CASSCF+CASPT2 for Vanadium Cation： remarks and summary

V+(H2O)：

A) Quintet

symmetry：C2V [1-A1; 2-B1; 3-B2; 4-A2];     CASSCF(4, 9)

 {casscf
   close,8,3,3,0
   occ,12,5,5,1
   wf,32,4,4;state,10
   wf,32,1,4;state,10
   wf,32,2,4;state,10
   wf,32,3,4;state,10
   natorb,ci,print}

A1:  close [for 8 pairs] : 1s [V]; 2s[V]; 1s[O]; 2py[V]; 3s[V]; 3py[V]; 2s[O]; O-H sigma bond (2py-O：1s-H)

A1:  [9-12] : 9-[d2+(V): dx2-y2:-0.206947]; 10-[d0(V): dz2: -0.207388]; 11-[4s(V): -0.207217]; 12-[4py(V): -0.087493]


B1:  close [3 pairs] : 2px[V]; 3px[V]; 2px[O]

B1: [4-5]: 4-[3d2-(V):dxy:-0.209038]; 5-[4px(V): -0.12012]


B2: close [3 pairs] : 2pz[V]; 3pz[V]; 2pz[O]

B2:[4-5]:4-[d1-(V):dxz: -0.199839]; 5-[4pz(V): -0.111116]


A2: close 0

A2: 1-[3d1+(V):dyz: -0.218392]


B) Triplet

If calculating the triplet state only including the electronic state or configuration state with spin=2, then we can not get the correct active space in which the active orbitals are: the five 3d orbital，one 4s orbital, and three 4p orbital of vanadium

Only if we combine the spin=4 configuration state (quintet state) to calculate the triplet state,  then we can get the correct active space.

 Geometry={
 4
 V+(H2O)-t.dat
 V                  0.00000000    0.00000000    0.66236305
 O                  0.00000000    0.00000000   -1.40863240
 H                  0.00000000    0.77937774   -1.98264542
 H                  0.00000000   -0.77937774   -1.98264542
}

 spherical
 basis=cc-pvtz


 {casscf
  close,8,3,3,0
  occ,12,5,5,1
  wf,32,1,4;state,6
  wf,32,2,4;state,6
  wf,32,3,4;state,6
  wf,32,4,4;state,6
  wf,32,1,2;state,6
  wf,32,2,2;state,6
  wf,32,3,2;state,6
  wf,32,4,2;state,6
  natorb,ci,print}


 {rs2,shift=0.3,thrvar=1.0d-8,thrden=1.0d-8;maxit,100;
  wf,32,1,4
  state,1,1}
 {rs2,shift=0.3,thrvar=1.0d-8,thrden=1.0d-8;maxit,100;
  wf,32,4,4
  state,1,1}
 {rs2,shift=0.3,thrvar=1.0d-8,thrden=1.0d-8;maxit,100;
  wf,32,1,2
  state,1,1}
 {rs2,shift=0.3,thrvar=1.0d-8,thrden=1.0d-8;maxit,100;
  wf,32,4,2
  state,1,1}


put,molden,test1.molden

---

V+O：
A) Triplet
B) Singlet
V+OH：
A) Quartet
B) Doublet



V+(H2O)2：

A) Quintet

Symmetry :D2h : 1-Ag; 2-B3u; 3-B2u; 4-B1g; 5-B1u; 6-B2g; 7-B3g; 8-Au      CASSCF(4, 9)



1Ag:  close [for 6 pairs] : 1s [V]; 2s[V]; 1s[O];  3s[V]; 2s[O]; 2pz(O)-1s(H) [sigma bond]


1Ag[7-9]
7-[4s(V)+3d0:3dz2(V)]; 8-[3d2+:3dx2-y2(V)]; 9-[3d0:3dz2(V)];


2B3u:  close [3 pairs] : 2px[V]; 3px[V]; 2px(O)-1s(H) [sigma bond];

2B3u: [4]



3B2u: close [3 pairs] : 2py[V]; 3py[V]; 2py(O) [lone pair]

3B2u: [4]


4B1g: close 0
4B1g: 1-[3d2-:3dxy(V): -0.204883]


5B2u: close [5 pair]: 1s[O]; 2pz[V]; 3pz[V]; 2s[O]; 2pz[O]-1s[H] [sigma bond]

5B2u[6]


6B2g: close [1pair]: 2px[O]-1s[H] [sigma bond]
6B2g:[2]
2-[3d1+:3dxz(V):-0.171353]

7B3g: close [1 pair] 2py[O] [lone pair]
7B3g:[2]
2-[3d1-:3dyz(V):-0.133280]

8Au: close [0 pair]

B) Triplet : D2H

1Ag[close 6]: 1s[V]; 2s[V]; 1s[O]; 3s[V]; 2s[O]; sigma O-H [2pz(O)-1s(H)]
7-

2B3u[close 3]: 2px[V]; 3px[V];  sigma O-H [2px(O)-1s(H)]


3B2u[close 3]: 2py[V]; 3py[V]; non bond [2py(O)]

4B1g[close 1]: 1-[d2-:dxy]

5B1u[close 5 ]: 1s[O]; 2pz[V]; 3pz[V]; 2s[O]; sigma O-H [2pz(O)-1s(H)]

6B2g[close 1]: sigma O-H [2px(O)-1s(H)]

7B3g[close 1]: non bond [2py(O)]

8Au[close 0]





V+(H2O)3

A) Quintet : Symmetry Cs: A'; A'' 

1A'[close 19]

1-1s[V]; 2-2s[V]; 3-1s[O1]; 4-1s[O3]; 5-1s[O2]; 6-2py[V]; 7-2px[V]; 8- 3s[V]; 9-3py[V]; 10-3px[V]; 11-2s[O1]; 12-2s[O3]; 13-2s[O2]; 14-sigma bond [2px(O1)-1s(H1)]; 15-sigma bond []

2A''[close 5]

relationship of oscillator strength and dipole moment

V+(H2O)--Method Experiemt

Outline

1. Illustrator: several sentences

2. The reaction of V+(H2O) to release H2--> serious spin contamination

3. Post-HF Methods [CASSCF good]

4 val del wall interations

Molpro阅读笔记（1）

1. Molpro 是用于分子电子结构计算的完整的从头计算程序体现。重点是高精度，可多方面处理电子关联问题。用最近开发的直接积分局域电子关联方法可以极大地减少随分子尺寸增加的计算量。

第二章 Molpro 运行

molpro  datafile

第三章 定义Molpro 输入语言

1. 输入格式
(1) Molpro的exe 由输入文件控制。通常每个输入记录由一个keyword开始，之后可是数据或是其它keyword. Molpro的input 包含命令，指令，选项和数据。

(2) In fact，in one row 可以输入几个逻辑输入记录，并用分号隔开。即，一个给定的输入行可以包含多个有效命(用分号隔开)。这些用分号隔开的基本命令单位(记录)在这个手册中也经常称为卡片(card).

2. 命令
一个命令调用一个特定的程序。它之后可接该程序的局域输入，并用花括号括起来。

{命令，选项
指令
数据
}
,
命令的例子有HF，MP2，CCSD(T)等等，指令的例子有OCC, CLOSED, WF, PRINT。


第四章 一般程序结构

4.1 输入结构

典型的输入结构如下图

4.2 文件

Molpro使用3个连续的文本文件，分别为input，output 和 punch.

4.3 记录

记录的名称是正整数，通常引用的格式为记录.文件(record.file)


4.8 对称性

Molpro只能使用阿贝尔点群对称性。使用所用的对称群在积分输入中通过对称元素x,y,z的组合来定义，它们指定哪些坐标轴在相应的生成对称性操作下改变符合。可能的话，选择z轴作为唯一的轴通常是最好的。这种情况下的可能性示于表4.1.

每个点群的不可约表示用编号表示为1至8.他们的顺序非常重要，在表4.2-4.4给出。

轨道或基函数的引用格式一般是序号.不可约表示编号，也就是说，3.2表示使用点群对称性第二个不可约表示的第三个轨道。

4.9 定义波函

在需要这一信息的所有的程序模块中，N垫子波函数的总对称性在WF(wavefunctuion的缩写)卡定义，方式为：
WF, nelec,irrep,spin
或是用
WF,[NELEC=nelec],[SYM[METRY]=irrep],[spin=spin],[CHARGE=charge]
其中是nelec总电子数，irrep是不可约表示，spin等于2*S，其中S是总的自旋量子数。除了nelec外，也可以用charge，它定义分子的总电荷。
For example：对于10个电子C2v对称性的计算，WF, 10, 3, 0 表示1B2态；WF, 10, 1, 2表示3A1态。电荷也可以通过设置变量CHARGE来定义：
SET，CHARGE=charge
这一电荷将用于输入之后的所有能量计算。注意SET是必须的，因为CHARGE是系统变量。

4.10定义轨道子空间

在SCF，MCSCF，和CI程序中，可能需要指定每个对称性中有多少个占据轨道(或者在CI中有多少内部轨道)，以及这些轨道中哪些是芯壳层或闭壳层(也就是在所有的CSF中都是双占据的)。这一信息由OCC, CORE,和CLOSED卡提供，方式为：
OCC, m1,m2,...,m8;CORE, co1,co2,...,co8;CLOSED,cl1,cl2,...,cl8;
FROZEN, fr1,fr2,...,fr8;
其中mi是不可约表示i的占据轨道数，coi是芯轨道数，cli是闭壳层轨道数(包括芯轨道)。通常mi大于等于cli，cli大于等于coi。程序假定这些序号是从每个不可约表示最低的轨道开始。FROZEN只能用于MCSCF程序，表示不进行优化的冻芯轨道。(注意，在旧版本的MOLPRO程序中，冻芯轨道表示为CORE)

***注意，在SCF，MCSCF，以及CI和CCSD程序中的OCC和CLOSED卡，有略微不同的含义。在SCF，MCSCF中，OCC是任何出现在CSF(configuration state function)中的轨道。而在电子关联方法(CI, MPn, CCSD等)中，OCC表示在所有参考CSF中占据的轨道。在MCSCF中，FROZEN轨道中所有CSD中都是双占据的，并且冻结的(也就是不优化)，而CLOSED指所有的双占据轨道(冻结的加上做优化的)。在CI和CCSD程序中，芯轨道是不做相关能处理的轨道，CLOSED轨道是在所有的参考CSF中保持双占据的轨道。***

第十二章

12.2 对称性说明

Ab-Initio Simulations of Materials Using VASP: Density-Functional Theory and Beyond

Introduction

1. In 1985, Car and Parrinello published the work in which they proposed to solve the equations of motions of the coupled many-atom, many electron system via a dynamical simulated annealing strategy. The Car-Paarinello (P) method was designed to replace the traditional approach consisting of the iterative self-consistent solution of the Kohn-Sham equations for the electrons, the calculation of the fores acting on the atoms via Hellmann-Feynman theorem, and the integration of the Newtonian equations of the motions of the ions-the procedure having to be repeated after each ionic integration step until the ground state of the many-atom, many-electron system had been reached.

2. Strong Point of CP: CP paper introduced several other important innovations. One which is very important for the methodology is the use of Fast Fourier Transforms to switch between real-space and momentum-space representations of the wave function because different parts of the calculation can be done most efficiently in one space or another. The Kinetic Energy has a diagonal representation in momentum space while the Potential Energy is diagonal in real space. The second step forward was based on the observation that it is inefficient to do one part of the calculation with very high accuracy while one other part is still far from convergence. This led immediately to the bold idea--already referred to above-- that the total energy of a system could be minimized simultaneously with respect to both the electronic and ionic degrees of freedom.

3. Weakness of CP: Although much of recent development was undoubtedly triggered by the CP paper, it is a bit ironical that the development of modern DFT calculations is characterized by a rather quick return to the more traditional approach. The reason is twofold: First, the CP method of a dynamical updating of electronic degrees of freedom requires electrons and ions to be decoupled such that, once the electronic ground-state has been reached, the system remains closed to the adiabatic Born-Oppenheimer surface. This condition is met with good accuracy for insulators and wide-gap semiconductors but violated for metals and narrow-gap materials. The Second reason is that the minimization of the total energy does not allow an efficient control of charge-density fluctuations during the iterative process--for metallic systems such fluctuations (often referred to as "Charge-sloshing") may even prevent a convergence of this process.

The Vienna Ab Initio Simulation Package VASP - Basic methodology:
Why Plane Wave?

4. In a work of Gruber et al, they compared the performance of  plane-wave (VASP) and local-basis set methods (GAUSSIAN and SIESTA package) in structural study of small gold clusters. For a wide class of relatively compact cluster structures the authors found excellent agreement between the binding energies calculated using both methods, while planar structures where found to have a somewhat reduced stability in the local-basis set calculations. 

This difference was attributed to the fact that the quality of the plane-wave basis set is independent of the topology of the system while the quality of a basis composed of atom-centred local orbitals depends on the relative atomic positions(a situation which is evidently reminiscent of the basis-set superposition error)/ It was concluded that the relatively lower binding energy of planar clusters provided by SIESTA and GAUSSIAN03 could be a consequence of a lower "effective quality" of the basis set for systems that are more extended in one or two dimensions compared with more compact structures.

Potentials, pseudo-potentials

5. Pseudo-potential have been introduced to avoid the need for an explicit treatment of the strongly bound and chemical inert core electrons.

6. Methods for generating pseudo-potentials include the 'norm-conserving' pseudo-potential (the "norm-conservation" criterion applied to the node-less pseudo wave functions ensures  that not only the logarithmic derivative of the exact and pseudo-wave-functions, but also their derivatives with respect to the energy agree at the chosen reference energy and cut-off radius) and  the 'ultrasoft' pseudo-potential (where the norm-conservation criterion is dropped, but the logarithmic derivatives are matched at two or more reference energies spanning the entire range of eigenvalues of the valence electrons).

7.The criterion for the quality of a pseudo-potential is not how well it matches experiment, but how well it reproduces the results of accurate all-electron calculations. A certain drawback of pseudo-potential calculations is that because of the non-linearity of the exchange interaction between valence and core electrons, elaborate non-linear core corrections are required for all systems where the overlap between valence- and core-electron densities is not completely negligible. This deficiency may be removed by using the projector-augmented wave method.

Projector-augmented waves

8.

Essence of others works

Essence of others works:

1.       Source [ C:\Users\Andy\hzhang\Projects\Vanadium\literature\05302013 ]

Energetics of the Ligated Vanadium Dictions VO²⁺, VOH²⁺, and [V, O, H2]²⁺

Point1: Experiment: Charge-stripping mass spectrometry

Point2: Abstract: According to the theoretical results, [V (OH₂)] ²⁺ is also a thermochemically stable dication, whereas [HVOH] ²⁺ is suggested to be metastable.

Point3: [M (OH₂)] ²⁺, for larger values of n, these species can easily be generated from solution by means of electrospray ionization. A key aspect of these isolated dications on the dilute gas phase concerns their stability with respect to the relevant dissociation and charge-separation asymptotes.   

Point4: for [M (OH₂)] ²⁺, three types of fragmentation can occur, similar schemes apply for metal dications with other open- or closed- shell ligands.

Ligand Evaporation: [M (OH₂) _n] ²⁺ à [M (OH₂) _n-1 ] ²⁺ + H₂O

Electron Transfer: [M (OH₂) _n] ²⁺ à [M (OH₂) _n-1 ] ²⁺ + H₂O^+.

Proton Transfer: [M (OH₂) _n] ²⁺ à [M (OH)(OH₂) _n-2 ] ²⁺ + H₃O⁺

Rules: For large n, the evaporation of water predominates. The smaller the number of ligands n, and the larger the ionization energy, IE(M⁺), [large ionization energy means it needs more energy to release one electron from M⁺ to form M²⁺ ], the more likely become the competing electron- and proton-transfer reactions.

Point5: experiment

The monocationic precursors were generated via two independent routes: a) fast-atom bombardment of an aqueous slurry of V₂O₅; and b) electron ionization of trimethoxy vanadate, OV(OCH₃)₃

Armentrout，1994，JCP，98，7538-7544

Point 1: These ideas show that if the metal 4s orbital (and to a lesser extent the 3dσ) is occupied, the interaction of the metal ion with water will be repulsive at short range because the 4s (3dσ) orbital correlates to an anti-bonding orbital of the intermediate.  Oxidative addition of O-D to a metal center can be achieved by donation of electrons in σ bonding orbitals into empty 4s and 3dσ orbitals on the metal and molecular fragments and back-donation of metal 3dπ electron into σ* anti-bonding orbitals. This increases the electron density between the metal and molecular fragments and also lengthens the O-D bond.

Notes of Literature【2】--JCP-1989 Highly correlated systems. Ionization energies of first row transition metals Sc-Zn

Introduction

1. Electron correlation effects are extremely important to provide an accurate description of the electronic states arising from different occupations of the 3d and 4s orbitals of transition metal atoms.

2 They have calculated the dns2 --> dn+1s1 excitation energies of atoms Sc-Cu using both MP4 and quadratic configuration interaction (QCI) method. While the MP4 was clearly inadequate, they obtained excellent agreement with experiment using QCI method with a mean deviation of 0.14eV after including the effects of relativistic corrections. The remaining deviation was found to be systematic and can be ascribed partly to basis set deficiencies.

3. In this paper, they consider low-lying ionization energies of all the first-row transition metal atoms Sc-Zn using similar theoretical methods.

Theoretical Methods

4. Methods: QCISD, QCISD(T), MP4

5. Basis set: spd, spdf

6. Relativistic corrections
Relativistic corrections are known to be quite important for the transition metal atoms, the differential effects in some cases being as large as 0.5eV.

7. Martin and Hay have calculated such corrections for all the ionic states considered in this study at the HF level. These calculated corrections assume that the inclusion of electron correlation effects does not change the relativistic corrections. However, in the paper, the author was comparing the neutral atoms with the corresponding ions whose behavior may be somewhat different, the effect of electron correlation on the calculated relativistic corrections was not clear. Thus, the author of this paper have used the computed corrections of Martin and Hay.

Results

8. When they using MPn series method, the results is clearly inadequate, especially for Co-Zn. Closer inspection reveals that the large deviations for Co-Zn arise in cases where the d electron population changes from that of the neutral atom, clearly related to the correlation associated with the breaking of a d electron pair.

9.