def get_delta_BAR(BAR_estimate, k_b_T):
    """ Return the change in free energy and standard deviation for the BAR estimates.

    """
    error_estimate = 0.0

    for i in range(len(BAR_estimate.d_delta_f_) - 1):
        error_estimate += BAR_estimate.d_delta_f_.values[i][i + 1] ** 2

    delta = BAR_estimate.delta_f_.iloc[0, -1] * k_b_T
    std_delta = k_b_T * error_estimate ** 0.5
    return delta, std_delta