c CCLRC
Section 2.5
in which (Q
(k
1
, k
2
, k
3
))
is the complex conjugate of Q
(k
1
, k
2
, k
3
) and
B(k
1
, k
2
, k
3
) = |b
1
(k
1
)|
2
|b
2
(k
2
)|
2
|b
3
(k
3
)|
2
.
(2.156)
The function G(k
1
, k
2
, k
3
) is thus a relatively simple product of the gaussian screening term
appearing in the conventional Ewald sum, the function B(k
1
, k
2
, k
3
) and the discrete Fourier
transform of Q(k
1
, k
2
, k
3
).
4. Calculating the atomic forces, which are given formally by:
f
j
= -
U
recip
r
j
= -
1
V
o 0 k
1
,k
2
,k
3
G
(k
1
, k
2
, k
3
)
Q(k
1
, k
2
, k
3
)
r
j
.
(2.157)
Fortunately, due to the recursive properties of the B-splines, these formulae are easily evaluated.
The virial and the stress tensor are calculated in the same manner as for the conventional Ewald
sum.
The DL POLY 3 subroutines required to calculate the SPME contributions are:
1. spme container containing
(a) bspgen, which calculates the B-splines
(b) bspcoe, which calculates B-spline coefficients
(c) spl cexp, which calculates the FFT and B-spline complex exponentials
2. parallel fft and gpfa wrap (native DL POLY 3 subroutines that respect the domain
decomposition concept) which calculate the 3D complex fast Fourier transforms
3. ewald spme forces, which calculates the reciprocal space contributions (uncorrected)
4. ewald real forces, which calculates the real space contributions (corrected)
5. ewald excl forces, which calculates the reciprocal space corrections due to the coulombic
exclusions in intramolecular interactions
6. ewald frozen forces, which calculates the reciprocal space corrections due to the exclu-
sion interactions between frozen atoms
7. two body forces, in which all of the above subroutines are called sequentially and also the
] for electrically non-neutral MD cells is applied if needed.
2.5
Polarisation Shell Models
An atom or ion is polarisable if it develops a dipole moment when placed in an electric field. It is
commonly expressed by the equation
µ = E ,
(2.158)
where µ is the induced dipole and E is the electric field. The constant is the polarisability.
In the static shell model a polarisable atom is represented by a massive core and massless shell,
connected by a harmonic spring, hereafter called the core-shell unit. The core and shell carry
different electric charges, the sum of which equals the charge on the original atom. There is no
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