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A new approximation method is proposed in this article for the discussion of molecular structures,and this new method includes the two well-known theories,molecular orbital theory and electron-pair bond theory as two special cases.Let a molecule have n bonds and let the ith bond be described by the anti-symmetrical two-electron bond function ψ_i(v_(2i-1),v_(2i)).(If there exist one- electron,three-electron or many-electron bonds,they can be similarly described by the corresponding one-electron,three-electron...

A new approximation method is proposed in this article for the discussion of molecular structures,and this new method includes the two well-known theories,molecular orbital theory and electron-pair bond theory as two special cases.Let a molecule have n bonds and let the ith bond be described by the anti-symmetrical two-electron bond function ψ_i(v_(2i-1),v_(2i)).(If there exist one- electron,three-electron or many-electron bonds,they can be similarly described by the corresponding one-electron,three-electron or many-electron bond func- tions.) Then the stationary state of the molecule is represented by the follow- ing wave function Ψ, where the summation is over all permutations of 1,2,……,2n except those within the interior of the functions,since each ψ_i is already anti-symmetrical.Obviously (2~n/((2n)/!))~(1/2) is the normalization factor. By quantum mechanics the energy of the molecule equals (1) here H_i,T_(ij) and S_(11)' are respectively the following three kinds of operators, (2) (3) (4) The third term of equation (1) is the exchange integral of electrons 1 and 1', while (1,2') is that of electrons 1 and 2'.According to the definition of bond functions,ψ_i may be written as (5) Substituting equation (5) into equation (1) and carrying out the integration over spin coordinates,we obtain (6) It can be easily seen from equation (6) that the combining energy of a mole- cule consists of two parts,one being the binding energy of the bonds represent- ed by the first term of equation (6),and the other being the interaction energy of the bonds denoted by the second term of that equation. If we choose certain functions φ_i~('s) involving several parameters and substi- tute them into equation (6),we may determine the values of those parameters by means of the variation principle. For the discussion of bond interaction energies,we develop a new method for the evaluation of certain types of three-center and four-center integrals.The interaction energy of a unit positive charge and an electron cloud of cylindrical- symmetry distribution may be written as (7) where (8) and R_0~2=a~2+b~2+c~2 The interaction energy of two electron clouds both of cylindrical-symmetry distributions with respect to their own respective axes is evaluated to be (9) (10) where is to sum over j from zero to the lesser value of n-2i and m, is to sum over i from zero to the integral one of n/2 and (n-1)/2,and is to sum over all cases satisfying the relation =m-j,while b_(n,n-2i) represents the coefficient of x~(n-2i) in the n th Legendre polynomial.

本文在分子结构理论方面,作了下列两点贡献:首先建议了用双电子或多电子键函数作为近似基础,来计算分子的近似能量和近似电子云分布。这样计算得来的结果,一定会比用分子轨道理论或电子配对理论好,因为它更真实的反映了分子的化学性质,同时它也包括了后两者,而以它们为特例。我们得到了分子结合能的表示式,用表示式证明了分子结合能由两部分组成:一部分是键的结合能,另一部分是键与键间的作用能。其次是建议了一种新方法,把在计算化学键相互间的作用能中遇到的一些三中心和四中心积分,还原为容易计算的二中心积分。这方法比以往所用的好,因为它计算比较简单,同时限制性也小。

Although James and Coolidge (1933) solved the molecular hydrogen problem in almost complete agreement with experiment by using a 13-term 2-electron eigenfunction, his method can hardly be applied to more complex molecules. For this and other reasons (Coulson, 1938), it is still desirable to obtain a good one-electron eigenfunction, i.e., molecular orbital, for the hydrogen molecule. The best molecular orbital treatment available in the literature was given by Coulson (1938), who used a trial eigenfunction in...

Although James and Coolidge (1933) solved the molecular hydrogen problem in almost complete agreement with experiment by using a 13-term 2-electron eigenfunction, his method can hardly be applied to more complex molecules. For this and other reasons (Coulson, 1938), it is still desirable to obtain a good one-electron eigenfunction, i.e., molecular orbital, for the hydrogen molecule. The best molecular orbital treatment available in the literature was given by Coulson (1938), who used a trial eigenfunction in elliptical coordinates involving 5 parameters and obtained 3.603 eV for the binding energy of H_2, which is to be compared with the ex- perimental value of 4.72 eV. In the present investigation we have proposed a new type of trial eigenfunction for the molecular orbital: (1) with p = centers a, b, g, c, d,…… i = electron 1 or 2 (2) where the p's are centers along the bond axis a-b (Fig. 1). In this simple problem both the Fock and Hartree methods yield the same result. The molecular orbital ψ must satisfy the following integral equation: (3) where ε is the energy of the molecular orbital, F is the Fock operator which is equal to H+G(1), while H is the one-electron Hamiltonian operator: H = -1/2▽~2-1/r_a-1/r_b (4) and G(1) is the interaction potential (5) Substituting (1) into (3), we obtain the linear combination coefficients c_p, which must satisfy the following secular equation: (6) where is the solution of the secular determinant and The F_(pq)'s are not at first known, but depend upon the c_p's. A method of successive approximation must therefore be adopted. A set of c_p values may be assumed, the F_(pq)'s calculated, the secular determinant (7) solved, and a new set of c_p values found. This process is repeated until a "self-consistent" set of c_p values is obtained. The above procedure was first proposed by Roothaan (1951), not for H_2 but for more complex molecules. It was called by him the "LCAO SCF (linear combination of atomic orbitals self-consistent field) method". The new feature of the present investigation is that we not only use LCAO but also LCNAO (linear combination of non-atomic orbitals, such as x_g, x_c, x_d, …). The order of secular determinant (7) may be reduced to half if we replace the eigen- functions x_a, x_b .... by their symmetrical and anti-symmetrical linear combinations x_a + x_b and x_a-x_b. Numerical calculations have been carried out both for the three- and the two-centered molecular orbitals. The three-centered molecular orbital is (10) (11) where S_(ab) and S(ag) are the overlapping integrals between x_a and x_b, and between x_a and x_g respectively. The parameters a and g have 'been obtained to give minimum energy by the method described above. They are a=l.190, g=0.22, and the binding energy is 3.598 eV, which is almost as good as that obtained by Coulson (3.603 eV) using a trial function of 5 parameters. The two-centered molecular orbital is (12) (13) which gives a maximum binding energy of 3.630 eV for a=1.190 and R~(ac)=R(bd)=0.105 (Fig. 1). This result is 'better than Coulson's. If we allow different values for the ex-ponent α in x_a and x_g in equation (11), or if we use a four-centered molecular orbital, such as ψ=a(x_a + x_b) + b(x_c + x_d) with four parameters, namely α_a=α_b, α_c=α_d, R_(ac)=R_(bd) and the ratio b/a, it is possible to obtain a still better result. Extension of the present method to the treatment of more complex molecules is now under investigation.

(1)討論了用自洽勢場多中心分子軌道法來處理H_2分子的一般方法。 (2)用僅含兩個參變數三中心分子軌道進行了具體計算,求得H_2分子的結合能為3.598eV,接近於Coulson用五個參變數的雙中心分子軌道所得的結果(3.603eV)。 (3)用不在原子核上的兩中心的分子軌道求得H_2分子的結合能為3.630 eV,此上述結果為好。並指出如用不同的α值和四個或四個以上中心的分子軌道,很有可能得到更好的結果。以上處理方法有可能推廣到比H_2更為複雜的分子。

By means of Friedel-Crafts reaction, the following compounds were prepared from 4-methyl- imidazolone-2 and four different ω-carbethoxy acyl halides: 4-methyl-5-(δ-carbethoxy-γ-methyl- butyryl)-imidazolone-2, 4-methyl-5-(δ-carbethoxy-γ, γ-dimethylbutyryl)-imidazolone-2, 4-methyl- 5-(ω-carbethoxy-n-nonanoyl)-imidflzolone-2, and 4-methyl-5-(ω-carbethoxy-n-heptadecanoyl)- imidazolone-2. With PtO_2 as catalyst, they were readily reduced to the four corresponding imidazolidone compounds. These compounds were hydrolyzed...

By means of Friedel-Crafts reaction, the following compounds were prepared from 4-methyl- imidazolone-2 and four different ω-carbethoxy acyl halides: 4-methyl-5-(δ-carbethoxy-γ-methyl- butyryl)-imidazolone-2, 4-methyl-5-(δ-carbethoxy-γ, γ-dimethylbutyryl)-imidazolone-2, 4-methyl- 5-(ω-carbethoxy-n-nonanoyl)-imidflzolone-2, and 4-methyl-5-(ω-carbethoxy-n-heptadecanoyl)- imidazolone-2. With PtO_2 as catalyst, they were readily reduced to the four corresponding imidazolidone compounds. These compounds were hydrolyzed with 1 N NaOH and then followed by acidification to give the following acids: 4-methyl-5-(δ-carboxy-y-methylbutyl)- imidazolidone-2, 4-methyl-5-(δ-carboxy-γ, γ-dimethylbutyl)-imidazolidone-2, 4-methyl-5-(ω-car-boxy-n-nonanyl)- imidazolidone-2, and 4-methyl-5-(ω-carboxy-n-heptadecanyl)-imidazolidone-2. Microbiological tests indicated that the first three acids are good anti-biotins towards lactobacillus casei and saccharomyces cerevisiae strain No. 139. Due to its extreme insolubility in water, the last compound has not yet been tested for its microbiological activity.

(1)利用Friedel-Crafts反應,由4-甲基-2-氧代-二氫化咪唑及四個不同的醯氯羧酸酯,得到下列四個化合物:4-甲基-5-(δ-乙氧羰基-γ-甲基丁醯)-2-氧代-二氫化咪唑,4-甲基-5-(δ-乙氧羰基-γ,γ-二甲基丁醯)-2-氧代-二氫化咪唑,4-甲基-5-(ω-乙氧羰基-正壬醯)-2-氧代-二氫化咪唑及4-甲基-5-(ω-乙氧羰基-正十七醯)-2-氧代-二氫化咪唑。 (2)用Cr_(2)O_3精製過的乙酸爲溶劑,PtO_2爲觸媒,這四個4-甲基-2-氧代-二氫化咪唑的衍生物,很順利的吸收相當於3分子的氫,還原為相對應的4-甲基-2-氧代-四氫化咪唑的衍生物,水解後得到下列四個酸:4-甲基-5-(δ-羧基-γ-甲基丁基)-2-氧代-四氫化咪唑,4-甲基-5-(δ-羧基-γ,γ-二甲基丁基)-2-氧代-四氫化咪唑,4-甲基-5-(ω-羧基-正壬基)-2-氧代-四氫化咪唑及4-甲基-5-(ω-羧基-正十七基)-2-氧代-四氫化咪唑。前三者已作過初步的微生物效應試驗,對於lactobacillus casei及saccharomyces cerevisiae都有顯著的反促生素效應。第四個化合物因為...

(1)利用Friedel-Crafts反應,由4-甲基-2-氧代-二氫化咪唑及四個不同的醯氯羧酸酯,得到下列四個化合物:4-甲基-5-(δ-乙氧羰基-γ-甲基丁醯)-2-氧代-二氫化咪唑,4-甲基-5-(δ-乙氧羰基-γ,γ-二甲基丁醯)-2-氧代-二氫化咪唑,4-甲基-5-(ω-乙氧羰基-正壬醯)-2-氧代-二氫化咪唑及4-甲基-5-(ω-乙氧羰基-正十七醯)-2-氧代-二氫化咪唑。 (2)用Cr_(2)O_3精製過的乙酸爲溶劑,PtO_2爲觸媒,這四個4-甲基-2-氧代-二氫化咪唑的衍生物,很順利的吸收相當於3分子的氫,還原為相對應的4-甲基-2-氧代-四氫化咪唑的衍生物,水解後得到下列四個酸:4-甲基-5-(δ-羧基-γ-甲基丁基)-2-氧代-四氫化咪唑,4-甲基-5-(δ-羧基-γ,γ-二甲基丁基)-2-氧代-四氫化咪唑,4-甲基-5-(ω-羧基-正壬基)-2-氧代-四氫化咪唑及4-甲基-5-(ω-羧基-正十七基)-2-氧代-四氫化咪唑。前三者已作過初步的微生物效應試驗,對於lactobacillus casei及saccharomyces cerevisiae都有顯著的反促生素效應。第四個化合物因為在水中溶度太低,故尚未能作它的微生物效應試驗。

 
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