# Re: Cross-term (CMAP)

From: Faramarz Joodaki (fjoodaki_at_my.uri.edu)
Date: Sat Jul 08 2017 - 07:25:27 CDT

Hi everyone,

I should mention that d2ya is the derivative of dya respect to t.

Best Regards,
Faramarz

> On Jul 7, 2017, at 7:04 PM, Faramarz Joodaki <fjoodaki_at_my.uri.edu> wrote:
>
> Hi everyone!
>
> I have a question about the cross-term in NAMD source code. From the source code, file "ComputeCrossterms.C", I found that NAMD is using bicubic spline interpolation to find the energy and first derivative of cross-term energy respect to Phi and Psi.
>
> As I found:
>
> dU/d(phi) is
> fx += dxa[i] * ya[j] * table[ij].d00
> + dxb[i] * ya[j] * table[ij].d10
> + dxa[i] * yb[j] * table[ij].d01
> + dxb[i] * yb[j] * table[ij].d11;
>
>
> and dU/d(psi) is
> fy += xa[i] * dya[j] * table[ij].d00
> + xb[i] * dya[j] * table[ij].d10
> + xa[i] * dyb[j] * table[ij].d01
> + xb[i] * dyb[j] * table[ij].d11;
>
> I would like to calculate the second derivative respect to Phi and Psi. According to these formulae, for example, I am using to use below formula for d2U/d(Psi)2
>
> fyy += xa[i] * d2ya[j] * table[ij].d00
> + xb[i] * d2ya[j] * table[ij].d10
> + xa[i] * d2yb[j] * table[ij].d01
> + xb[i] * d2yb[j] * table[ij].d11;
>
> I would be so grateful if you could guide is the way of my thought is correct?
>
> Best Regards,
> Faramarz

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