Fragmentation methods reproduce the result of the exponential scaling full system calculation within an error about 1 kcal/mol. They serve as a robust linear scaling regime of quantum treatment for large molecular systems. As the response of fragmentation methods to convergence criteria in SCF iterations is different from that of full system calculation and the propagated convergence error is much smaller than the fragmentation error, the speed of fragmentation ab initio calculation can be further enhanced via loosening the convergence criterion in the calculation of each fragment without sacrificing the accuracy of the overall energy. Tests on single configuration calculations, geometry optimization and molecular dynamics simulation are performed. (C) 2017 Elsevier B.V. All rights reserved.