Re: [ccp4bb] Clipper: Agarwal density gradients and AtomShapeFn::rho grad

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CCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999

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Subject: Postdoctoral opportunity at Case Western Reserve University
From: Brad Bennett bcb28 {- at -} CASE {- dot -} EDU
Date: 2007-11-13

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Subject: Re: Clipper: Agarwal density gradients and AtomShapeFn::rho grad
From: Athanasios Dousis ndousis {- at -} RICE {- dot -} EDU
Date: 2007-11-13

Thank you all for your helpful suggestions and advice.

Kevin,
I'll attempt to implement the analytical derivatives in Clipper and get
back to you if I'm successful or stuck.

Thanks again and kind regards,
Nasos

Kevin Cowtan wrote:
> OK, that's a good question. Unfortunately the answer is hard,
> otherwise I would have done it already.
>
> The a[] and b[] coeffs are the Gaussian coefficients used for
> calculating an atomic shape function in reciprocal space, i.e. for use
> in a structure factor calculation.
>
> The aw[] and bw[] coeffs are the corresponding Gaussian coefficients
> used for calculating the electron density in real space.
>
> For anisotropic atoms, you can't use bw, so the class constructs
> uaninv[], which is a vector of aniso Gaussian coefficients which
> combine both the ADP and shape function coefficients.
>
> So this function:
>
> ftype AtomShapeFn::rho( const Coord_orth& xyz ) const
> {
> // iso
> const Coord_orth dxyz( xyz - coord_ );
> if ( is_iso ) return rho( dxyz.lengthsq() );
> // aniso
> return occ_ * ( aw[0]*exp( uaninv[0].quad_form( dxyz ) ) +
> aw[1]*exp( uaninv[1].quad_form( dxyz ) ) +
> aw[2]*exp( uaninv[2].quad_form( dxyz ) ) +
> aw[3]*exp( uaninv[3].quad_form( dxyz ) ) +
> aw[4]*exp( uaninv[4].quad_form( dxyz ) ) +
> aw[5]*exp( uaninv[5].quad_form( dxyz ) ) );
> }
>
> returns the electron density at position xyz in the cell due to the
> atom located at coord_. The corresponding isotropic form is simple,
> but when you want aniso density, you need to construct the quadratic
> form of the difference coodinate with the U_aniso tensor.
>
> To implement the corresponding gradient function, there are two
> possible approaches:
>
> 1. Calculate it by finite difference methods, using 4 calls to the
> above function. This is computationally wasteful and less precise, but
> simple to do, and you should always do this anyway as a cross-check of
> the analytical approach.
>
> 2. Calculate is analytically by differentiating the above expression
> with respect to dxyz.x(), dxyz.y(), dxyz.z(). This will probably be
> about twice as fast as the above method, and more precise.
>
> If you can do this, I'll be very glad to incorporate the code. If you
> get stuck, get back to me and I'll see if I can do it, although I am
> pressed for time at the moment.
>
> Kevin
>
> Athanasios Dousis wrote:
>> Hello all,
>>
>> I have the latest Clipper libraries (v2.0), and I'd like to calculate
>> the Agarwal density gradients for anisotropic atomic displacement
>> parameters. Unfortunately, the method
>> clipper::AtomShapeFn::rho_grad(...) only works for the isotropic
>> ADP's. Is there code available for the anisotropic parameters? If
>> no, do you have any advice on how to implement the density
>> gradients? I understand how to do this in principle, but I'm
>> somewhat confused by the aw[.] and bw[.] coefficients in the code.
>> Are these related to the Jacobian determinant of the reciprocal-real
>> space transformation?
>>
>> Also, please let me know if there is a more appropriate forum to ask
>> this question.
>>
>> Thank you,
>> Nasos Dousis
>>
>>
>

CCP4bb navigation

CCP4bb <-- 1999 <-- November 1999 <-- 30 November 1999

Previous message:
Subject: Postdoctoral opportunity at Case Western Reserve University
From: Brad Bennett bcb28 {- at -} CASE {- dot -} EDU
Date: 2007-11-13

Next message:
Subject: Re: B-factors, H/D exchange and protein flexibility
From: Ethan Merritt merritt {- at -} U {- dot -} WASHINGTON {- dot -} EDU
Date: 2007-11-13