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From: Ray Luo <rluo.uci.edu>

Date: Tue, 24 May 2005 22:54:50 -0700

Hi Jenk,

To discuss properties of dielectric in electrostatic field, it is very

useful to use the concept of induced surface charge. Suppose there are M

atomic charges, Q_1, ..., Q_M. After solving Poisson's equation, the

electrostatic potential distribution around these charges can be obtained.

Inversely, we can recover these charges according to Gauss' Law:

\nabla E = 4 \pi \rho,

where E is electrostatic field and \rho is charge density. Note that

\rho is non-zero apparently at atomic centers because we put charges

there. However, \rho is non-zero also at the dielectric boundary. This

is due to the discontinuity of E when there is a discontinuity of

dielectric constant at the boundary. E is very easy to obtain given

electrostatic potential according to the finite-difference method. So it

is straightforward to obtain \rho at the dielectric boundary.

Now suppose there are N included surface charges, q_1, ..., q_N at the

boundary. An interesting finding is that the reaction field energy is

equal to

1/2 \sum_{i=1, M} \sum_{j=1, N} Q_i q_j

This is equivalent to

1/2 \sum{{i=1, M} Q_i \phi_i^{reac}

where \phi_i^{reac} is reaction field potential at atomic charge Q_i.

The latter equation is used in Lu and Luo, JCP. The equivalence of the

two relations can be proven based on Poisson's equation and Green's

Theorem, or just divergence theorem.

The induced surface charge approach is more intuitive but slower. We are

replacing the nonuniform dielectric media by induced boundary charges.

So electrostatic interactions between solute and solvent can be

described by pairwise interactions between atomic solute charges and

induced boundary solvent charges.

All the best,

Ray

Cenk Andac wrote:

*>Dear Prof. Luo,
*

*>
*

*>I do not have any versions of Delphi. Would you
*

*>possibly provide me with an equation for electrostatic
*

*>potential at the solute-solvent boundary that
*

*>is coded in pbsa for single-point Poisson computations
*

*>at zero salt concentrations?
*

*>
*

*>Best regards,
*

*>
*

*>Jenk
*

*>
*

*>
*

*>
*

Date: Tue, 24 May 2005 22:54:50 -0700

Hi Jenk,

To discuss properties of dielectric in electrostatic field, it is very

useful to use the concept of induced surface charge. Suppose there are M

atomic charges, Q_1, ..., Q_M. After solving Poisson's equation, the

electrostatic potential distribution around these charges can be obtained.

Inversely, we can recover these charges according to Gauss' Law:

\nabla E = 4 \pi \rho,

where E is electrostatic field and \rho is charge density. Note that

\rho is non-zero apparently at atomic centers because we put charges

there. However, \rho is non-zero also at the dielectric boundary. This

is due to the discontinuity of E when there is a discontinuity of

dielectric constant at the boundary. E is very easy to obtain given

electrostatic potential according to the finite-difference method. So it

is straightforward to obtain \rho at the dielectric boundary.

Now suppose there are N included surface charges, q_1, ..., q_N at the

boundary. An interesting finding is that the reaction field energy is

equal to

1/2 \sum_{i=1, M} \sum_{j=1, N} Q_i q_j

This is equivalent to

1/2 \sum{{i=1, M} Q_i \phi_i^{reac}

where \phi_i^{reac} is reaction field potential at atomic charge Q_i.

The latter equation is used in Lu and Luo, JCP. The equivalence of the

two relations can be proven based on Poisson's equation and Green's

Theorem, or just divergence theorem.

The induced surface charge approach is more intuitive but slower. We are

replacing the nonuniform dielectric media by induced boundary charges.

So electrostatic interactions between solute and solvent can be

described by pairwise interactions between atomic solute charges and

induced boundary solvent charges.

All the best,

Ray

Cenk Andac wrote:

-- ==================================================== Ray Luo, Ph.D. Department of Molecular Biology and Biochemistry University of California, Irvine, CA 92697-3900 Office: (949)824-9528 Lab: (949)824-9562 Fax: (949)824-8551 e-mail: rluo.uci.edu Home page: http://rayl0.bio.uci.edu/rayl/ ==================================================== ----------------------------------------------------------------------- The AMBER Mail Reflector To post, send mail to amber.scripps.edu To unsubscribe, send "unsubscribe amber" to majordomo.scripps.eduReceived on Wed May 25 2005 - 21:53:01 PDT

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