Efficient exponential type basis sets constructed from new hyperbolic cosine type B functions have been used in self consistent field calculations for the ground states of the atoms from Helium to Argon and their ions. Different hyperbolic cosine type functions are incorporated into the B functions to increase the accuracy of atomic orbitals and correctly describe the electronic density of systems. The presented results for the minimal basis sets are shown that the quality of generalized hyperbolic cosine type B functions is one of the most appropriate basis sets of B functions, especially for increasing atomic number. A comparison with the standard B functions, hyperbolic cosine type B functions and the corresponding numerical Hartree-Fock values are given in tables. Our study shows that the modification of B functions can be an efficient way of increasing the accuracy of the atomic and molecular SCF calculations. These basis sets may also be used in the calculation of atomic properties such as cusp condition and density properties of atomic electrons. Some numerical results and comparisons are given to clarify the basis sets quality from the density point of view. An improved description of atomic orbitals based on the use of modified B functions will also play an important role in ion-atom collisions problems, semi-emprical and density functional methods. (C) 2018 Elsevier B.V. All rights reserved.