жинақтылық жылдамдығы мен ортақвадратталған ауытқу 
(MSD)  тұрғысынан  салыстырдық.  Зерттеулер MATLAB орталығында  жүргізілді.  Модельдеудің  жетістігі,  екі  типтегі 
кіріс сигналдарыны үшін: қосымша ақ Гаусс шуы (AWGN) мен қосымша корреляциялық Гаусс шуы (ACGN), ұсынылып 
отырған алгоритм басқада алгоритмдерден үстемділігінің артықшылығын көрсетеді. 
 
Поступила 16.05.2016 г. 

ISSN 2224–5227                                                                                                                               
№ 3. 2016  
 
 
17 
REPORTS OF THE NATIONAL ACADEMY OF SCIENCES  
OF THE REPUBLIC OF KAZAKHSTAN 
ISSN 2224-5227 
Volume 3, Number 307 (2016), 17 – 22 
 
УДK 541.1+530.145 
 
АНАЛИЗ ВЗАИМОДЕЙСТВИЯ ПОВЕРХНОСТИ МЕТАЛЛИЧЕСКОЙ 
РТУТИ С АММОНИЙНЫМИ ОСНОВАНИЯМИ НА ОСНОВАНИИ 
ТЕОРИИ ФУНКЦИОНАЛА ПЛОТНОСТИ 
 
O. Х. Полещук
1
, С. В. Ковалева
2
, М.Н. Ермаханов
3
,  
П.А. Саидахметов
3
, А.Б.Утелбаева
3
, М.А. Нуруллаев
3 
 
1
Национальный исследовательский Томский политехнический университет, Томск, Россия; 
2
Кафедра неорганической химии, Томский государственный педагогический университет, Томск; Россия; 
3
Южно-Казахстанский государственный университет им. М. Ауезова, Шымкент, РК 
 
Ключевые  слова:  теория  функционала  плотности,  псевдопотенциал,  аммонийные  основания, 
металлическая ртуть, натуральные орбитали связи. 
Аннотация.  Проведены  расчеты  некоторых  ртутьсодержащих  молекул  в  газовой  фазе  на  основании 
расчетов  методом  функционала  плотности  с  использованием  псевдопотенциального  базисного  набора  для 
атома ртути и 6-311+G(d,p) для других атомов в программном пакете GAUSSIAN 03 и TZ2P+ в программе 
Амстердамский функционал плотности. Показано, что катион аммония по сравнению с радикалом аммония 
с  большей  вероятностью  может  взаимодействовать  с  поверхностью  металлической  ртути.  Рассчитанные 
термодинамические  параметры  указывают  на  невозможность  взаимодействия  с  поверхностью 
металлической ртути таких аминов, как гидроксиламин, гидразин и тетраметиламин. 
 
UDK 541.1+530.145 
 
USING OF DENSITY FUNCTIONAL THEORY FOR ANALYSIS  
OF SURFACE INTERACTION BETWEEN METALLIC MERCURY  
AND AMMONIUM BASES 
 
O. Kh. Poleshchuk
1
, S.V. Kovaleva
2
, M.N. Ermakhanov
3
, 
P.A. Saidakhmetov
3
, A.B Utelbaeva
3
, M.A. Nurullaev
3
 
 
1
National Research Tomsk Polytechnic University, Tomsk, Russia; 
2
Inorganic chemistry department. Tomsk state pedagogical university, Tomsk, Russia; 
3
M.Auezov South Kazakhstan state University, Shymkent, RK 
poleshch@tspu.edu.ru, myrza1964@mail.ru, timpf_ukgu@mail.ru, nurmarat75@mail.ru 
 
Key words: density functional theory, pseudopotential, ammonium bases, metallic mercury, natural bond 
orbital. 
Abstract. The calculations of some mercury-containing molecules in the gas phase on the basis of calculations 
by the density functional method with use of the pseudopotential basis set for mercury atom and 6-311+G(d,p) for 
other atoms in the software package GAUSSIAN’03 and TZ2P+ in the Amsterdam density functional program were 
implemented. It is shown that the ammonium cation in comparison with the ammonium radical is more likely to 
interact with the surface of the metallic mercury. The calculated thermodynamic parameters indicate the inability of 
amines such as hydroxylamine, hydrazine and tetramethylamine to interact with the surface of metallic mercury. 
 
Introduction. Pseudo metal amalgams, which include amalgams of ammonia, pyrrolidine and their 
derivatives represent of great interest. The most studied is an amalgam of ammonium, which was first 

Доклады Национальной академии наук Республики Казахстан  
 
 
   
18  
obtained by electrolysis of ammonium carbonate solution on mercury cathode, as well as a result of the 
exchange reaction of ammonium salts with alkali metal amalgam. 
Generalization of the works on the preparation and the study of physical and chemical properties of 
ammonium amalgam is represented in the survey [1], but question about form of existence of the 
potential-defining of amalgam particles remains controversial to this day. In most studies ammonium 
amalgam is presented as NH
4
(Hg) [2-6], or NH
4
(Hg)
n
 [7, 8]. 
In [9] it has been suggested that the radical NH
4
, obtained by reduction of ammonium cation on a 
mercury electrode, is dissolved in mercury and gives one electron to the conduction zone. 
Based on the linear relationship between the concentration of ammonia in mercury and temperature 
freezing of amalgam [10] have been concluded that the amalgam ammonium represent a solution of NH
4
 
radical in mercury. In [11] it has been found that the reduction R
4
N
+
 cation on mercury, lead and tin are 
formed solid products: 
R
4
N
+
 + 5М
(catod)
 + е→ [R
4
N
+
(M
5
-
)]
solid
, 
 
representing a cation R
4
N
+
, associated with a polyanion M
5
-
. The stoichiometry of the resulting 
compounds was proved by elemental analysis.  
Based on diamagnetic properties of ammonium amalgam, obtained by reduction of NH
4
+
 cation on a 
mercury electrode at temperatures below point of mercury freezing, it is concluded that the existence of 
NH4 radical in mercury is unlikely, therefore amalgam ammonium structure is similar to [R
4
N
+
(M
5
-
)]
solid
. 
According to [11] the name "Ammonium amalgam" does not reflect the nature of the solid 
compound and "Ammonium - mercury" is more preferred term.  
A similar view is expressed in our paper [12]. Unstable free radicals of ammonium and its analogues 
are stabilized in mercury phase due to the transfer of electron in the zone of mercury conduction. For 
amalgams of pseudometal hydrides in analogy with amalgams of alkali metals hydrides may be adopted 
as R
+
[Hg
n
H]
-
 structure [13]. 
Therefore, the aim of this work is the quantum-chemical calculation of the interaction of certain 
amines with metallic mercury to determine their spatial structure and thermodynamic parameters. 
Experimental part. The calculations were performed with use of a standard software package 
GAUSSIAN’03 [14]. We have used the relativistic potential for a mercury atom, including 46 basic 
electrons [15]. For light atoms there were used the full-electronic basis set with the inclusion of diffuse 
and polarization functions 6-311+G(d,p). 
Calculations were performed by the hybrid method of density functional B3LYP with the functional 
Beke B3 [16] and correlation functional Lee, Yang and Parr (LYP) [17]. Currently, this method is 
generally accepted to describe the thermodynamic characteristics and is best agreed with the experimental 
values [18]. The geometrical parameters of calculated molecules and ions have been fully optimized, 
absence of imaginary vibrational frequencies confirmed their stationary character. 
The thermodynamic parameters of the molecules calculated were corrected for zero-point vibrational 
energy (ZPVE) and reduced to normal conditions (298.15K, 1 atm) using thermal corrections to enthalpy 
and free energy. 
The calculations of ammonium cation and NH
4
 radical with zero charge, as well as mercury cluster 
was also carried out in the approximation of natural bond orbitals [19]. 
On the other hand, these compounds also have been studied by use of ADF program [20]. We used 
exchange functional OPTX [21], combined with PBE correlation functional [22] with the irreducible 
Slater triple-zeta + polarization basis set using the frozen-core approximation to the inner electrons. 
Relativistic effects of heavy atoms have been accounted with use of the regular zero-order approximation 
(ZORA) [23], which gives more realistic results than the widely used Pauli formalism in the Gaussian 
package. 
Results and their discussion. To assess the "quality" of the calculations it is necessary to rely on 
some physical and chemical properties of these compounds for which it is known experimental reasonably 
accurate values. As a last we used the bond lengths, as well as the vibrational frequencies in the IR spectra 
of some simple mercury compounds. 
Fig. 1 shows correlation dependence between experimental [24] and calculated bonds lengths for 
some mercury compounds: 
 
 
R(exp.) = -0.14+1.03R(calc.)      r = 0.999; s = 0.03; n = 7 
 (1) 
 

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№ 3. 2016  
 
 
19 
In these and the following correlation equations r - is the coefficient of correlation, s - standard 
deviation, and n - number of compounds included in the correlation. 
A similar best dependence was obtained at calculation of the same molecules in the ADF program: 
 
 
R(exp.)= -0.02+1.01R(calc.)     r = 0.999; s = 0.02; n = 7 
 (2) 
 
Table 1 shows the calculated and experimental values of the frequencies of the valence and 
deformation vibrations in the IR spectra of some mercury compounds [25]. 
Fig. 2 shows a linear correlation of excellent quality, which testifies that calculations correctly 
describe the electron-vibrational transitions. 
 
 
ω(exp.) = 13.4+1.05ω(calc.)      r = 0.999; s = 12; n = 21 
 (3) 
 
1,5
2,0
2,5
3,0
3,5
4,0
1,5
2,0
2,5
3,0
3,5
4,0
HgI
2
HgBr
2
HgCl
2
HgH
HgH
2
HgH
+
Hg
2
E
x
pe
ri
m
e
nt
al
 bo
nd
 l
e
ng
th
,A
Calculated bond length,A
0
200
400
600
800
1000
1200
1400
0
200
400
600
800
1000
1200
1400
ω
(e
x
p
.)
,c
m
-1
ω
(calcul.),cm
-1
Fig. 1 - Dependence between calculated and experimental 
lengths of bonds of some simple compounds of mercury. 
Fig. 2 - Dependence between experimental and calculated 
freguencies of variations in IR-spectrum of some compounds of 
mercury. 
 
The good correlation of experimental and calculated lengths of bonds and vibrational frequencies, 
and the coefficients at R (calc.), close to one, indicates a high reliability of the calculations on the used 
level of the theory. 
 
Tabl. 1. Experimental and calculated vibranational frequencies in IR spectra of mercury compounds 
 
Compound 
ω (calc.). cm
-1
ω (exp.). cm
-1 
HgH 1303  1381 
HgF 431 
491 
HgCl 257 
293 
HgBr 168 
186 
HgI 127  126 
HgF
2 
150; 531; 601 
170; 568; 642 
HgCl
2 
82; 312; 370 
107; 348; 405 
HgBr
2 
59; 202; 273 
73; 228; 294 
HgI
2 
45; 145; 220 
63; 158; 237 
HgCl
3
- 
67; 79; 257; 263 
100; 113; 263; 273 
 
How it follows from an introduction, principally the interaction of the metallic mercury surface can be 
implemented both with an ammonium cation, and with a radical of zero charge. 
We calculated the two systems, and the results are shown in Table. 2. The most significant difference 
between the ammonium cation and the radical is concluded in a significant reduction in the last index of 
Wiberg N-H bonds, which represents a decrease of their strength. 
In addition, unlike of ammonium cation the lone electron pair of the nitrogen atom is presented in the 
radical, with a population of about 1 electron. And finally, there is a significant reduction of the energy 
difference between the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals in 
the radical. 
This allows to confirm that the radical on electron structure is close to the metals in which this 

Доклады Национальной академии наук Республики Казахстан  
 
 
   
20  
difference is small [25]. 
We have also carried out similar calculations of several systems NH
4
+
Hg
n 
(n = 4-6). 
It was found that only systems wherein n = 4 are optimized as NH
4
+
Hg
4
 and NH
4
0
Hg
4
 in gas phase 
and increase of number of mercury atoms results in obtainment of a non stable structures with large 
distances between the cation and mercury atoms. 
 
Tabl 2 – Analysis of natural bond orbitals of ammonium 
 
 
Molecule 
 
Orbital 
Population of 
orbital, е 
Polarization of N-H 
bond, % 
Е
HOMO
 –Е
LUMO
, 
eV 
Index of 
Wiberg 
NH
4
+ 
Bonding 2.000 
73.0 
16.1 
0.789 
NH
4 
Bonding 
 
LP (N) 
0.946 (α) 
0.999 (β) 
0.967 (α) 
62.8 (α) 
72.9 (β) 
100 
3.3 0.200 
(α) 
0.197 (β) 
 
For the calculation we used the pseudopotential on mercury atom and the 6-31G (d) basis set for 
other atoms. 
Fig. 3 shows the optimized structure of NH
4
+
Hg
4 
molecule. It can be seen that its internal part has a 
strictly tetrahedral structure around of which four mercury atoms are tetrahedral arranged. 
 
The distances between the nitrogen and mercury atoms in the 
compound with the ammonium cation are the same and equal to 
3.78Å (3.82Å in the ADF program), and the distance in the 
connection with radical makes up 3.85Å (4.3Å in the ADF program). 
If for ion NH
4
+
Hg
4 
calculation gives structure with global minimum so 
at calculation of molecule NH
4
0
Hg
4
 is observed 3 imaginary 
frequencies of about 300 cm
-1
. 
These frequencies correspond to the deformation frequencies of 
NH
4
0 
fragment, that indicate on a transition structure in the case of the 
radical. Some of the molecular orbitals of the NH
4
+
Hg
4 
cation are 
shown in Fig. 4. 
Calculations show that the 4 higher occupied MO are about the 
same as for the energy and by type, i.e. the electron density at the 
same time belongs to all atoms of mercury. 
The lower free MO includes all atoms in the molecule, and large electronic density belongs to 
ammonium ion. Reliable stationary state of NH
4
+
Hg
4 
cation and transition structure of NH
4
0
Hg
4 
molecule 
indicates on greater stability of the first. 
 
а) 
б) 
 
Fig. 4 – Molecular orbitals of molecule NH
4
+
Hg
4
: HOMO (а), LUMO (b) 
 
Usage of the method of natural bond orbitals from the point of view of the second-order perturbation 
theory [19] allows to evaluate the energy interaction between donor and acceptor part of the cluster with 
account of bonding orbitals and the lone electron pairs of the atoms. 
The results of calculation of NH
4
+
Hg
4 
ion showed that the system becomes stable due to quite 
significant by the energy of interaction (23 kcal/mol) between lone pairs of electrons of mercury atoms 
that constitute its s-orbital, with antibonding orbitals of N-H bonds. 
 
Fig. 3 – Optimized structure of 
NH
4
+
Hg
4
 molecule 
 

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№ 3. 2016  
 
 
21 
Table 3 – Thermodynamic characteristics of 4Hg + L = Hg
4
L (L = NH
4
+
, N
2
H
4
, NH
2
OH) reaction 
 
Molecule 
Н, a.e. 
G, a.e. 
∆Н, 
kcal/mol 
∆G, 
kcal/mol 
E (ADF), 
kcal/mol 
∆E (ADF), 
kcal/mol 
Hg 
-153.080 (-153.154)* 
-153.100 (-153.174)* 
 
 
-4 
 
NH
4
+ 
-56.840 
-56.860 
  -377 
 
NH
4
0 
-57.037 
-57.06 
  -474 
 
NH
4
+
Hg
4 
-669.200 -669.270 -28 
-6 
-407 
-15 
NH
4
0
Hg
4 
-669.37 -669.43 -6 
22 
-491 
-1 
NH
2
OH 
-131.660 
-131.687 
  -570 
 
NH
2
OHHg
4 
-744.000 -744.069 -12 
11 
-581 
5 
N
2
H
4 
-111.696 
-111.824 
  -701 
 
N
2
H
4
Hg
4 
-724.139 -724.209 -77 
9 
-704 
12 
NMe
4 
-213.982
* 
-214.018
*
  -1894 
 
NMe
4
Hg
4 
-826.611
* 
-826.692
*
-8 14 -1911 
-1 
*Values for BP86 functional 
 
For radical NH
4
0
Hg
4
 the energy of this interaction was significantly lower (10 kcal/mol), which is an 
additional explanation for the less stability of last structure. Also, both compounds analysis showed no 
significant population of bond Hg-N, because of the significant distances between the atoms of mercury 
and an amine. 
In addition, the thermodynamic calculations from Table 3 which were conducted by two methods of 
density functional, lead to the same conclusion. 
Not profitable also thermodynamically interaction with the surface of the mercury such amines as 
hydroxylamine, hydrazine and tetramethylamine, as evidenced the absence of the experimental data for 
such systems. 
This is indicated by positive values of Gibbs free energy and positive or nearly zero change of the 
total energy of the system in the ADF calculations. In the case of calculation of the tetramethylamine and 
its compounds with mercury were used BP86 functional, which allows to better optimize the spatially 
hindered structure. 

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