Define a new quantity
$$ E_L(\boldsymbol{R},\boldsymbol{\alpha})=\frac{1}{\psi_T(\boldsymbol{R},\boldsymbol{\alpha})}H\psi_T(\boldsymbol{R},\boldsymbol{\alpha}), \tag{1} $$called the local energy, which, together with our trial PDF yields
$$ E[H(\boldsymbol{\alpha})]=\int P(\boldsymbol{R})E_L(\boldsymbol{R}) d\boldsymbol{R}\approx \frac{1}{N}\sum_{i=1}^N E_L(\boldsymbol{R_i},\boldsymbol{\alpha}) \tag{2} $$with \( N \) being the number of Monte Carlo samples.