Ad hoc methods for accurate determination of Bader's atomic boundary

In addition to the recently published triangulation method [P. M. Polestshuk, J. Comput. Chem. 34, 206 (2013)], two new highly accurate approaches, ZFSX and SINTY, for the integration over an atomic region covered by a zero-flux surface (zfs) were developed and efficiently interfaced into the TWOE program. ZFSX method was realized as three independent modules (ZFSX-1, ZFSX-3, and ZFSX-5) handling interatomic surfaces of a different complexity. Details of algorithmic implementation of ZFSX and SINTY are discussed. A special attention to an extended analysis of errors in calculations of atomic properties is paid. It was shown that uncertainties in zfs determination caused by ZFSX and SINTY approaches contribute negligibly (less than 10(-6) a.u.) to the total atomic integration errors. Moreover, the new methods are able to evaluate atomic integrals with a reasonable time and can be universally applied for the systems of any complexity. It is suggested, therefore, that ZFSX and SINTY can be regarded as benchmark methods for the computation of any Quantum Theory of Atoms in Molecules atomic property.