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：

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：

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

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:

• Emamian, S., Lu, T., Kruse, H., and Emamian, H., 2019, Exploring nature and predicting strength of hydrogen bonds: A correlation analysis between atoms‐in‐molecules descriptors, binding energies, and energy components of symmetry‐adapted perturbation theory, J. Comput. Chem., 40 (32), 2868–2881.