Three-eighths rule

Another rule, Simpson s three-eighths rule, is given by... 

In cases where n is divisible neither by 2 nor by 3, the range of integration may be split into two parts, one for Simpson s one-third rule, the other for Simpson s three-eighths rule. Alternatively, if the curve is approximately linear in one or two intervals, the trapezoidal rule may be used in these intervals. 

Simpson s three-eighths rule (four-point) (Figure A-4). An improved version of Simpson s one-third rule can be made by applying Simpson s second rule ... 

Examples.—(1) Compare Simpson s one-third rule and the three-eighths rule when h = 1, with the result of the integration of... 

The first seven configurations remain almost exclusively perfect-paired. As for the eighth configuration, it too turns out to be almost exclusively perfect-paired the coefficient of the perfectly-paired YK spin function is in fact 0.982. In any case, the fact that its first two orbitals are identical rules out nine YK spin functions out of fourteen, and symmetry requirements further mandate three linear constraints on the coefficients of the five allowed spin functions, so that only two of them are truly independent. Anyway, one can legitimately conclude that the seven-configuration wavefunction is qualitatively robust with respect to the inclusion of this kind of inner shell correlation. 

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