Molecular Properties and Conversion Factors These two papers are of general interest: A.D.Buckingham, J.Chem.Phys. 30, 1580-1585(1959). D.Neumann, J.W.Moskowitz J.Chem.Phys. 49, 2056-2070(1968). The first deals with multipoles, and the second with other properties such as electrostatic potentials. All units are derived from the atomic units for distance and the monopole electric charge, as given below. distance 1 au = 5.291771E-09 cm monopole 1 au = 4.803242E-10 esu 1 esu = sqrt(g-cm**3)/sec dipole 1 au = 2.541766E-18 esu-cm 1 Debye = 1.0E-18 esu-cm quadrupole 1 au = 1.345044E-26 esu-cm**2 1 Buckingham = 1.0E-26 esu-cm**2 octopole 1 au = 7.117668E-35 esu-cm**3 electric potential 1 au = 9.076814E-02 esu/cm electric field 1 au = 1.715270E+07 esu/cm**2 1 esu/cm**2 = 1 dyne/esu electric field gradient 1 au = 3.241390E+15 esu/cm**3 The atomic unit for the total electron density is electron/bohr**3, but 1/bohr**3 for an orbital density. The atomic unit for spin density is excess alpha spins per unit volume, h/4*pi*bohr**3. Only the expectation value is computed, with no constants premultiplying it. IR intensities are printed in Debye**2/amu-Angstrom**2. These can be converted into intensities as defined by Wilson, Decius, and Cross's equation 7.9.25, in km/mole, by multiplying by 42.255. If you prefer 1/atm-cm**2, use a conversion factor of 171.65 instead. A good reference for deciphering these units is A.Komornicki, R.L.Jaffe J.Chem.Phys. 1979, 71, 2150-2155. A reference showing how IR intensities change with basis improvements at the HF level is Y.Yamaguchi, M.Frisch, J.Gaw, H.F.Schaefer, J.S.Binkley, J.Chem.Phys. 1986, 84, 2262-2278. Raman activities in A**4/amu multiply by 6.0220E-09 for units of cm**4/g. One of the many sources explaining how activity relates to intensity is D.Michalska, R.Wysokinski Chem.Phys.Lett. 403, 211-217(2005) Polarizabilities Static polarizabilities are named alpha, beta, and gamma; these are called the polarizability, hyperpolarizability, and second hyperpolarizability. They are the 2nd, 3rd, and 4th derivatives of the energy with respect to uniform applied electric fields, with the 1st derivative being the dipole moment. It is worth mentioning that a uniform (static) electric field can be applied using $EFIELD, if you wish to develop custom usages, but $EFIELD input must not be given for any kind of run discussed below. A general approach to computing static polarizabilities is numerical differentiation, namely RUNTYP=FFIELD, which should work for any energy method provided by GAMESS. A sequence of computations with fields applied in the x, y, and/or z directions will generate the three alpha, beta, and gamma tensors. See $FFCALC for details. Analytic computation of all three tensors is available for closed shells only, see RUNTYP=TDHF and $TDHF input, or TDDFT=HPOL and $TDDFT input. If you need to know just the static alpha polarizability, see POLAR in $CPHF during any analytic hessian job. A break down of the static alpha polarizability in terms of contributions from individual localized orbitals can be obtained by setting POLDCM=.TRUE. in $LOCAL. Calculation will be by analytic means, unless POLNUM in that group is selected. This option is available only for SCFTYP=RHF. The keyword LOCHYP in $FFCALC gives a similar analysis for all three static polarizabilities, determined by numerical differentiation. Polarizabilities in a static electric field differ from those in an oscillating field, such as a laser produces. These are called frequency dependent alpha, beta, or gamma, and in the limit of entering a zero frequency, become the static quantities discussed just above. For RHF cases, various frequency dependent alpha, beta, and gamma polarizabilities can be generated, depending on the experiment. A particularly easy one to understand is 'second harmonic generation', governed by a beta tensor describing the absorption of two photons with the emission of one photon at doubled frequency. See RUNTYP=TDHF, and papers listed under $TDHF, for many other non-linear optical experiments. A program for the computation of the frequency dependent beta hyperpolarizability at the DFT level is also available, for closed shell molecules: see TDDFT=HPOL and keywords in $TDDFT input. Nuclear derivatives of the dipole moment and the various polarizabilities are also of interest. For example, knowledge of the derivative of the dipole with respect to nuclear coordinates yields the IR intensity. Similarly, the nuclear derivative of the static alpha polarizability gives Raman activities: see RUNTYP=RAMAN. Analytically computed 1st or 2nd nuclear derivatives of static or frequency dependent polarizabilities are available for SCFTYP=RHF, see RUNTYP=TDHFX and $TDHFX, giving rise to experimental observations such as resonance Raman and hyper-Raman. Finally, instead of considering polarizabilities to be a function of real frequencies, they can be considered to be dependent on the imaginary frequency. The imaginary frequency dependent alpha polarizability can be computed analytically for SCFTYP=RHF only, using POLDYN=.TRUE. in $LOCAL. Integration of this quantity over the imaginary frequency domain can be used to extract C6 dispersion constants. Polarizabilities are tensor quantities. There are a number of different ways to define them, and various formulae to extract "scalar" and "vector" quantites from the tensors. A good reference for learning how to compare the output of a theoretical program to experiment is A.Willetts, J.E.Rice, D.M.Burland, D.P.Shelton J.Chem.Phys. 97, 7590-7599(1992)