Single point energies# 单点能

Single point energies are the simplest properties one might aim to obtain, they are the lowest energy solution for the Schrödinger equation. However, there are different methods to compute those, with varying quality levels:
单点能是最简单的目标性质，它们是薛定谔方程的最低能量解。然而，计算这些能量的方法多种多样，质量水平各异：

Hartree-Fock (HF)# 哈特里-福克（HF）

It is one of the first approximations developed [Slater1951], which does not include the so-called dynamic or even static correlation. To run an example HF single point calculation, simply use:
这是最早提出的近似方法之一[Slater1951]，它未包含所谓的动态或静态相关性。要运行一个 HF 单点计算示例，只需使用：

!HF DEF2-SVP
* xyz 0 1
O         -3.56626        1.77639        0.00000
H         -2.59626        1.77639        0.00000
H         -3.88959        1.36040       -0.81444
*

on your main input, and the basis DEF2-SVP will be assigned to each atom on your list. The total energy will be printed in the end of the file, e.g.:
在你的主要输入中，列表中的每个原子将分配 DEF2-SVP 基组。总能量将在文件末尾打印，例如：

-------------------------   --------------------
FINAL SINGLE POINT ENERGY       -75.959334985643
-------------------------   --------------------

It is one of the oldest and simpler methods, and it is not in general recommended if you need good energies. However, it is the basis of more complete methods such as CCSD and CASSCF.
这是最古老且较为简单的方法之一，通常不建议在需要高质量能量时使用。然而，它是更完善方法如 CCSD 和 CASSCF 的基础。

Unrestricted HF (UHF)# 无限制高频（UHF）

If one chooses any multiplicity other than one, say three for a triplet, an UHF calculation is performed. In this particular case, one should always check the spin contamination of the results.
如果选择除一以外的任何多重度，例如三重态选择三，则会执行 UHF 计算。在此特定情况下，应始终检查结果的自旋污染情况。

Warning 警告

If the expectation value of the $S^{2}$ (written as <S**2>) operator differs significantly from the ideal value, it might be that your system could only be treated with a multi-reference calculation such as CASSCF.
如果 $S^{2}$ （记作）算符的期望值与理想值存在显著差异，可能表明您的系统需采用多参考计算方法，如 CASSCF。

In the case of the water above as a triplet, one gets:
对于上方的水作为三重态的情况，可得：

----------------------
UHF SPIN CONTAMINATION
----------------------

Expectation value of <S**2>     :     2.005700
Ideal value S*(S+1) for S=1.0   :     2.000000
Deviation                       :     0.005700

which shows a minimal deviation and is thus suitable for use here.
这表明偏差极小，因此适合在此使用。

Acceleration of the SCF (RIJDX and RIJCOSX)#
SCF（RIJDX 和 RIJCOSX）的加速

One way to accelerate the solution of the SCF equations, necessary to compute the energy, is to use the RI option to compute the Coulomb integrals [Neese2003]. In that case, an auxiliary basis is also necessary. For the DEF2 family, the DEF2/J is set by default:
加速求解 SCF 方程以计算能量的方法之一，是使用 RI 选项来计算库仑积分[Neese2003]。在这种情况下，还需要一个辅助基组。对于 DEF2 系列，默认设置为 DEF2/J：

!HF DEF2-SVP DEF2/J RIJDX

If the basis chosen has no corresponding auxiliary basis, you can include de AUTOAUX flag for an automatic generation of this auxiliary basis:
如果所选基组没有对应的辅助基组，可以包含 de AUTOAUX 标志以自动生成该辅助基组：

!HF 6-31+G(d,p) AUTOAUX RIJDX

For an even faster speed-up, the COSX algorithm [Helmich-Paris2021] can be used together with the RI to compute the exchange integrals efficiently.
为了实现更快的加速，可以结合 RI 使用 COSX 算法[Helmich-Paris2021]来高效计算交换积分。

!HF DEF2-SVP DEF2/J RIJCOSX

Density functional theory (DFT)#
密度泛函理论 (DFT)

DFT energies can be obtained in a similar fashion, by choosing any functional from the ones available. For instance:
DFT 能量可以通过类似方式获得，只需从可用功能中任选其一。例如：

!B3LYP DEF2-SVP
* xyz 0 1
O         -3.56626        1.77639        0.00000
H         -2.59626        1.77639        0.00000
H         -3.88959        1.36040       -0.81444
*

requests a calculation using the B3LYP [Becke1993], [Parr1988] functional. The calculated energy is:
请求使用 B3LYP [Becke1993], [Parr1988]泛函进行计算。计算所得能量为：

-------------------------   --------------------
FINAL SINGLE POINT ENERGY       -76.320253532344
-------------------------   --------------------

The same argument for checking spin-contamination applies here. Always have in mind that the DFT results may change depending on the functional, so one should check before using these and never compare energies from different methods!
检查自旋污染的相同论点在此同样适用。始终牢记，DFT 结果可能因泛函而异，因此在采用这些结果前应进行核查，切勿将不同方法的能量进行比较！

ORCA 6 is fully compatible with functionals from LibXC. For a complete list of functionals and more details, please check the ORCA manual.
ORCA 6 完全兼容 LibXC 中的泛函。如需查看完整的泛函列表及更多详细信息，请参阅 ORCA 手册。

Note 注释

As standard DFT does not cover correlation effects, including London dispersion, the application of a dispersion correction is generally recommended.
由于标准密度泛函理论未涵盖包括伦敦色散在内的相关效应，通常建议应用色散校正。

Note 注释

The same approximations to accelerate the SCF, the RIJDX and RIJCOSX described above can be used with DFT. Of course, the RIJCOSX only makes sense when using a hybrid functional, where HF exchange is also calculated.
同样用于加速 SCF 的近似方法，即上述的 RIJDX 和 RIJCOSX，也可用于 DFT 计算。当然，RIJCOSX 仅在使用混合泛函时才有意义，因为此时还需计算 HF 交换部分。

Important 重要

The RIJDX approximation is the default for non-hybrid functionals and RIJCOSX the default for hybrid ones. To turn these of, you can use !NORI or !NOCOSX.
RIJDX 近似是非杂化泛函的默认设置，而 RIJCOSX 则是杂化泛函的默认设置。若要关闭这些设置，可以使用 !NORI 或 !NOCOSX 。

MP2 perturbation theory#
MP2 微扰理论

MP2 is a post Hartree-Fock method, which means it starts with HF as a basis and tries to include its missing dynamic correlation. It is implemented in ORCA in a very efficient way using the RI approximation or even in a pair-natural variant (DLPNO) that is extremely efficient [Neese2015], both can be called using:
MP2 是一种后 Hartree-Fock 方法，意味着它以 HF 为基础，并试图纳入其缺失的动态相关性。在 ORCA 中，MP2 通过使用 RI 近似或甚至更高效的成对自然变体（DLPNO）来实现，这两种方法均可通过以下方式调用：

!RI-MP2 cc-pVTZ cc-pVTZ/C

or 或

!DLPNO-MP2 cc-pVTZ cc-pVTZ/C

Because it is a so called correlated method, it needs a special basis "/C" for the RI part. These are not available for all basis sets, but can be obtain through AUTOAUX:
由于它是一种所谓的相关方法，因此需要为 RI 部分使用特殊的基组“/C”。并非所有基组都具备这些条件，但可以通过 AUTOAUX 获取：

!DLPNO-MP2 6-311++G(2d,2p) AUTOAUX
*XYZ 0 1
O         -3.56626        1.77639        0.00000
H         -2.59626        1.77639        0.00000
H         -3.88959        1.36040       -0.81444
*

You can check the correlation energy contribution as:
您可以检查相关能的贡献如下：

------------------------------------------------------
 DLPNO-MP2 CORRELATION ENERGY:      -0.240752222110 Eh
------------------------------------------------------

and the final energy is printed as usual.
最终能量按惯例打印输出。

Warning 警告

Correlated methods are typically more basis set size dependent than DFT. Choose sufficiently large basis sets to avoid large errors.
相关方法通常比密度泛函理论（DFT）更依赖于基组大小。选择足够大的基组以避免较大误差。

Spin-component-scaled MP2 (SCS-MP2)#
自旋成分缩放的 MP2 方法 (SCS-MP2)

The accuracy of MP2 can be greatly improved by introduction of spin-component-scaling. The spin-component-scaling parameters PS of the opposite-spin and PT of the same-spin components can be adjusted via the %mp2block:
通过引入自旋分量缩放，MP2 的精度可以得到显著提升。反自旋分量和同自旋分量的自旋分量缩放参数 PS 和 PT 可以通过 %mp2 块进行调整：

!RI-SCS-MP2 cc-pVTZ cc-pVTZ/C

%mp2
  DOSCS       true
  PS          1.2    
  PT          0.333
end

*XYZFILE 0 1 structure.xyz

If only the RI-SCS-MP2 keyword is used, default values for PS=1.2 and PT=0.333 are used.
如果仅使用 RI-SCS-MP2 关键字，则使用 PS=1.2 和 PT=0.333 的默认值。

Orbital optimized MP2 (OO-MP2)#
轨道优化的 MP2 (OO-MP2)

By making the Hylleraas functional stationary with respect to the orbital rotations one obtains the orbital-optimized MP2 method that is implemented in ORCA. The RI-accelerated variant can be envoked by:
通过使 Hylleraas 泛函相对于轨道旋转保持平稳，可以得到在 ORCA 中实现的轨道优化 MP2 方法。RI 加速变体可通过以下方式调用：

!OO-RI-MP2 cc-pVTZ cc-pVTZ/C

*XYZFILE 0 1 structure.xyz

Warning 警告

Note that every iteration of the OO-RI-MP2 method is as expensive as a single RI-MP2 relaxed density calculation!
注意，OO-RI-MP2 方法的每一次迭代都与一次 RI-MP2 松弛密度计算同样耗费资源！

Regularized MP2# 正则化 MP2

The regularization approach by Shee, Head-Gordon, and co-workers [Shee2021] introduces a single-parameter, energy-gap dependent regularization term that dampens overestimated pairwise additive contributions, thus renormalizing first-order amplitudes to empirically mimic higher-order correlations. Three regularization functions are available in ORCA, $κ$ , $σ$ , and $σ^{2}$ . The most commonly used regularizer is $κ$ which can be controlled via the %mp2 block:
Shee、Head-Gordon 及其同事提出的正则化方法[Shee2021]引入了一个依赖于能隙的单参数正则化项，该项抑制了过高估计的成对加性贡献，从而将一阶振幅重新归一化，以经验上模拟高阶相关性。ORCA 中提供了三种正则化函数， $κ$ 、 $σ$ 和 $σ^{2}$ 。最常用的正则化器是 $κ$ ，可通过 %mp2 块进行控制：

!RI-MP2 cc-pVTZ cc-pVTZ/C

%mp2
    DoRegMP2     true   # activates MP2 regularization
    RegMP2Type   0      # 0 = kappa regularizer
    RegMP2Kappa  1.1    # kappa parameter
end

*XYZFILE 0 1 structure.xyz

Note 注释

No gradients are available for regularized MP2.
正则化 MP2 无法提供梯度。

Double-hybrid DFT (DH-DFT)#
双杂化密度泛函理论 (DH-DFT)

By replacing part of the correlation component oft a density functional by e.g. MP2 improved results can be obtained for a variety of properties. These methods are called double-hybrid functionals [Grimme2006] as they include both HF exchange and MP2 correlation. Many pre-defined double hybrid functionals can be envoked via simple keyword similar to conventional functionals. An exemplary input for the B2PLYP functional would look like:
通过将密度泛函中的一部分相关成分替换为例如 MP2，可以对多种性质获得改进的结果。这些方法被称为双杂化泛函[Grimme2006]，因为它们同时包含 HF 交换和 MP2 相关性。许多预定义的双杂化泛函可以通过类似于传统泛函的简单关键词来调用。一个 B2PLYP 泛函的示例输入如下：

!B2PLYP DEF2-QZVPP

*XYZFILE 0 1 structure.xyz

Double hybrids can also benefit from RI approximations
双杂交系统亦可受益于重组近似方法

!RI-B2PLYP DEF2-QZVPP DEF2-QZVPP/C

*XYZFILE 0 1 structure.xyz

and even the DLPNO scheme to speed up the MP2 calculation.
以及 DLPNO 方案以加速 MP2 计算。

!DLPNO-B2PLYP DEF2-QZVPP DEF2-QZVPP/C

*XYZFILE 0 1 structure.xyz

A prominent double hybrid further making use of SCS-MP2 is revDSD-PBEP86-D4. This empirical functional is obtained by also incorporating the D4 dispersion correction into the fit and typically yields very good results for thermochemistry.
显著的双杂化方法进一步利用 SCS-MP2 的是 revDSD-PBEP86-D4。该经验性泛函通过纳入 D4 色散校正进行拟合，通常在热化学方面能产生非常好的结果。

!revDSD-PBEP86-D4 DEF2-QZVPP DEF2-QZVPP/C

*XYZFILE 0 1 structure.xyz

Note 注释

Note that double hybrid functionals typically also require larger basis sets compared to conventional DFT functionals. Double hybrids can also be combined with dispersion corrections like D4. Functionals like revDSD-PBEP86-D4 were fit with the D4 correction and should never be used without it!
请注意，与传统 DFT 泛函相比，双杂化泛函通常也需要更大的基组。双杂化泛函还可以与 D4 等色散校正相结合。例如 revDSD-PBEP86-D4 泛函在拟合时就已包含 D4 校正，因此绝不应在没有 D4 校正的情况下使用！

Coupled Cluster (CC)# 耦合簇（CC）

Coupled cluster calculations, in particular the CCSD(T) variant, are the gold standard for single point energies. However, in their usual formulation, they are also extremely costly from a computational point of view.
耦合簇计算，特别是 CCSD(T)变体，是单点能计算的金标准。然而，在其通常的表述中，它们在计算上也是极其昂贵的。

ORCA features a DLPNO variant that is much more efficient and presents almost linear scaling growth for larger systems [Neese2016], [Neese2013a], [Neese2013b]. In order to use that, simply set DLPNO-CCSD(T) in your input and choose an appropriate basis (also needs a "/C" basis or AUTOAUX)
ORCA 提供了一种 DLPNO 变体，该变体在处理较大系统时效率显著提升，且几乎呈现线性扩展增长[Neese2016], [Neese2013a], [Neese2013b]。要使用此功能，只需在输入中设置 DLPNO-CCSD(T)，并选择合适的基组（同样需要“/C”基组或 AUTOAUX）。

!DLPNO-CCSD(T) cc-pVTZ cc-pVTZ/C
*XYZ 0 1
O         -3.56626        1.77639        0.00000
H         -2.59626        1.77639        0.00000
H         -3.88959        1.36040       -0.81444
*

and the CC results are printed as:
CC 结果打印如下：

----------------------
COUPLED CLUSTER ENERGY
---------------------- 
 
E(0)                                       ...    -76.055469392
E(CORR)(strong-pairs)                      ...     -0.267934875
E(CORR)(weak-pairs)                        ...     -0.000104142
E(CORR)(corrected)                         ...     -0.268039017
E(TOT)                                     ...    -76.323508409
Singles Norm <S|S>**1/2                    ...      0.018659847
T1 diagnostic                              ...      0.006597252

with the final single point energy at the end:
最终单点能计算结果为：

-------------------------   --------------------
FINAL SINGLE POINT ENERGY       -76.330949256808
-------------------------   --------------------

Please always check the T1 diagnostic value printed. A rule of thumb says, that for a value of the diagnostic of larger than 0.02 the results are not to be trusted and the HF reference might be poor.
请始终检查打印出的 T1 诊断值。经验法则表明，若诊断值大于 0.02，则结果不可信，且 HF 参考可能不佳。

There are many different coupled cluster and coupled pair methods that can be use in ORCA, check the ORCA manual for more details.
ORCA 中可以使用许多不同的耦合簇和耦合对方法，详情请查阅 ORCA 手册。

Note 注释

The RIJCOSX algorithm can be used to significantly accelerate MP2 and CC calculations!
RIJCOSX 算法可显著加速 MP2 和 CC 计算！

Semiempirical Methods (SQM)#
半经验方法（SQM）

Various semi-empirical methods are available within ORCA. These methods are fast but lack the accuracy and robustness of more sophisticated DFT or WFT methods. Nevertheless, they are very useful for high-throughput screening or treatment of very large systems with hundreds to thousands of of atoms. A prominent example is Grimme's GFN2-xTB extended tight-binding method [Grimme2019]. It can be easily invoked by:
ORCA 中提供了多种半经验方法。这些方法虽然快速，但相较于更为复杂的 DFT 或 WFT 方法，其准确性和鲁棒性有所欠缺。然而，它们在高通量筛选或处理包含数百至数千个原子的超大体系时极为有用。一个突出的例子是 Grimme 的 GFN2-xTB 扩展紧束缚方法[Grimme2019]。通过以下方式可以轻松调用：

!XTB2

*XYZ 0 1
O         -3.56626        1.77639        0.00000
H         -2.59626        1.77639        0.00000
H         -3.88959        1.36040       -0.81444
*

Warning 警告

The xtb methods are currently invoked through an interface to the xtb standalone program. Therefore, make sure to use xtb 6.4.0 or later to ensure full compatibilty!
xtb 方法目前通过与 xtb 独立程序的接口调用。因此，请确保使用 xtb 6.4.0 或更高版本以确保完全兼容性！

Single point energies# 单点能

Hartree-Fock (HF)# 哈特里-福克（HF）

Unrestricted HF (UHF)# 无限制高频（UHF）

Acceleration of the SCF (RIJDX and RIJCOSX)#SCF（RIJDX 和 RIJCOSX）的加速

Density functional theory (DFT)#密度泛函理论 (DFT)

MP2 perturbation theory#MP2 微扰理论

Spin-component-scaled MP2 (SCS-MP2)#自旋成分缩放的 MP2 方法 (SCS-MP2)

Orbital optimized MP2 (OO-MP2)#轨道优化的 MP2 (OO-MP2)

Regularized MP2# 正则化 MP2

Double-hybrid DFT (DH-DFT)#双杂化密度泛函理论 (DH-DFT)

Coupled Cluster (CC)# 耦合簇（CC）

Semiempirical Methods (SQM)#半经验方法（SQM）

Acceleration of the SCF (RIJDX and RIJCOSX)#
SCF（RIJDX 和 RIJCOSX）的加速

Density functional theory (DFT)#
密度泛函理论 (DFT)

MP2 perturbation theory#
MP2 微扰理论

Spin-component-scaled MP2 (SCS-MP2)#
自旋成分缩放的 MP2 方法 (SCS-MP2)

Orbital optimized MP2 (OO-MP2)#
轨道优化的 MP2 (OO-MP2)

Double-hybrid DFT (DH-DFT)#
双杂化密度泛函理论 (DH-DFT)

Semiempirical Methods (SQM)#
半经验方法（SQM）