目录

如何使用AIM方法计算键径和键临界点、环临界点,以及临界点电子密度、密度梯度、能量密度、多种能量密度变化率、氢键强弱

以苯为例进行说明:

参数设置

结果查看

点击SCM logo > View > Properties > QTAIM(Topology)显示如下:

灰白色的球是(3,-3),与原子核位置一致,绿色的球是环临界点,红色的球是键临界点,线条是键径。鼠标放置在CP上时,会显示坐标值,该坐标值单位为Bohr,1 Bohr=0.52917721 Å,而Out文件中显示的坐标单位是Å。

点击窗口左下方AIM > Show details,可以看到表示原子、键、环、笼临界点的小球的各种颜色,例如:

临界点的详细信息

SCM - Output - Bond path 往上翻,就是各个临界点的各种数据,例如:

CP #   25
(RANK,SIGNATURE):     (3,-1)    

CP COORDINATES:      0.000000    1.799289   -5.263447

EIGENVALUES OF HESSIAN MATRIX:

     -0.7744589E+00  -0.7639204E+00   0.5386842E+00

EIGENVECTORS (ORTHONORMAL) OF HESSIAN MATRIX (COLUMNS):

      0.2396951E-17   0.1000000E+01  -0.4151615E-17
     -0.5000023E+00   0.4793880E-17   0.8660241E+00
      0.8660241E+00   0.0000000E+00   0.5000023E+00


HESSIAN MATRIX:

     -0.7639204E+00  -0.4720628E-17  -0.2725845E-17
                      0.2103954E+00   0.5686094E+00
                                     -0.4461701E+00

VALUES OF SOME FUNCTIONS AT CPs (a.u.):

                Rho =    0.2854255E+00
        |GRAD(Rho)| =    0.4797565E-15
         GRAD(Rho)x =   -0.6094092E-17
         GRAD(Rho)y =    0.2437286E-15
         GRAD(Rho)z =    0.4131894E-15
          Laplacian =   -0.9996951E+00
 (-1/4)Del**2(Rho)) =    0.2499238E+00
            Diamond =    0.1473542E+01
        Metallicity =   -0.8529043E+01
        Ellipticity =    0.1379520E-01

INHOMOGENEITY PARAMETERS AT CPs (a.u.)

            Delta_u =    0.6976387E+00
            Delta_s =    0.5999796E+00
            Delta_t =    0.7588694E+00
            Inhom_s =    0.1666723E+01
           Inhom_ex =    0.1167634E+01
 
ENERGY COMPONENTS AT CPs (a.u.)

        Gb(Abramov) =    0.1886526E+00
        Vb(Abramov) =   -0.6272290E+00
        Hb(Abramov) =   -0.4385764E+00
             Ex_ueg =   -0.1387955E+00
             Ec_ueg =   -0.1763575E-01
           Delta_ex =    0.1018033E+00
           Delta_ec =    0.2304692E-01
           Delta_et =   -0.5607528E+00
                Pxc =    0.7870122E+01
                Qxc =    0.4417219E+01

其中:

  1. CP COORDINATES:临界点的坐标
  2. Rho:电子密度
  3. |GRAD(Rho)|:电子密度的梯度的模
  4. GRAD(Rho)x:电子密度x方向梯度
  5. Laplacian:电子密度的Laplacian运算值
  6. (-1/4)Del2(Rho)):Laplacian的1/4
  7. Metallicity:Jenkins' metallicity (eq 67 in Comput.Theor.Chem. 2015,1053,112)
  8. Ellipticity:椭圆率
  9. delta_ex、delta_ec、delta_et:能量变化率(eqs 24 and 25 in Phys.Chem.Chem.Phys. 2014,16,14539)
  10. delta_u, delta_s, delta_t: evaluation of CP inhomogeneity descriptors,也就是variation rates for the (reduced) density gradient(eq5 in J.Phys.Chem.A 2009,113,12322 and eq27 in Phys.Chem.Chem.Phys. 2014,16,14539),the double integral is evaluated numerically using standard Gauss-Legendre quadrature
  11. inhom_s, inhom_ex:inhomogeneity lengths (eqs 5 and 8 in Chem.Phys.Lett. 2013,579,122)
  12. Gb(Abramov),Vb(Abramov),Hb(Abramov): Abramov's ActaCryst. 1997,153,264,也可以参考: eqs 1 and 2 in Chem.Phys.Lett. 1998,285,170。其中 G_abramov = cTF*CPpoints(i,4)**F53 + F16*laplacian, V_abramov = F14*laplacian - two*G_abramov, H_abramov = G_abramov + V_abramov
  13. ex_ueg, ec_ueg:DFT energy densities from the uniform electron gas (UEG),Dirac-Slater exchange is used,correlation: 2/2 Pade approximant (eq 23 in Phys.Chem.Chem.Phys. 2014,16,14539)
  14. Pxc, Qxc:eqs 9 and 12 in J.Chem.Phys. 2010,132,211101

氢键强弱

电中性体系的氢键键能估算:E$_{HB}$ = -223.08*ρ$_{BCP}$+0.7423,其中ρ$_{BCP}$为氢键BCP处电子密度,单位为a.u.(ADF默认输出的电子密度单位即a.u.),E$_{HB}$单位为kcal/mol,参考: