3.1. Structural properties of nanocages
In this section, Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 nanocages and Mechlorethamine are optimized. The optimized structures of Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 and Mechlorethamine are presented in Fig. 1.
The adoption energy (Eadoption) values of V atoms on C76 and Al38N38 nanocages are examined:
Eadoption = EV−C76 – EC76 – EV and Eadoption = EV−Al38N38 – EAl38N38 – EV (1)
Where the EV−C76 and EV−Al38N38 are total energy of complexes of V with C76 and Al38N38 nanocages and the EV is isolated energy of V atom and the EC76 and EAl38N38 are total energy of C76 and Al38N38 nanocages.
The Eadoption of V-Si76, V-C76, V-Al38N38 are negative values and negative values of Eadoption are shown that V atoms are adopted to Si76, C76 and Al38N38 and therefore V-Si76, V-C76, V-Al38N38 are chemical and physical stable structures. The V atoms are formed the strong bonds with Si, C and AlN atoms of V-Si76, V-C76, V-Al38N38 nanocages.
Here, to investigate the structural stability of Si76, C76 and Al38N38 nanocages the cohesive energy [24] is obtained:
Ecohesive = (EC76 – 76*EC) / 76 and Ecohesive = (EAl38N38 – 76*EAlN) / 76 (2)
Results shown that the Ecohesive of C76 and Al38N38 are negative values as reported in Table 1.
Table 1. The Eadoption, EHLG and Ecohesive of Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 nanocages in eV and the Eadsorption, ΔHadsorption, ΔGadsorption, EHLG, q (e) and τ (sec) of Si76-Mechlorethamine, C76-Mechlorethamine, Al38N38-Mechlorethamine, V-Si76-Mechlorethamine, V-C76-Mechlorethamine, V-Al38N38-Mechlorethamine nanocages complexes in eV.
PW91PW91/6-311+G (2d, 2p)
|
M06-2X/cc-pVQZ
|
Nanocages
|
Eadoption
|
EHLG
|
Ecohesive
|
Eadoption
|
EHLG
|
Ecohesive
|
C76
|
------
|
2.60
|
-7.94
|
------
|
2.63
|
-7.87
|
Al38N38
|
------
|
2.26
|
-8.26
|
------
|
2.29
|
-8.19
|
Si76
|
------
|
2.08
|
-8.51
|
------
|
2.11
|
-8.43
|
V-C76
|
-4.26
|
2.35
|
-8.12
|
-4.20
|
2.40
|
-8.02
|
V-Al38N38
|
-4.38
|
2.07
|
-8.32
|
-4.33
|
2.10
|
-8.25
|
V-Si76
|
-4.51
|
1.89
|
-8.61
|
-4.46
|
1.94
|
-8.49
|
PW91PW91/6-311+G (2d, 2p) in gas phase
|
Complexes
|
Eadsorption
|
ΔHadsorption
|
ΔGadsorption
|
EHLG
|
q (e)
|
τ (sec)
|
C76-Mechlorethamine (a)
|
-2.50
|
-2.89
|
-2.85
|
3.64
|
0.372
|
45.38
|
Al38N38-Mechlorethamine (c)
|
-2.64
|
-3.01
|
-2.97
|
3.34
|
0.390
|
48.14
|
Si76-Mechlorethamine (i)
|
-2.70
|
-3.10
|
-3.06
|
3.26
|
0.400
|
49.10
|
V-C76-Mechlorethamine (e)
|
-3.16
|
-3.56
|
-3.53
|
3.43
|
0.450
|
51.07
|
V-Al38N38-Mechlorethamine (g)
|
-3.27
|
-3.67
|
-3.61
|
3.14
|
0.471
|
55.19
|
V-Si76-Mechlorethamine (k)
|
-3.38
|
-3.80
|
-3.75
|
3.07
|
0.484
|
55.79
|
C76-Mechlorethamine (b)
|
-2.45
|
-2.83
|
-2.79
|
3.68
|
0.366
|
44.47
|
Al38N38-Mechlorethamine (d)
|
-2.59
|
-2.95
|
-2.91
|
3.38
|
0.385
|
47.18
|
Si76-Mechlorethamine (j)
|
-2.65
|
-3.03
|
-2.99
|
3.30
|
0.394
|
48.12
|
V-C76-Mechlorethamine (f)
|
-3.09
|
-3.49
|
-3.46
|
3.48
|
0.445
|
50.04
|
V-Al38N38-Mechlorethamine (h)
|
-3.21
|
-3.60
|
-3.54
|
3.19
|
0.467
|
54.08
|
V-Si76-Mechlorethamine (l)
|
-3.31
|
-3.72
|
-3.68
|
3.12
|
0.479
|
54.66
|
M06-2X/cc-pVQZ in gas phase
|
Complexes
|
Eadsorption
|
ΔHadsorption
|
ΔGadsorption
|
EHLG
|
q (e)
|
τ (sec)
|
C76-Mechlorethamine (a)
|
-2.43
|
-2.80
|
-2.76
|
3.76
|
0.353
|
43.12
|
Al38N38-Mechlorethamine (c)
|
-2.56
|
-2.92
|
-2.88
|
3.45
|
0.371
|
45.73
|
Si76-Mechlorethamine (i)
|
-2.62
|
-3.00
|
-2.96
|
3.37
|
0.380
|
46.65
|
V-C76-Mechlorethamine (e)
|
-3.06
|
-3.46
|
-3.43
|
3.53
|
0.427
|
48.51
|
V-Al38N38-Mechlorethamine (g)
|
-3.18
|
-3.56
|
-3.51
|
3.23
|
0.447
|
52.42
|
V-Si76-Mechlorethamine (k)
|
-3.28
|
-3.69
|
-3.64
|
3.16
|
0.459
|
52.99
|
C76-Mechlorethamine (b)
|
-2.38
|
-2.75
|
-2.71
|
3.81
|
0.350
|
42.26
|
Al38N38-Mechlorethamine (d)
|
-2.50
|
-2.86
|
-2.82
|
3.49
|
0.366
|
44.82
|
Si76-Mechlorethamine (j)
|
-2.56
|
-2.95
|
-2.90
|
3.41
|
0.376
|
45.72
|
V-C76-Mechlorethamine (f)
|
-3.00
|
-3.38
|
-3.35
|
3.56
|
0.422
|
47.54
|
V-Al38N38-Mechlorethamine (h)
|
-3.12
|
-3.49
|
-3.44
|
3.27
|
0.443
|
51.38
|
V-Si76-Mechlorethamine (l)
|
-3.21
|
-3.61
|
-3.56
|
3.19
|
0.454
|
51.93
|
COSMO in water
|
Complexes
|
Eadsorption
|
ΔHadsorption
|
ΔGadsorption
|
EHLG
|
q (e)
|
τ (sec)
|
C76-Mechlorethamine (a)
|
-2.58
|
-2.97
|
-2.93
|
3.530
|
0.39
|
47.65
|
Al38N38-Mechlorethamine (c)
|
-2.72
|
-3.11
|
-3.06
|
3.240
|
0.41
|
50.55
|
Si76-Mechlorethamine (i)
|
-2.78
|
-3.19
|
-3.14
|
3.165
|
0.42
|
51.56
|
V-C76-Mechlorethamine (e)
|
-3.25
|
-3.66
|
-3.62
|
3.320
|
0.47
|
53.62
|
V-Al38N38-Mechlorethamine (g)
|
-3.36
|
-3.79
|
-3.71
|
3.040
|
0.50
|
57.95
|
Si76-Mechlorethamine (j)
|
-3.47
|
-3.91
|
-3.85
|
2.973
|
0.51
|
58.57
|
C76-Mechlorethamine (b)
|
-2.53
|
-2.91
|
-2.87
|
3.570
|
0.39
|
46.70
|
Al38N38-Mechlorethamine (d)
|
-2.67
|
-3.04
|
-3.00
|
3.280
|
0.41
|
49.54
|
Si76-Mechlorethamine (j)
|
-2.73
|
-3.12
|
-3.08
|
3.202
|
0.42
|
50.53
|
V-C76-Mechlorethamine (f)
|
-3.19
|
-3.59
|
-3.55
|
3.350
|
0.47
|
52.55
|
V-Al38N38-Mechlorethamine (h)
|
-3.30
|
-3.72
|
-3.63
|
3.090
|
0.49
|
56.79
|
V-Si76-Mechlorethamine (l)
|
-3.41
|
-3.84
|
-3.77
|
3.011
|
0.50
|
57.40
|
In this study, to examine of electronic properties of Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 nanocages and Mechlorethamine the gap energy (EHLG) are calculated through the difference of energy of HOMO and LUMO orbitals [25] by theoretical methods:
EHLG = ELUMO – EHOMO (3)
Where the EHOMO and ELUMO are energies of HOMO and LUMO orbitals of Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 nanocages and Mechlorethamine.
The EHLG of Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 nanocages and Mechlorethamine are stated in Table 1. When Si, C and AlN atoms of Si76, C76, Al38N38 nanocages are replaced with V atoms the EHLG are reduced. Therefore, the V-Si76, V-C76, V-Al38N38 nanocages with lower EHLG than C76 and Al38N38 nanocages have higher potential and abilities to transfer electrons and interactions with Mechlorethamine. In V-Si76, V-C76, V-Al38N38 nanocages the V atoms are the important sites and suitable positions for transferring the electrons and charges to Mechlorethamine.
3.2. Adsorption of Mechlorethamine on nanocages
In this study, to examine the abilities of Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 nanocages for carrier of Mechlorethamine, the electronic properties and adsorption parameters of Si76-Mechlorethamine, C76-Mechlorethamine, Al38N38-Mechlorethamine, V-Si76-Mechlorethamine, V-C76-Mechlorethamine and V-Al38N38-Mechlorethamine complexes are calculated. The possible positions for adsorption of Mechlorethamine on Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 nanocages are investigated and structures of Si76-Mechlorethamine, C76-Mechlorethamine, Al38N38-Mechlorethamine, V-Si76-Mechlorethamine, V-C76-Mechlorethamine and V-Al38N38-Mechlorethamine complexes are presented in Fig. 1.
Here, adsorption energy (Eadsorption) values for Si76-Mechlorethamine, C76-Mechlorethamine, Al38N38-Mechlorethamine, V-Si76-Mechlorethamine, V-C76-Mechlorethamine and V-Al38N38-Mechlorethamine complexes are calculated in Table 1:
Eadsorption = EMechlorethamine−nanocage – (Enanocage + EMechlorethamine) (4)
Where, Enanocage, EMechlorethamine−nanocage and EMechlorethamine are total energy of nanocages (C76, Al38N38, V-C76, V-Al38N38), Mechlorethamine and nanoacge-Mechlorethamine complexes (C76-Mechlorethamine, Al38N38-Mechlorethamine, V-C76-Mechlorethamine and V-Al38N38-Mechlorethamine) [26–28].
In this study, to investigate the stability of Si76-Mechlorethamine, C76-Mechlorethamine, Al38N38-Mechlorethamine, V-Si76-Mechlorethamine, V-C76-Mechlorethamine and V-Al38N38-Mechlorethamine complexes from thermodynamic view point, the thermodynamic indexes including the enthalpy change (ΔH) and Gibbs free energy (ΔG) are calculated. Here, ΔH and ΔG values for nanocage-Mechlorethamine complexes are calculated in Table 1:
ΔGadsorption = GMechlorethamine−nanocage – (Gnanocage + GMechlorethamine) (5)
ΔHadsorption = HMechlorethamine−nanocage – (Hnanocage + HMechlorethamine) (6)
The Gnanocage, GMechlorethamine−nanocage and GMechlorethamine are Gibbs free energy of nanocages (C76, Al38N38, V-C76, V-Al38N38), Mechlorethamine and nanoacge-Mechlorethamine complexes (C76-Mechlorethamine, Al38N38-Mechlorethamine, V-C76-Mechlorethamine and V-Al38N38-Mechlorethamine). Also, in this study the Hnanocage, HMechlorethamine−nanocage and HMechlorethamine are enthalpy of nanocages, Mechlorethamine and nanoacge-Mechlorethamine complexes [29].
The Fig. 1a to 1k are presented the structures of possible nanoacge-Mechlorethamine complexes (Si76-Mechlorethamine, C76-Mechlorethamine, Al38N38-Mechlorethamine, V-Si76-Mechlorethamine, V-C76-Mechlorethamine and V-Al38N38-Mechlorethamine). The geometries of metal doped nanocages (V-C76 and V-Al38N38) after adsorption of Mechlorethamine are changed and there are strong interactions between atoms of Mechlorethamine with V atoms of V-C76 and V-Al38N38. The Mechlorethamine are adsorbed on surfaces of V sites of metal doped nanocages and about V-Si76-Mechlorethamine, C76-Mechlorethamine, Al38N38-Mechlorethamine the Mechlorethamine has week interaction with C and AlN atoms of C76 and Al38N38.
The calculated the suitable distances between the Mechlorethamine and Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 nanocages as drug delivers to achieve the best adsorption energy of drug-nanocage complexes (Si76-Mechlorethamine, C76-Mechlorethamine, Al38N38-Mechlorethamine, V-Si76-Mechlorethamine, V-C76-Mechlorethamine and V-Al38N38-Mechlorethamine) are reported in Fig. 1. Results shown that for each drug-nanocage complexes (Si76-Mechlorethamine, C76-Mechlorethamine, Al38N38-Mechlorethamine, V-Si76-Mechlorethamine, V-C76-Mechlorethamine and V-Al38N38-Mechlorethamine) the one reported distance between the Mechlorethamine and Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 nanocages can achieve the best adsorption energy of drug-nanocage complexes.
The calculated Eadsorption, ΔGadsorption and ΔHadsorption of nanoacge-Mechlorethamine complexes including the structures a to k are reported in Table 1. The all of Eadsorption, ΔGadsorption and ΔHadsorption values are negative and so, adsorption of Mechlorethamine on surfaces of Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 are spontaneous interactions and exothermic reactions.
The calculated EHLG of nanoacge-Mechlorethamine complexes including the structures a to h by are reported in Table 1. The EHLG of Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 after Mechlorethamine adsorption are changed, significantly. The Mechlorethamine has suitable effects on EHLG of C76, Al38N38, V-C76 and V-Al38N38 which is indicated the strong interactions between the Mechlorethamine and nanocages. The EHLG of V-Al38N38-Mechlorethamine are lower than V-C76-Mechlorethamine and also the Al38N38-Mechlorethamine has lower the EHLG than C76-Mechlorethamine.
In this study, the recovery or desorption time (τ) as important index for Mechlorethamine delivery is calculated to predict the needed time to desorb the Mechlorethamine from Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 nanocages [30]. The τ index is exponentially associated to Eadsorption and the high adsorption interactions of Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 with Mechlorethamine are needed to high desorption time. The τ index is calculated in Table 1:
τ = (1/ϑ) * exp (-Eadsorption / KT) (7)
Where, K is Boltzmann’s constant, T is temperature in Kelvin and ϑ is attempt frequency of nanoacge-Mechlorethamine complexes (C76-Mechlorethamine, Al38N38-Mechlorethamine, V-C76-Mechlorethamine and V-Al38N38-Mechlorethamine). Results indicated that, the τ index of V-C76-Mechlorethamine and V-Al38N38-Mechlorethamine due to strong interactions between metal doped naonocages and Mechlorethamine are higher than C76-Mechlorethamine and Al38N38-Mechlorethamine. The τ index of V-Si76-Mechlorethamine and V-Al38N38-Mechlorethamine are higher than V-C76-Mechlorethamine and also the Al38N38-Mechlorethamine has higher the τ index than C76-Mechlorethamine.
In this study, results indicated that V-C76-Mechlorethamine and V-Al38N38-Mechlorethamine have lower EHLG values, higher Eadsorption and ΔGadsorption values and also have higher the recovery or desorption time than Al38N38-Mechlorethamine and C76-Mechlorethamine. Finally, through examined parameters including the Eadsorption ΔGadsorption and τ index it can be concluded the V-Al38N38 and V-C76 have high potential to Mechlorethamine adsorption and V-Al38N38 and V-C76 are acceptable nanocages to Mechlorethamine carry and delivery of Mechlorethamine.
3.3. Solvent effects on Mechlorethamine adsorption on nanocages
In this study, effects solvent is examined on Mechlorethamine adsorption on Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 nanocages. Here, the Eadsorption, ΔGadsorption and ΔHadsorption values of nanoacge-Mechlorethamine complexes (C76-Mechlorethamine, Al38N38-Mechlorethamine, V-C76-Mechlorethamine and V-Al38N38-Mechlorethamine) are calculated. The calculated EHLG, q and τ index of interactions of Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 with Mechlorethamine including the structures a to k by are calculated in water and results are reported in Table 1.
In water, all calculated Eadsorption, ΔGadsorption and ΔHadsorption values are negative similar to gas phase which is shown interactions of Mechlorethamine with Si76, C76, Al38N38, V-Si76, V-C76, V-Al38N38 nanocages are exothermic reactions. The Eadsorption, ΔGadsorption and ΔHadsorption values of V-C76-Mechlorethamine and V-Al38N38-Mechlorethamine are more negative than C76-Mechlorethamine and Al38N38-Mechlorethamine in water. Also the Al38N38 has more negative Eadsorption, ΔGadsorption and ΔHadsorption values than C76 to Mechlorethamine adsorption in water. The water as polar solvent is increased and improved the interactions of Mechlorethamine with nanocages.