ms2: A Molecular Simulation Tool for Thermodynamic Properties

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2.2. Intermolecular interactions Point dipole interactions. The interaction between a point dipole with moment µi and a point charge qj at a distancerij is given by [6, 7] u Dq ij (rij,θi,µi,qj) = − 1 µiqj 4πε0 r2 cosθi . (16) ij Here,θi is the angle between the distance vector of the point charge and the orientation vector of the point dipole, as illustrated in Figure 2 in the associated paper. Point quadrupole interactions. The interaction potential of a linear point quadrupoleQi with a point charge qj at a distancerij is given by [1, 8] u Qq ij (rij,θi,Qi,qj) = 1 4πε0 Qiqj 4r3 2 3cos θi −1 ij , (17) where θi is the angle between the distance vector of the point charge and the orientation vector of the point quadrupole, as illustrated in Figure 2 in the associated paper. The interaction between a linear point quadrupole with moment Qi and a point dipole with momentµj is given by [6, 8] u Qµ ij (rij,θi,θj,φij,Qi,µj) = 1 4πǫ0 3Qiµj 2 r4 cosθi −cosθj ij 1+3cosθicosθj −2cosφij sinθisinθj , where the angles θi, θj and φij indicate the relative angular orientation of the point dipole j and the point quadrupolei, as shown in Figure 2 in the associated paper. 2.3. Reaction field method The truncation of electrostatic interactions of first and second order are corrected for with the reaction field method [9, 10]. Here, all dipoles within the cut-off radius rc polarize the fluid surrounding the cut-off sphere, which is modeled as a dielectric continuum with a relative permittivity εs. The polarization gives rise to a homogeneous electric field within the cut-off radius, called the reaction fieldE RF i of magnitude E RF i 1 2 = 4πε0 εs −1 2εs +1 1 r 3 c m b=1 Nb j=1 rij
where u µRF i is its contribution to the potential energy. In Eq. (20), it is assumed that the system is sufficiently large so that tinfoil boundary conditions (εs → ∞) are applicable without a loss of accuracy, e.g.N ≥ 500 [12, 13, 14, 15]. The reaction field method can also be applied to correct for sets of point charges, as long as they add up to a total charge of zero. Therefore, a point charge distribution is reduced to a dipole vectorµ q according to µ q = n riqi , (21) i=1 where n denotes the total number of point charges and ri the position vector of charge qi. The resulting dipole µ q is transferred into the correction term according to Eqs. (19) and (20). 2.4. Cut-off mode In the site-site cut-off mode, the LJ contributions of molecules beyond the cut-off radiusrc to the internal energy are estimated by [1] The contributions to the pressure are considered by [1] ∆U L∗ = 8 9 Nρ∗π 1 r∗ 9 1 −3 c r∗ 3 . (22) c ∆p L∗ = 32 9 (ρ∗ ) 2 π 1 r ∗ c 9 3 1 − 2 r∗ 3 . (23) c Using the center of mass cut-off mode, the LJ contributions of molecules beyond the cut-off radius rc are estimated on the basis of the correction terms of Lustig [16]. The correction ∆u L∗ for the residual internal energy can be divided into three contributions, the contributions by interactions between two molecule centers (TICC), between one molecule center and one site (TICS), and between two molecule sites (TISS). The first contributions describe the long range contributions between molecular interaction sites that are positioned in the center of the mass of the individual molecules. The TICS terms describe the contributions, where one site is located in the center of mass of its molecule, while the other site is not. The TISS terms correct for contributions between molecular sites that are not positioned in the center of mass of their molecules. Using these formulations, the correction term for the residual internal energy is defined by ∆u L∗ ⎧ TICCu(−6)−TICCu(−3) NC NC NLJ,i NLJ,j ⎪⎨ = 2πρ xixj4ε TICSu(−6)−TICSu(−3) i=1 j=1 α=1 β=1 ⎪⎩ TISSu(−6)−TISSu(−3) . Here, NC is the number of components in the system and NLJ,i the number of LJ sites of the molecule of componenti. The TIXXu functions are calculated by the following equations, where the argument in the brackets defines the exponentn TICCu(n) = (24) r2n+3 c σ2n , (25) (2n+3) 7
Page 1 and 2: ms2: A Molecular Simulation Tool fo
Page 3 and 4: 2. Introduction Due to the advances
Page 5 and 6: 3. Simulation programms2 The simula
Page 7 and 8: sense that the specified chemical p
Page 9 and 10: 3.3.3. Chemical potential The chemi
Page 11 and 12: 3.3.6. Transport properties In ms2,
Page 13 and 14: −0.5 < x, y, z < 0.5. The advanta
Page 15 and 16: Q = 2aq. The electrostatic interact
Page 17 and 18: Programming (OOP). It should be men
Page 19 and 20: motion, kinetic energy calculation,
Page 21 and 22: • PGI pgf95 4 with ”-r8 -fastss
Page 23 and 24: memory scales linearly with the num
Page 25 and 26: Applyingms2par is simple and should
Page 27 and 28: Table 1: Computational demand for t
Page 29 and 30: Table 3: NEC SX8R ”ftrace” prof
Page 31 and 32: i r ij ij Figure 2: Schematic of t
Page 33 and 34: Figure 4: UML class diagram of ms2,
Page 35 and 36: Figure 6: Runtime for the equimolar
Page 37 and 38: (a) (b) Figure 8: ms2 runtime of th
Page 39 and 40: Figure 10: Snapshot of ms2par gener
Page 41 and 42: Figure 12: Snapshot of a ternary mi
Page 43 and 44: [24] Eckl, B., Vrabec, J., and Hass
Page 45 and 46: Supplementary Material to ms2: A Mo
Page 47 and 48: The partial derivative of the resid
Page 49: 2. Details ofms2 This section provi
Page 53 and 54: 3. Modular structure - example The
Page 55 and 56: Table 2 continued Parameter Option
Page 57 and 58: An example for a *.par file is give
Page 59 and 60: Table 4: Parameters and options spe
Page 61: References [1] Allen, M. and Tildes

ms2: A Molecular Simulation Tool for Thermodynamic Properties

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