Paul Dirac's stated "The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known and the difficulty is only in that the exact application of these laws lead to equations much too complicated to be soluble".    
Dirac PA, Proc. R. Soc. London 1929; A123: 714-733.


"On account of this formidable complexity, chemistry possesses inevitably one aspect of depending on the analogy through experience. This is in a sense said to be the fate allotted to chemistry, and the source of a great difference in character from physics."
Fukui K. Nobel Lecture. 1981


Fukui in 1982 stated that "chemistry inevitably depends on analogy through experience due to the formidable complexity".
Fukui K. Angew. Chem., Int. Ed. Engl. 1982; 21: 801-809.


In 1988 Michael Dewar stated "It should be remembered that no current procedure, ab initio or semiempirical, can lead by itself to reliable predictions of reaction mechanisms. The best approach is to combine experiment with calculation, including data for as many different properties and for as many different molecules as possible".
Dewar MJS, Healy EF, Ruiz JM, J. Am. Chem. Soc. 1988; 110: 2666-2667.


In 1985 Dewar stated  "The problems of chemistry cannot be solved, and will not be solved in the forseeable future, by a priori quantum mechanical calculation".
Dewar MJS, J. Phys. Chem. 1985; 89: 2145-2150.



Methods for determining the occurence and extent of mesomerism have been developed by Pauling and others, but they belong to the modern period. The device of writing down the possible structures and estimating the contribution which each makes to the actual condition of the molecule is a calculus and not a theory of structure, though it has often been misunderstood as such.
Robert Robinson J. Chem. Soc. 1947; 1288-1301.


In 2008 Stefan Grimme (a quantum chemist) stated that “a systematic increase of the accuracy of thermodynamic computations based on ab initio methods is not feasible for large systems”. He also stated that “even if only the electronic contributions are considered quantum mechanically (what is normally done in QC), the necessary equations will be too complex to be solved but for the simplest (one-electron) systems” and in relation to post-HF correlated approaches “this increases the computational requirements drastically, and for highly accurate methods, the hardware and CPU-time requirements are so demanding that only systems with about 5-10 atoms heavier than hydrogen can be treated.” Furthermore he stated “Nevertheless, the accuracy of MP2, as well as of DFT, is often not sufficient in many application”. He also spoke of the self-interaction error problem that still plagues current DFT and he is developing new quantum chemicals methods to deal with large molecules.
Schwabe T, Grimme S, Acc. Chem. Res. 2008; 41 ; 569-579.



In 1978 S.W. Benson stated in relation to the prediction of equilibrium constants "An ab initio quantum mechanical approach to such a task is not feasible now or in the near future"
S.W. Benson Angew. Chem. Int. Ed. Engl. 1978; 17: 812-819.


In 1990 Roth and Doering stated in relation to the present quantum chemical techniques that "the ability to calculate within 1 kcal/mol or better enthalpies of formation of any arrangement of a chemically reasonable number of atoms, seems to remain out of reach for the indefinite future".
Roth WR, Lennartz H-W, Doering W von E, Birladeanu E.L, Guyton CA, Kitagawa T, J. Am. Chem. Soc. 1990; 112: 1722-1732.


In 1990 Carpenter stated that full-scale trajectory calculations "are impractical, even with modern supercomputers, for molecules of interest to organic chemists"
Newman-Evans RH, Simon RJ, Carpenter BK, J. Org. Chem. 1990; 55: 695-711.


Murray Gell-Mann in 1994 stated that "In practise, even with the aid of the largest and fastest computers available today, only the simplest chemical problems are amenable to actual calculations from basic physical theory. The number of such amenable problems is growing, but most situations in chemistry are still described using concepts and formulae at the level of chemistry rather than that of physics".
Gell-Mann M. The Quark and the Jaguar: Adventures in the Simple and the Complex, Abacus 1995.   


In 2003 Irmgard Frank stated that "if the reaction pathway is not a priori restrictable to a few internal degrees of freedom, the determination of the corresponding multidimensional surface of the corresponding multidimensional surface becomes prohibitive, no matter what quantum-chemical method is used…in addition, it may be difficult even in relatively small molecular systems to assess the real motion of the system on the basis of the potential surface".
Frank I,  Angew. Chem., Int. Ed. Engl. 2003; 42: 1569-1571.



In 2006 Bierbaum stated that 'Determing activation enthalpies with an accuracy of 0.5 kcal mol-1 or better is a difficult computational task'. This paper also highlights the fact that small deviations in the activation enthalpy can have a large effect on the branching ratios in chemical reactions.
Villano SM, Kato S, Bierbaum VM, J. Am. Chem. Soc 2006; 128: 736-737.



In 2004 Leszczynski stated that 'Despite progress in this field, it is still quite difficult to calculate the properties of molecules in their electronic excited states, especially for relatively large molecular systems".
Sheng Y, Leszczynski J, Garcia AA, Rosario R, Gust D, Springer J, J. Phys. Chem. B 2004; 108: 16233-16243.


Dannenberg recognises that quantum predictions must ultimately be supported by experiment and are 'likely to be in error in at least some detail'.
Dannenberg JJ, Angew. Chem. Int. Ed. Engl. 1976; 15: 519-525.


Warner recognises the problem of knowing which results can be trusted, given that not all systems can be subjected to the expensive G2 treatment
Warner PM, J. Org. Chem. 1996; 61: 7192-7194.