- Contemporary messages sorted: [ by date ] [ by thread ] [ by subject ] [ by author ] [ by messages with attachments ]

From: Thomas Cheatham <tec3.utah.edu>

Date: Mon, 23 Jul 2007 20:30:19 -0600 (Mountain Daylight Time)

*> Thanks for your response. But I could not understand some parts of your
*

*> answer. Let me explain how I look at this issue: The volume of a truncated
*

*> octahedron is defined as
*

*>
*

*> V = 11.3137085 * a^3
*

*>
*

*> in http://en.wikipedia.org/wiki/Truncated_octahedron
*

Wikepedia is a source of information, however "truncated octahedron" can

be defined in multiple ways. For example, look at the definition used in

Allen & Tildesley which essentially lopes off corners of a cubic box

compared to that implemented in AMBER (as a triclinic unit cell).

*> In amber, the box information is defined with 6 values;
*

*>
*

*> 51.9046302 51.9046302 51.9046302 109.4712190 109.4712190 109.4712190
*

*>
*

*> and as far as I understood, each of the first 3 values are the half of a
*

*> cube's edge length (l/2; assuming we have a cube with edge length of 'l').
*

*> From these 6 parameters, someone needs to find what 'a' is.
*

No, the actual lengths of the periodic unit cell are there, not 1/2 the

box length. If orthorhombic (i.e. rectangular with 90 degree angles),

these are the lengths of each side of the box.

*> I do not understand what 109.4712190 is. In your explanation, u define a
*

This is the angle between the sides; as an example, use ptraj to image

your truncated octahedron without specifying the "familiar" keyword. It

will look like a slanted rectangle. The angles are all 109.47... between

each side.

*> parameter 'a' which is not clear to me. It is not the edge length of a
*

*> truncated octahedron defined in the above website.
*

Do not trust the above mentioned website :-)

You can look through the ptraj or sander or PMEMD code and see:

V = x * y * z * sqrt(1.0 - cos(alpha)**2 - cos(beta)**2 - cos(gamma)**2 +

2.0 * cos(alpha) * cos(beta) * cos(gamma))

x, y, z are the box lengths: x = y = z = a in your example. alpha, beta,

gamma are the box angles which equal 109.47... for a truncated

octahedron.

An easier shape (since the angles are integral and hence do not suffer

from finite precision) which we haven't exploited in AMBER is the rhombic

dodecahedron (12-sided, equal sides) which has x=y=z and alpha=60,

beta=90, gamma=60). This is the shape that is closest to a sphere, yet

space filling.

We discuss this in Current Protocols in Nucleic Acid Chemistry (articles

by Cheatham, Kollman and Brooks) from ~2000-2003. See the attached PDF

for a summary.

-- tec3

Received on Wed Jul 25 2007 - 06:07:26 PDT

Date: Mon, 23 Jul 2007 20:30:19 -0600 (Mountain Daylight Time)

Wikepedia is a source of information, however "truncated octahedron" can

be defined in multiple ways. For example, look at the definition used in

Allen & Tildesley which essentially lopes off corners of a cubic box

compared to that implemented in AMBER (as a triclinic unit cell).

No, the actual lengths of the periodic unit cell are there, not 1/2 the

box length. If orthorhombic (i.e. rectangular with 90 degree angles),

these are the lengths of each side of the box.

This is the angle between the sides; as an example, use ptraj to image

your truncated octahedron without specifying the "familiar" keyword. It

will look like a slanted rectangle. The angles are all 109.47... between

each side.

Do not trust the above mentioned website :-)

You can look through the ptraj or sander or PMEMD code and see:

V = x * y * z * sqrt(1.0 - cos(alpha)**2 - cos(beta)**2 - cos(gamma)**2 +

2.0 * cos(alpha) * cos(beta) * cos(gamma))

x, y, z are the box lengths: x = y = z = a in your example. alpha, beta,

gamma are the box angles which equal 109.47... for a truncated

octahedron.

An easier shape (since the angles are integral and hence do not suffer

from finite precision) which we haven't exploited in AMBER is the rhombic

dodecahedron (12-sided, equal sides) which has x=y=z and alpha=60,

beta=90, gamma=60). This is the shape that is closest to a sphere, yet

space filling.

We discuss this in Current Protocols in Nucleic Acid Chemistry (articles

by Cheatham, Kollman and Brooks) from ~2000-2003. See the attached PDF

for a summary.

-- tec3

- APPLICATION/pdf attachment: triclinic.pdf

Custom Search