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The effect of non-axial quadrupole forces on the anisotropy of mean-squared force and torque
CHEMICAL PHYSICS LETTERS
10 Feebruar_v 1984
COMMENT THE EFE;ECT OF NON-AXIAL ON THE ANISOTROPY
QUADRUPoLE
FORCES
OF MEAN-SQUARED
FORCE AND TORQUE
S. MURAD
C.G. GRAY
and K-E. GUBBINS
and SM. THOMPSON
Received 25 October
1983; in final form 6 December 1983
W’e report the rmik af 9 mokcuhr b~namics stubp ufi the effccr of srcm3shl qffsdrupok forces an the values oPCi$ and (pi), where cu=x.y or z (components of the mean-squared force and torque). The results show that ewn strong nonaxial quadrupolar interactions do not cause any significant anisotropk in (F’) or (I’).
We recently reported [l] the results of a molecular dynamics study for a liquid in which the molecules in-
simulation consisted of 4000 time steps with A.t* = (~/r?z)~&~-~At = 0.0004. Here p =X/V is number
teract with a pair potential consisting of a central Lennard-Jones plus non-axial quadrupole-quadrupole (Qxx # Q,,,,) parts. Thermodynamic properties (configurational energy, pressure, specific heat), meansquared force, mean-squared torque and correlation functions were calculated and compared with perturbation theory [2} _ We now report the ef ‘ect of non-axial quadrupolar forces on the anisotropy af the mea&s+auzd fnrcsl and torque. (F;) and (Ga), where CY=x, y or z, can be obtained individually from infrared spectroscopy ex-
density, T is temperature. E and (r are the LennardJones parameters, k the Boltzmann constant, and NZ the molecular mass. These state conditions were also studied previously [ 1] for thermodynamic properties and correlation functions. Table 1 shows results obtained from our molecular dynvnics simu&iGons. For Q_& - Q?. = 1.o the anisotropy in CFx) is ~3_0% and in (r~?=2_5%_ For Q_L - Q$!, = ?_n CbC ani..tmpy in CF’ 5 is. ==7 55 2xx-l in @) e_O%. It thus appears that even with quadrupole moments that are 4uite non-axial. the anisotropy
periments I33 and are therefore ofinterest _As far as we are aware, these individual contributions to the mean-squared force and torque have not previously been simulated_ The details of our simulation method have been described in detail [1,4],The simulations were carried out atp*mpo~=0_8,rC~kT/e~2_7,QZ*~
in (F2) and h2) is not too significant.
Q,,/(EI$)~~~
Experimental measurements of ki> and
= 1.0, Q.& - Q$. = 1.0 and 2.0. Each
0 0092614~84~S (North-Holland
03BQo Q Elsevier Science Publihers Physics Publishing Division)
KY.
407
CHEMICAL-PHYSICS LETTERS
\rolume104; number 4
Tab& 1 Properties of non-axial quadrudolar liuuids from molecular dynamics a)
0.8 0.8
4573 6254 X**2)
1.0 1.0
2797 2.743
1511 1949 -(r$
l-0 2.0
This work was supporfed by the National Science Foundation (Grants CPES209 187 z&d NSF 79.09 It%), the Petroleum Research Fund administered by the American Chemical Society, and by the Natural Sciences and Engineering Rese;irch @until (Canada).
Refemms
1593 2094
1469 2080
<***> Y
(7;s
115.6
39.0
38.5
38.1
3035
99.4
100.4
103.5
=) P* = pd;
10 February 1984
CC. Gray, K-E. Gubbins, S. Murad and KS. Shing, Chem_ Phys. Letters 95 (1983) 543. 121 K-E- Gubpins, C-G_Gray and J-R_& &&ado. Mol. Phys. 42 (1981) 817; C.G. Gray and K.E. Gubbins. Mol. Phys. 42 (1981) 843. [3] CC. Gray and K.E. Gubbins, Theory of molecular fluids (Oxford Univ. Press, London), to be published. 14) DJ. Evans and S. Murad, Mol. Phys. 34 (1977) 327. ilj
UC&% -6.73 -1152
T* = kT/e; Q’ = Q/(E~)‘~;
pfpkT
2.70 1.41
F* = F&e; I* = r/e.
ERRATUM
C. Nokes, G. Gilbert and R-J_ Donovan, Direct kinetic
study of CH(A 2A), Chem. Phys. Letters 99 (1983) 491. The axesin figs. I,2 and 3 were omitted and should have been as follows: Fig3xe 1, vertical axis: fluorescence
intensity (If),
horizontal axis: time (t). Figure 2, vertical -axis: logeff, horizontal (ns). Figure 3, vertical axis: k (1 O6 s-l), Pcrr4 (kN ms2)_
4-08
axis: time
horizontal axis:
10 Feebruar_v 1984
COMMENT THE EFE;ECT OF NON-AXIAL ON THE ANISOTROPY
QUADRUPoLE
FORCES
OF MEAN-SQUARED
FORCE AND TORQUE
S. MURAD
C.G. GRAY
and K-E. GUBBINS
and SM. THOMPSON
Received 25 October
1983; in final form 6 December 1983
W’e report the rmik af 9 mokcuhr b~namics stubp ufi the effccr of srcm3shl qffsdrupok forces an the values oPCi$ and (pi), where cu=x.y or z (components of the mean-squared force and torque). The results show that ewn strong nonaxial quadrupolar interactions do not cause any significant anisotropk in (F’) or (I’).
We recently reported [l] the results of a molecular dynamics study for a liquid in which the molecules in-
simulation consisted of 4000 time steps with A.t* = (~/r?z)~&~-~At = 0.0004. Here p =X/V is number
teract with a pair potential consisting of a central Lennard-Jones plus non-axial quadrupole-quadrupole (Qxx # Q,,,,) parts. Thermodynamic properties (configurational energy, pressure, specific heat), meansquared force, mean-squared torque and correlation functions were calculated and compared with perturbation theory [2} _ We now report the ef ‘ect of non-axial quadrupolar forces on the anisotropy af the mea&s+auzd fnrcsl and torque. (F;) and (Ga), where CY=x, y or z, can be obtained individually from infrared spectroscopy ex-
density, T is temperature. E and (r are the LennardJones parameters, k the Boltzmann constant, and NZ the molecular mass. These state conditions were also studied previously [ 1] for thermodynamic properties and correlation functions. Table 1 shows results obtained from our molecular dynvnics simu&iGons. For Q_& - Q?. = 1.o the anisotropy in CFx) is ~3_0% and in (r~?=2_5%_ For Q_L - Q$!, = ?_n CbC ani..tmpy in CF’ 5 is. ==7 55 2xx-l in @) e_O%. It thus appears that even with quadrupole moments that are 4uite non-axial. the anisotropy
periments I33 and are therefore ofinterest _As far as we are aware, these individual contributions to the mean-squared force and torque have not previously been simulated_ The details of our simulation method have been described in detail [1,4],The simulations were carried out atp*mpo~=0_8,rC~kT/e~2_7,QZ*~
in (F2) and h2) is not too significant.
Q,,/(EI$)~~~
Experimental measurements of ki> and
= 1.0, Q.& - Q$. = 1.0 and 2.0. Each
0 0092614~84~S (North-Holland
03BQo Q Elsevier Science Publihers Physics Publishing Division)
KY.
407
CHEMICAL-PHYSICS LETTERS
\rolume104; number 4
Tab& 1 Properties of non-axial quadrudolar liuuids from molecular dynamics a)
0.8 0.8
4573 6254 X**2)
1.0 1.0
2797 2.743
1511 1949 -(r$
l-0 2.0
This work was supporfed by the National Science Foundation (Grants CPES209 187 z&d NSF 79.09 It%), the Petroleum Research Fund administered by the American Chemical Society, and by the Natural Sciences and Engineering Rese;irch @until (Canada).
Refemms
1593 2094
1469 2080
<***> Y
(7;s
115.6
39.0
38.5
38.1
3035
99.4
100.4
103.5
=) P* = pd;
10 February 1984
CC. Gray, K-E. Gubbins, S. Murad and KS. Shing, Chem_ Phys. Letters 95 (1983) 543. 121 K-E- Gubpins, C-G_Gray and J-R_& &&ado. Mol. Phys. 42 (1981) 817; C.G. Gray and K.E. Gubbins. Mol. Phys. 42 (1981) 843. [3] CC. Gray and K.E. Gubbins, Theory of molecular fluids (Oxford Univ. Press, London), to be published. 14) DJ. Evans and S. Murad, Mol. Phys. 34 (1977) 327. ilj
UC&% -6.73 -1152
T* = kT/e; Q’ = Q/(E~)‘~;
pfpkT
2.70 1.41
F* = F&e; I* = r/e.
ERRATUM
C. Nokes, G. Gilbert and R-J_ Donovan, Direct kinetic
study of CH(A 2A), Chem. Phys. Letters 99 (1983) 491. The axesin figs. I,2 and 3 were omitted and should have been as follows: Fig3xe 1, vertical axis: fluorescence
intensity (If),
horizontal axis: time (t). Figure 2, vertical -axis: logeff, horizontal (ns). Figure 3, vertical axis: k (1 O6 s-l), Pcrr4 (kN ms2)_
4-08
axis: time
horizontal axis: