ADDITIONAL REMARKS Dr H-J. Werner (J. W. Goethe Uniuersitat Frankfurt West-Germany) (communi- cated). My first comment concerns Prof. Siegbahn's paper. Recently we have also done some calculations on transition-metal atoms and simple molecules containing transition metals. In these calculations we found it extremely difficult to achieve a similar accuracy as we are used to calculations which involve first- or second-row atoms only. The problems start with the choice and size of the basis sets generally one needs diffuse d-functions and at least twof-functions on each first-row transition metal atom. Secondly the results obtained in multireference-CI calculations may sometimes be surprisingly sensitive to the choice of the one-electron orbital basis (e.g. SCF MCSCF or natural orbitals).Thirdly higher than double excitations in particular their unlinked cluster contributions may be very important ;for example their effect increases the dissociation energy of Cu,' from 0.23 eV (CISD) to 1.SO eV (CEPA-1) (exptl 2.05 eV). Finally relativistic effects are usually not negligible as was assumed in many previous calculations. Many of these difficulties arise from the large electron correlation effects in the compact 3d shells. On the other hand the diffuse 4s electrons give only a small contribution to the correlation energy. This leads to very large differential electron correlation effects to the relative energies of the atomic s2dn sldn+land dn+2electron states. For instance the &o -s2d8separation in Ni is reduced from 5.47 eV at the SCF level to ca.2.0 eV at the CEPA-1 level. The relativistic effect increases this value to 2.55 eV which is ca. 0.85 eV larger than the experimental value (1.71 eV). Note that we tried very hard to improve this result employing very large basis sets with up to 4f 3g and lh functions so far without significant success. Since as Prof. Siegbahn noted 3d's hybridization may be important in bond formation it appears to me essential first to understand and solve the atomic problems before doing large-scale calculations on transition-metal complexes. It is my feeling that the results obtained with present methods and basis sets for such large molecules are quite questionable. Also in my opinion the MCSCF or CASSCF method alone is not an appropriate tool for treating transition-metal compounds even though recently much progress has been made in optimizing very long CASSCF expansions2? (we have been able to optimize CASSCF wavefunctions with up to 178916 configurations).The CASSCF method should be used to describe near-degeneracy effects and dissociation processes correctly but in order to account for the important dynamical correlation effects it must be followed by a multireference CI calculation. In conclusion I have the feeling that my view about our ability to do reasonable calculations for transition-metal compounds is more pessimistic than Prof. Siegbahn's. H-J. Werner and R. Martin Chem. Phys. Lett. 1985 113 451. H-J. Werner and P. J. Knowles J. Chem. Phys. in press. P. J. Knowles and H-J.Werner Chem. Phys. Lett. 1985 115 259. My next comment refers to a remark of Prof. Wright concerning the use of bond-centred basis functions printed on p. 187. It is certainly correct that the use of such functions can apparently improve the results in particular if rather small (DZ or DZP) atom-centred basis sets are employed. Since bond functions do not contribute to the energy at large (infinite) internuclear distances it is obvious that the use of such functions will always lead to an increase in the calculated dissociation energies and 202 ADDITIONAL REMARKS usually to better agreement with the experimental values. It appears quite possible however that the addition of several bond functions will lead to binding energies which are too large.Hence the use of bond functions makes it possible to influence (within certain limits) the results arbitrarily. The problem is to find those bond functions which lead to a balanced description of the molecule and the separated atoms. It appears to me that this is possible only by comparison with known experimental data. I admit however that it may eventually be reasonable to optimize the bond functions for a number of molecules for which experimental data are known in order to make predictions for other closely related molecules. With reference to Dr Hunter’s comment on p. 188 I did not say that the use of bond functions would violate the variational principle and such a statement is of course wrong. The problem is that we are always dealing with incomplete basis sets and that certain incomplete basis sets can lead to an unbalanced description of different regions of the potential-energy function.I would now like to make a comment on the question of Dr Davies printed on p. 184. I can confirm Prof. Peyerimhoff s experience that the dipole length operator appears to be preferable to the velocity operator for the calculation of electronic transition probabilities. Generally the transition moments calculated with the length operator appear to bemuchless sensitive to the basis set and electroncorrelationeffects than those obtained with the velocity operator. A particular problem with the velocity form is that the calculated values must be divided by the energy difference to obtain the transition moment.We found that the errors of the values obtained from the velocity operator often become very large as the energy difference between the states under consideration becomes small; e.g. at large internuclear distances when both potentials have the same dissociation limit. We have calculated transition-moment functions for considerable numbers of diatomic molecules and molecular ions. These calculations showed that electron correlation effects on the calculated radiative lifetimes are often very large; for example for the A-X transitions in CH or OH they are of the order of 100%.In order to obtain accurate results it is therefore necessary to use very large and flexible basis sets and highly correlated multireference CI wavefunctions. MCSCF and CASSCF wavefunctions often yield poor results.Typical errors of our calculated radiative lifetimes are 10-1 5% as compared with the most reliable experimental values. In many cases the differences between various measurements are much larger even though the (statistical) error bounds of the individual measurements are mostly fairly small. I therefore believe that the calculation of radiative transition probabilities provides a useful opportunity for quantum chemists to provide experimentalists with much needed quantitative information. I do not think that there is an established basis for the ‘6 electron’ or ‘20 electron’ limit in ab initio calculations of accurate transition moments. The problem seems to be rather the proper vibrational averaging of the transition-moment surfaces of polyatomic molecules.For a review see H-J. Werner and P. Rosmus ‘Ab initio Calculations of Radiative Transition Probabilities in Diatomic Molecules’ in Comparisonof ab initio Calculations with Experiments -The State of the Art ed. R. Bartlett (D. Reidel in press). Finally I turn to Prof. Peyerimhoff s paper :In the section ‘transition probabilities and radiative lifetimes’ and in fig. 5 there is an erroneous reference to our calculations of the dipole-moment function for OH. The MCSCF and MC-CI results in fig. 5 were obviously derived from dipole-moment functions of Stevens et a1.l and Chu et a1.,2 204 ADDITIONAL REMARKS respectively. These functions yield Einstein coefficients which are in error by 50% or more.To my knowledge the ‘experimental’ Einstein coefficients for Av = 1 to v’ = 8 are unknown. There have been a few measurements of A A and A which differ however by several hundred percent. The empirical dipole-moment function of Murphy3 was based on relative intensities and its slope at re is therefore undetermined [arbitrarily set to 1 D A-l in ref. (3)]. We have employed the MCSCF-CI method for the calculation of an accurate dipole-moment function of OH.4The reliability of the dipole-moment functions can be checked indirectly by comparing calculated and measured transition-probability ratios. As has been shown by Mieq5 for such an analysis it is essential to take vibration-rotation and spin-uncoupling effects into account and to average exactly over the same rovibrational lines as in the experiments.With our MCSCF-CI dipole-moment function and an RKR potential-energy function this yields (experimental values in brackets) &/A = 0.38 Ifr 0.06 (0.44+ 0.03,30.41),6 A;/Ai = 1.10k0.37 (1.15+0.05,3 1.25).6 With the MCSCF (17) dipole moment function of ref. (1) one obtains the ratios 0.46 If:0.06 and 1.62 0.28 respectively. The ‘error bounds’ in the theoretical values arise from the averaging over several rotational lines (K = 2-7 in the P branches). W. J. Stevens G. Das A. C. Wahl M. Krauss and D. Neumann J. Chem. Phys. 1974 61 3686. S. I. Chu M. Yoshimine and B. Liu J. Chem. Phys. 1974 61 5389. R. E. Murphy J. Chem. Phys. 1971 54 4852. H-J. Werner P. Rosmus and E. A. Reinsch J. Chem. Ph-vs. 1983 79 905. F. H. Mies J. Mol. Spectrosc. 1974 53 150. F. Roux J. D’Incan and D. Cerny J. Astrophys. 1973 186 1141.