A new method is proposed in this paper for the evaluation of the following three important kinds of three-center and four-center integrals needed in molecular quantum mechanics: (1) (2) (3) Obviously, integral (2) is a special case of integral (3), so we need only to evaluate the first and the third. The following equations have been obtained for the evaluation of the above-mentioned two kinds of integrals (4) (5) where (6) (7) (8) (9) R_0 in equation (4) is the distance of point a apart from the origin located...

A new method is proposed in this paper for the evaluation of the following three important kinds of three-center and four-center integrals needed in molecular quantum mechanics: (1) (2) (3) Obviously, integral (2) is a special case of integral (3), so we need only to evaluate the first and the third. The following equations have been obtained for the evaluation of the above-mentioned two kinds of integrals (4) (5) where (6) (7) (8) (9) R_0 in equation (4) is the distance of point a apart from the origin located in bc line, while that in equation (5) is the distance between the two chosen origins separately located in ab and cd lines. θ_0 is the angle made byand, and θ_(10), θ_(20) and θ_(12) are respectively the angles made by and,and,and, The fourth term of equation (5) is, in general, negligible except in the case of R_0, which is less than two Bohr units. We propose two methods for the evaluation of and : the first one is to choose the origin at the end-point of the bond and evaluate the integral strictly inside and outside the sphere of radius, while the second one is to choose the origin at the mid-point of the bond and evaluate its value inside and outside the ellipsoid passing through the end-point of. The calculation involved in the second method is quite simple and, of course, a small error is introduced in changing the region of integration from the sphere to the ellipsoid, but it is quite negligible in comparison with the result of our first method. Equation (4) is exact in all cases, while equation (5) is exact in many cases but also involves certain errors in some other cases. From our actual calculations, we draw the conclusion that equation (5) is almost exact in the evaluation of integrals L_(aa, bc) and L_(ab, cd) and that certain error is involved in the evaluation of integral L_(ab, bc), but the error introduced does not exceed ten per cent.

The absorption spectra of cadmium sulphide single crystals were observed with natural light and polarized light, one piece of the crystals having a thickness of about 0.1 mm and another about 0.05 mm. At room and liquid air temperatures, the absorption spectra observed with natural light indicate that the wavelength of the long wavelength limit of Cd S depends upon the thickness and the temperature of the crystals. A change of the wavelength of the absorption edge which depended upon the orientation of...

The absorption spectra of cadmium sulphide single crystals were observed with natural light and polarized light, one piece of the crystals having a thickness of about 0.1 mm and another about 0.05 mm. At room and liquid air temperatures, the absorption spectra observed with natural light indicate that the wavelength of the long wavelength limit of Cd S depends upon the thickness and the temperature of the crystals. A change of the wavelength of the absorption edge which depended upon the orientation of the electric vector of the polarized light produced by a polaroid plate placed between the crystal and the slit of the spectrograph was observed.

Experiments are performed to use a brand of Chinese filter paper in paper chromatographic analysis. The paper used is the "fine" grade filter paper manufactured by the First Eastern Factory, Fou-Shun. It appears that the filter paper, after adequate treatment, may be used in paper chromatographic work. Treatment essentially consists of washing with dilute hydrochloric acid and distilled water and ascending with suitable solvents of the particular cation-groups. In this experiment, the solvents used for chromatographic...

Experiments are performed to use a brand of Chinese filter paper in paper chromatographic analysis. The paper used is the "fine" grade filter paper manufactured by the First Eastern Factory, Fou-Shun. It appears that the filter paper, after adequate treatment, may be used in paper chromatographic work. Treatment essentially consists of washing with dilute hydrochloric acid and distilled water and ascending with suitable solvents of the particular cation-groups. In this experiment, the solvents used for chromatographic analysis of aluminium, silver and arsenic groups were modified from that used by F. H. Burstall and others. The results are summarized as follows:Group I R_f: K 0.45, Na 0.56, Mg 0.71Group Ⅱ R_f: Ba 0.45, Sr 0.53, Ca 0.61Group Ⅲa R_f: Al 0.02, Zn 0.73Group Ⅲb R_f: Fe 0.99, Co 0.44, Mn 0.30, Ni 0.00Group Ⅳa R_f: Ag 0.16, Pb 0.00, Hg 0.80Group Ⅳb R_f: Pb 0.02, Cu 0.30, Bi 0.67, Cd 0.82, Hg 0.90Group V R_f: As 0.79, Sb 0.93, Sn 0.95Besides, we have found a number of common reagents which can be used to develop the cations on such kind of filter paper. After chromatographic separation, their sensitivity is determined. The R_f of both the ascending and descending processes has very close values. When temperature varies within 5°C, the R_f values change very little.