With the development of digital computers in the late 1950's came the opportunity to mechanise the tedious calculations of stability constants from data such as potentiometric titration data which, up to that time, were done using hand-calculations and graphical methods. The principle was well-known, having been developed by Gauss in the 19th. century - to minimise an objective function, a sum of (weighted) squared residuals, with respect to some parameters. A residual would be the difference between observed and calculated pH (or electrode potential) and the parameters would be the stability constants. According to Gauss, it is necessary to obtain the partial derivatives of each calculated quantity (such as calculated pH) with respect to each parameter in order to do the calculation. Here it is that there appears to be a serious obstacle: calculated pH is an implicit function of the stability constants and so the derivative cannot be obtained directly. Much of the early effort was directed at overcoming this apparent difficulty.

For detailed bibligraphy see: P. Gans, A. Sabatini and A. Vacca, *Talanta*,
(1996) **43**, 1739-1753.
(requires Acrobat reader)

1961 | Pit-mapping (Ingri and Sillén) was described as a means of minimising the objective function. The pit was assumed to be a quadratic function of the parameters so that its minimum could be located by fitting the function |

1963 | GaussG
(Tobias and Yasuda). Used Gauss's least squares method with partial derivatives
calculated numerically by means of a difference formula. Never widely used,
but part of this program formed the basis of SCOGS (see below) |

1964 | Letagrop
(Ingri and Sillén). The first general purpose computer program for
stability constant calculation. Used pit-mapping. Separate modules for different
kinds of data. |

1967 | SCOGS
(Perrin and Sayce). Generalised the approach used in GaussG. The most widely
used program after Letagrop. |

1974 | Miniquad
(Sabatini, Vacca and Gans) The objective function was derived from the total
concentrations of the reagents. Partial derivatives could be obtained from
analytical formulae. Outperformed SCOGS in speed and reliability and was
faster than Letagrop. (in those days execution speed was important as many
people had to "pay" for central processor time) |

1975 | SQUAD
(Leggett and McBryde) Applied the same process used in SCOGS
to spectrophotometric data |

1976 | Miniquad75
improvements in speed and reliability |

1978 | Psequad
(Zekany and Nagypal) Used implicit differentiation to minimize the objective
function in pH or absorbance. With hindsight it is a mystery why this was
not done earlier as the process is described in text-books on advanced calculus! |

1982 | Titfit
(Zuberbühlr and Kaden) The first published program in the field to
use a "game" computer. |

1985 | Specfit
(Kaden, Maeder and Zuberbühler). A general program for spectrophotometric
data with for an early "desk-top" computer (HP 9835). Further
developed and gained wide acceptance. |

1985 | Superquad
(Gans, Sabatini and Vacca). Used implicit differentiation as in Psequad,
though originally developed independently. Mainframe computer program. Over
1000 citations. |

1988 | Superquad
(2) (Pettit) A version for the IBM PC (as it was known then)
with a simple data editor integrated into the program. |

1992 | Hyperquad
(1) (Gans, Sabatini and Vacca) An extension of Superquad to allow
both potentiometric and spectrophotometric data to be treated. (Mainframe
program) |

1993 | EQNMR
(Hynes) The first general-purpose program for NMR data. |

1995 | HypNMR
(Gans, Sabatini and Vacca) Our program for NMR data. |

1996 | Hperquad
(2) A suite of 12 linked MS-DOS programs including data preparation
and analysis modules. |

1997 | Equispec
(Maeder) A development from Specfit. |

1999 | pHab
(Gans, Sabatini and Vacca) Designed for spectroscopic data at measured pH.
Windows application. |

2000 | Hyperquad2000
All modules now integrated into a single Windows application. |

2004 | HypNMR2004
An all-singing all dancing Windows application. |

2005 | yperHuadQata
Dfile
A single data
file to hold the data for all stability constant programs. Is used in Hyperquad2006 |

2006 | HypDH
Determination of stability constants and reaction enthalpies from calorimetric
data (under development). |

2008 | Hyperquad2008
Program written entirely in Visual basic. New structure with "live"
data. |