Koopmans' Analysis of Chemical Hardness with Spectral-Like Resolution

Table 1

Numerical parameters for the compact finite second (2C)-, fourth (4C)-, and sixth (6C)-order central differences; standard Padé (SP) schemes; sixth (6T)- and eight (8T)-order tridiagonal schemes; eighth (8P)- and tenth (10P)-order pentadiagonal schemes up to spectral-like resolution (SLR) schemes for chemical hardness of (18) [15, 24, 36, 63].

Scheme	𝑎2	𝑏2	𝑐2	𝛼2	𝛽2
2C	1	0	0	0	0
4C	1.333	−0.333	0	0	0
6C	1.091	0.273	0	0.182	0
SP	1.2	0	0	0.1	0
6T	1.5	−0.6	0.2	0	0
8T	0.967	0.537	−0.03	0.237	0
8P	0.814	0.789	0	0.292	0.01
10P	0.592	1.155	0.044	0.372	0.024
SLR	0.216	1.723	0.177	0.502	0.056