T_erf_coulomb Function

public function T_erf_coulomb(r, sigma, dT, grad) result(T)

$$\begin{aligned} T^\text{GG}_{ab}(\mathbf r,\sigma)&= \frac{\partial^2}{\partial r_a\partial r_b}\frac{\operatorname{erf}(\zeta)}r= \big(\operatorname{erf}(\zeta)-\Theta(\zeta)\big)T_{ab}(\mathbf r)+ 2\zeta^2\Theta(\zeta)\frac{r_ar_b}{r^5} \\ \Theta(\zeta)&=\frac{2\zeta}{\sqrt\pi}\exp(-\zeta^2),\qquad \zeta=\frac r\sigma \\ \frac{\mathrm d T_{ab}^\text{GG}(\mathbf r,\sigma)}{\mathrm dr_c}&= 2\zeta\Theta(\zeta)\left(T_{ab}(\mathbf r)+(3-2\zeta^2)\frac{r_ar_b}{r^5}\right) \frac{\mathrm d\zeta}{\mathrm dr_c} \\ &+\big(\operatorname{erf}(\zeta)-\Theta(\zeta)\big) \frac{\partial T_{ab}(\mathbf r)}{\partial r_c}- 2\zeta^2\Theta(\zeta)\left( \frac13\frac{\partial T_{ab}(\mathbf r)}{\partial r_c}+ \frac{r_c\delta_{ab}}{r^5} \right) \\ \qquad\frac{\mathrm d\zeta}{\mathrm dr_c}&= \frac{r_c}{r\sigma}-\frac r{\sigma^2}\frac{\mathrm d\sigma}{\mathrm dr_c} \end{aligned}$$

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	r(3)
real(kind=dp),	intent(in)			::	sigma
type(grad_matrix_re_t),	intent(out),	optional		::	dT
type(grad_request_t),	intent(in),	optional		::	grad

Return Value real(kind=dp) (3,3)

Contents

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