Table of Contents

The MRCI program

Multiconfiguration reference internally contracted configuration interaction

Bibliography:

H.-J. Werner and P.J. Knowles, J. Chem. Phys. 89, 5803 (1988).
P.J. Knowles and H.-J. Werner, Chem. Phys. Lett. 145, 514 (1988).

For excited state calculations:

P. J. Knowles and H.-J. Werner, Theor. Chim. Acta 84, 95 (1992).

For explicitly correlated MRCI (MRCI-F12):

T. Shiozaki, G. Knizia, and H.-J. Werner, J. Chem. Phys. 134, 034113 (2011);
T. Shiozaki and H.-J. Werner, J. Chem. Phys. 134, 184104 (2011);
T. Shiozaki and H.-J. Werner, Mol. Phys. 111, 607 (2013).

All publications resulting from use of the corresponding methods must acknowledge the above.

The first internally correlated MRCI program was described in:

H.-J. Werner and E.A. Reinsch, J. Chem. Phys. 76, 3144 (1982).
H.-J. Werner, Adv. Chem. Phys. 59, 1 (1987).

The command CI or CI-PRO or MRCI calls the MRCI program.
The command MRCI-F12 calls the explicitly correlated MRCI-F12 program.
The command CISD calls fast closed-shell CISD program.
The command QCI calls closed-shell quadratic CI program.
The command CCSD calls closed-shell coupled-cluster program.

The following options may be specified on the command line:

Introduction

The internally contracted MRCI program is called by the CI command. This includes as special cases single reference CI, CEPA, ACPF, MR-ACPF and MR-AQCC. For closed-shell reference functions, a special faster code exists, which can be called using the CISD, QCI, or CCSD commands. This also allows to calculate Brueckner orbitals for all three cases (QCI and CCSD are identical in this case).

The explicitly correlated variant is called by the command MRCI-F12, see section explicitly correlated MRCI-F12.

With no further input cards, the wavefunction definition (core, closed, and active orbital spaces, symmetry) corresponds to the one used in the most recently done SCF or MCSCF calculation. By default, a CASSCF reference space is generated. Other choices can be made using the OCC, CORE, CLOSED, WF, SELECT, CON, and RESTRICT cards. The orbitals are taken from the corresponding SCF or MCSCF calculation unless an ORBITAL directive is given. The wavefunction may be saved using the SAVE directive, and restarted using START. The EXPEC directive allows to compute expectation values over one-electron operators, and the TRAN directive can be used to compute transition matrix elements for one-electron properties. Natural orbitals can be printed and saved using the NATORB directive.

For excited state calculations see STATE, REFSTATE, and PROJECT.

Specifying the wavefunction

Note: All occupations must be given before WF, PAIRSS, DOMAIN, REGION or other directives that need the occupations.

Occupied orbitals

OCC,$n_1,n_2,\ldots,n_8$;

$n_i$ specifies numbers of occupied orbitals (including CORE and CLOSED) in irreducible representation number $i$. If not given, the information defaults to that from the most recent SCF, MCSCF or CI calculation.

Frozen-core orbitals

CORE,$n_1,n_2,\ldots,n_8$;

$n_i$ is the number of frozen-core orbitals in irrep number $i$. These orbitals are doubly occupied in all configurations, i.e., not correlated. If no CORE card is given, the program uses the same core orbitals as the last CI calculation; if there was none, then the atomic inner shells are taken as core. To avoid this behaviour and correlate all electrons, specify

CORE

Closed-shell orbitals

CLOSED,$n_1,n_2,\ldots,n_8$

$n_i$ is the number of closed-shell orbitals in irrep number $i$, inclusive of any core orbitals. These orbitals do not form part of the active space, i.e., they are doubly occupied in all reference CSFs; however, in contrast to the core orbitals (see CORE), these orbitals are correlated through single and double excitations. If not given, the information defaults to that from the most recent SCF, MCSCF or CI calculation. For calculations with closed-shell reference function (closed=occ), see CISD, QCI, and CCSD.

Defining the orbitals

ORBIT,name.file,[specifications];

name.file specifies the record from which orbitals are read. Optionally, various specifications can be given to select specific orbitals if name.file contains more than one orbital set. For details see section selecting orbitals and density matrices (ORBITAL, DENSITY). Note that the IGNORE_ERROR option can be used to force MPn or triples calculations with non-canonical orbitals.

The default is the set of orbitals from the last SCF, MCSCF or CI calculation.

Defining the state symmetry

The number of electrons and the total symmetry of the wavefunction are specified on the WF card:

WF,elec,sym,spin

where

The WF card must be placed after any cards defining the orbital spaces OCC, CORE, CLOSED.

The REF card can be used to define further reference symmetries used for generating the configuration space, see REF.

Additional reference symmetries

REF,sym;

This card, which must come after the WF directive, defines an additional reference symmetry used for generating the uncontracted internal and singly external configuration spaces. This is sometimes useful in order to obtain the same configuration spaces when different point group symmetries are used. For instance, if a calculation is done in $C_s$ symmetry, it may happen that the two components of a $\Pi$ state, one of which appears in $A'$ and the other in $A''$, come out not exactly degenerate. This problem can be avoided as in the following example:

for a doublet $A'$ state: 

WF,15,1,1;      !define wavefunction symmetry (1)
REF,2;          !define additional reference symmetry (2)

and for the doublet A” state: 

WF,15,2,1;      !define wavefunction symmetry (2)
REF,1;          !define additional reference symmetry (1)

For linear geometries the same results can be obtained more cheaply using $C_{2v}$ symmetry, 

WF,15,2,1;      !define wavefunction symmetry (2)
REF,1;          !define additional reference symmetry (1)
REF,3;          !define additional reference symmetry (3)

or 

WF,15,3,1;      !define wavefunction symmetry (2)
REF,1;          !define additional reference symmetry (1)
REF,2;          !define additional reference symmetry (2)

Each REF card may be followed by RESTRICT, SELECT, and CON cards, in the given order.

Selecting configurations

SELECT,ref1,ref2,refthr,refstat,mxshrf;

This card is used to specify a reference configuration set other than a CAS, which is the default. Configurations can be defined using CON cards, which must appear after the SELECT card. Alternatively, if ref1 is an existing Molpro record name, the configurations are read in from that record and may be selected according to a given threshold.

The select card must be placed directly after the WF or REF card(s), or, if present, the RESTRICT cards. The general order of these cards is

WF (or REF)
RESTRICT (optional)
SELECT (optional)
CON (optional)

Occupation restrictions

RESTRICT,nmin,nmax,orb$_1$,orb$_2$,$\ldots$orb$_n$;

This card can be used to restrict the occupation patterns in the reference configurations. Only configurations containing between nmin and nmax electrons in the specified orbitals orb$_1$, orb$_2$, $\ldots$, orb$_n$ are included in the reference function. If nmin and nmax are negative, configurations with exactly abs(nmin) and abs(nmax) electrons in the specified orbitals are deleted. This can be used, for instance, to omit singly excited configurations. The orbitals are specified in the form number.sym, where number is the number of the orbital in irrep sym. Several RESTRICT cards may follow each other.

The RESTRICT cards must follow the WF or REF cards to which they apply. The general order of these cards is

WF (or REF)
RESTRICT (optional)
SELECT (optional)
CON (optional)

If a RESTRICT cards precedes the WF card, it applies to all reference symmetries. Note that RESTRICT also affects the spaces generated by SELECT and/or CON cards.

Explicitly specifying reference configurations

CON,$n_1,n_2,n_3,n_4,\ldots$

Specifies an orbital configuration to be included in the reference function. $n_1$, $n_2$ etc. are the occupation numbers of the active orbitals (0,1,or 2). Any number of CON cards may follow each other, but they must all appear directly after a SELECT card.

Defining state numbers

STATE,nstate,nroot(1),nroot(2),…,nroot(nstate);

nstate is the number of states treated simultaneously; nroot(i) are the root numbers to be calculated. These apply to the order of the states in the initial internal CI. If not specified, nroot(i)=$i$. Note that it is possible to leave out states, i.e., 

STATE,1,2;    ! calculates second state
STATE,2,1,3;  ! calculates first and third state

All states specified must be reasonably described by the internal configuration space. It is possible to have different convergence thresholds for each state (see ACCU card). It is also possible not to converge some lower roots which are included in the list nroot(i) (see REFSTATE card). For examples, see REFSTATE card.

Defining reference state numbers

REFSTATE,nstatr,nrootr(1),nrootr(2),…,nrootr(nstatr);

nstatr is the number of reference states for generating contracted pairs. This may be larger or smaller than nstate. If this card is not present, nstatr=nstate and nrootr(i)=nroot(i). Roots for which no reference states are specified but which are specified on the STATE card (or included by default if the nroot(i) are not specified explicitly on the STATE card) will not be converged, since the result will be bad anyway. However, it is often useful to include these states in the list nroot(i), since it helps to avoid root flipping problems. Examples: 

state,2;

will calculate two states with two reference states. 

state,2;refstate,1,2;

will optimize second state with one reference state. One external expansion vector will be generated for the ground state in order to avoid root flipping. The results printed for state 1 are bad and should not be used (unless the pair space is complete, which might happen in very small calculations). 

state,1,2;refstate,1,2;

As the second example, but no external expansion vectors will be generated for the ground state. This should give exactly the same energy for state 2 as before if there is no root flipping (which, however, frequently occurs). 

state,2;accu,1,1,1;

Will calculate second state with two reference states. The ground state will not be converged (only one iteration is done for state 1) This should give exactly the same energy for state 2 as the first example.

Specifying correlation of orbital pairs

PAIR,iorb1.isy1,iorb2.isy2,np;

is a request to correlate a given orbital pair.

Default is to correlate all electron pairs in active and closed orbitals. See also PAIRS card.

PAIRS,iorb1.isy,iorb2.isy,np;

Correlate all pairs which can be formed from orbitals iorb1.isy1 through iorb2.isy2. Core orbitals are excluded. Either iorb2 must be larger than iorb1 or isy2 larger than isy1. If iorb1.isy1=iorb2.isy2 the PAIRS card has the same effect as a PAIR card. PAIR and PAIRS cards may be combined.

If no PAIR and no PAIRS card is specified, all valence orbitals are correlated. The created pair list restricts not only the doubly external configurations, but also the all internal and semi internals.

Restriction of classes of excitations

NOPAIR;

No doubly external configurations are included.

NOSINGLE;

No singly external configurations are included.

NOEXC;

Perform CI with the reference configurations only.

Coupled Electron Pair Approximation

CEPA(ncepa);

($0 \le ncepa \le 3$). Instead of diagonalizing the hamiltonian, perform CEPA calculation, CEPA type ncepa. This is currently available only for single configuration reference functions.

Coupled Pair Functional (ACPF, AQCC)

ACPF,options
AQCC,options

where options can be

Instead of diagonalizing the hamiltonian, perform ACPF calculation or AQCC calculation. Using the options GACPFI and GAPCPE The internal and external normalization factors gacpfi, gacpfe may be reset from their default values of 1, 2/nelec and 1, 1-(nelec-2)(nelec-3)/nelec(nelec-1), respectively.

The ACPF and related methods are currently not robustly working for excited states. Even though it sometimes works, we do not currently recommend and support these methods for excited state calculations.

Projected excited state calculations

PROJECT,record,nprojc;

Initiate or continue a projected excited state calculation, with information stored on record. If nprojc$>0$, the internal CI vectors of nprojc previous calculations are used to make a projection operator. If nprojc$=-1$, this calculation is forced to be the first, i.e. ground state, with no projection. If nprojc$=0$, then if record does not exist, the effect is the same as nprojc$=-1$; otherwise nprojc is recovered from the dump in record. Thus for the start up calculation, it is best to use project,record,-1; for the following excited calculations, use project,record; At the end of the calculation, the wavefunction is saved, and the information in the dump record updated. The project card also sets the tranh option, so by default, transition hamiltonian matrices are calculated.

For example, to do successive calculations for three states, use 

ci;...;project,3000.3,-1;
ci;...;project,3000.3;
ci;...;project,3000.3;

At the end of each calculation, Hamiltonian is diagonalized over the whole set of projected functions, and the diagonal and transition properties are transformed accordingly. The untransformed properties, if required, can be retrieved from the output.

Transition matrix element options

TRANH,option;

If option$>-1$, this forces calculation of transition hamiltonian matrix elements in a TRANS or PROJECT calculation. If option$<1$, this forces calculation of one electron transition properties.

Convergence thresholds

ACCU,istate,energy,coeff;

Convergence thresholds for state istate. The actual thresholds for the energy and the CI coefficients are 10**(-energy) and 10**-(coeff). If this card is not present, the thresholds for all states are the default values or those specified on the THRESH card.

Level shifts

SHIFT,shiftp,shifts,shifti;

Denominator shifts for pairs, singles, and internals, respectively.

Maximum number of iterations

MAXITER,maxit,maxiti;

Restricting numbers of expansion vectors

MAXDAV,maxdav,maxvi;

Selecting the primary configuration set

PSPACE,select,npspac;

Canonicalizing external orbitals

FOCK,$n_1,n_2,\ldots$;

External orbitals are obtained as eigenfunctions of a Fock operator with the specified occupation numbers $n_i$. Occupation numbers must be provided for all valence orbitals.

Saving the wavefunction

SAVE,savecp,saveco,idelcg;

or

SAVE [,CIVEC=savecp] [,CONFIG=saveco] [,DENSITY=dumprec] [,NATORB=dumprec] [,FILES] [,SPINDEN]

Starting wavefunction

START,readc1,irest;

One electron properties

EXPEC,oper$_1$,oper$_2$,oper$_3$,…;

After the wavefunction determination, calculate expectation values for one-electron operators oper$_i$. See section One-electron operators and expectation values (GEXPEC) for the available operators and their keywords. In multi-state calculations or in projected calculations, also the transition matrix elements are calculated.

Transition moment calculations

TRANS,readc1,readc2,[BIORTH],[oper$_1$,oper$_2$,oper$_3$,…];

Instead of performing an energy calculation, only calculate transition matrix elements between wavefunctions saved on records readc1 and readc2. See section One-electron operators and expectation values (GEXPEC) for a list of available operators and their corresponding keywords. If no operator names are specified, the dipole transition moments are calculated.

If option BIORTH is given, the two wavefunctions may use different orbitals. However, the number of active and inactive orbitals must be the same in each case. Note that BIORTH is not working for spin-orbit matrix elements. Under certain conditions it may happen that biorthogonalization is not possible, and then an error message will be printed. For transition properties which have nonzero nuclear contribution, the corresponding geometry is then that of the ket state (readc2). The same is valid when origin of operator is explicitly specified as a center number, i.e. its coordinates will be those for the ket state.

Saving the density matrix

DM,record.ifil,[idip];

The first order density matrices for all computed states are stored in record record on file ifil. If idip is not zero, the dipole moments are printed starting at iteration idip. See also NATORB. In case of transition moment calculation, the transition densities are also stored, provided both states involved have the same symmetry.

Natural orbitals

NATORB,[RECORD=]record.ifil,[PRINT=nprint],[CORE[=natcor]];

Calculate natural orbitals. The number of printed external orbitals in any given symmetry is nprint) (default 2). nprint=-1 suppressed the printing. If record is nonzero, the natural orbitals and density matrices for all states are saved in a dump record record on file ifil. If record.ifil is specified on a DM card (see above), this record is used. If different records are specified on the DM and NATORB cards, an error will result. The record can also be given on the SAVE card. If CORE is specified, core orbitals are not printed.

Note: The dump record must not be the same as savecp or saveco on the SAVE card, or the record given on the PROJECT.

Miscellaneous options

OPTION,code1=value,code2=value,$\ldots$

Can be used to specify program parameters and options. If no codes and values are specified, active values are displayed. The equal signs may be omitted. The following codes are allowed (max 7 per card):

Miscellaneous parameters

PARAM,code1=value,code2=value$\ldots$

Redefine system parameters. If no codes are specified, the default values are displayed. The following codes are allowed:

Miscellaneous thresholds

THRESH,code1=value,code2=value$\ldots$

If value=0, the corresponding threshold is set to zero, otherwise 10**(-value). The equal signs may be omitted. If no codes are specified, the default values are printed. The following codes are allowed (max 7 per card):

PRINT,code1=value,code2=value,$\ldots$

Print options. Generally, the value determines how much intermediate information is printed. value=-1 means no print (default for all codes). In some of the cases listed below the specification of higher values will generate even more output than described. The equal signs and zeros may be omitted. All codes may be truncated to three characters. The following codes are allowed (max 7 per card):

Examples

examples/h2o_cepa1.inp
***,Single reference CISD and CEPA-1 for water
r=0.957,angstrom
theta=104.6,degree;
geometry={O;              !z-matrix geometry input
          H1,O,r;
          H2,O,r,H1,theta}
{hf;wf,10,1;}                         !TOTAL SCF ENERGY     -76.02680642
{ci;occ,3,1,1;core,1;wf,10,1;}        !TOTAL CI(SD) ENERGY  -76.22994348
{cepa(1);occ,3,1,1;core,1;wf,10,1;}   !TOTAL CEPA(1) ENERGY -76.23799334
examples/h2op_mrci_trans.inp
***,Valence multireference CI for X and A states of H2O
gthresh,energy=1.d-8
r=0.957,angstrom,theta=104.6,degree;
geometry={O;              !z-matrix geometry input
          H1,O,r;
          H2,O,r,H1,theta}
{hf;wf,10,1;}         !TOTAL SCF ENERGY               -76.02680642
{multi;occ,4,1,2;closed,2;frozen,1;wf,9,2,1;wf,9,1,1;tran,ly}
                     !MCSCF ENERGY                   -75.66755631
                     !MCSCF ENERGY                   -75.56605896
{ci;occ,4,1,2;closed,2;core,1;wf,9,2,1;save,7300.1}
                     !TOTAL MRCI ENERGY              -75.79831209
{ci;occ,4,1,2;closed,2;core,1;wf,9,1,1;save,7100.1}
                     !TOTAL MRCI ENERGY              -75.71309879
{ci;trans,7300.1,7100.1,ly}
                     !Transition moment <1.3|X|1.1> = -0.14659810  a.u.
                     !Transition moment <1.3|LY|1.1> = 0.96200488i a.u.
examples/bh_mrci_sigma_delta.inp
***,BH singlet Sigma and Delta states
r=2.1
geometry={b;h,b,r}
{hf;occ,3;wf,6,1;}
{multi;
occ,3,1,1;frozen,1;wf,6,1;state,3;lquant,0,2,0;wf,6,4;lquant,2;
tran,lz;
expec2,lzlz;}
! Sigma states:- energies -25.20509620 -24.94085861
{ci;occ,3,1,1;core,1;wf,6,1;state,2,1,3;}
! Delta states:- energies -24.98625171
{ci;occ,3,1,1;core,1;wf,6,1;state,1,2;}
! Delta state:- xy component
{ci;occ,3,1,1;core,1;wf,6,4;}

Cluster corrections for multi-state MRCI

In the following, we assume that $$\begin{align} \Psi_{\rm ref}^{(n)} &=& \sum_R C_{Rn}^{(0)} \Phi_R \\ \Psi_{\rm mrci}^{(n)} &=& \sum_R C_{Rn} \Phi_R + \Psi_c\end{align}$$ are the normalized reference and MRCI wave functions for state $n$, respectively. $C_R^{(0)}$ are the coefficients of the reference configurations in the initial reference functions and $C_{Rn}$ are the relaxed coefficients of these configurations in the final MRCI wave function. $\Psi_c$ is the remainder of the MRCI wave function, which is orthogonal to all reference configurations $\Phi_R$.

The corresponding energies are defined as $$\begin{align} E_{\rm ref}^{(n)} &=& \langle \Psi_{\rm ref}^{(n)} | \hat H | \Psi_{\rm ref}^{(n)}\rangle,\\ E_{\rm mrci}^{(n)}&=& \langle \Psi_{\rm mrci}^{(n)} | \hat H | \Psi_{\rm mrci}^{(n)}\rangle.\end{align}$$ The standard Davidson corrected correlation energies are defined as \begin{align} E^{n}_{\rm D} &=& E_{\rm corr}^{(n)}\cdot \frac {1-c_n^2}{ c_n^2 } \label{eq:dav}\end{align} where $c_n$ is the coefficient of the (fixed) reference function in the MRCI wave function: \begin{align} c_n = \langle \Psi_{\rm ref}^{(n)}|\Psi_{\rm mrci}^{(n)} \rangle = \sum_R C_{Rn}^{(0)} C_{Rn}, \label{eq:cfix}\end{align} and the correlation energies are \begin{align} E_{\rm corr}^{(n)}=E_{\rm mrci}^{(n)}-E_{\rm ref}^{(n)} .\label{eq:ecorr}\end{align} In the vicinity of avoided crossings this correction may give unreasonable results since the reference function may get a small overlap with the MRCI wave function. One way to avoid this problem is to replace the reference wave function $\Psi_{\rm ref}^{(n)}$ by the the relaxed reference functions $$\begin{align} \Psi_{\rm rlx}^{(n)} &=& \frac{\sum_R C_{Rn} \Phi_R}{\sqrt{\sum_R C_{Rn}^2}},\end{align}$$ which simply leads to \begin{align} c_n^2 &=& \sum_R C_{Rn}^2. \label{eq:crlx} \end{align} Alternatively, one can linearly combine the fixed reference functions to maximize the overlap with the MRCI wave functions. This yields projected functions $$\begin{align} \Psi_{\rm prj}^{(n)} &=& \sum_m |\Psi_{\rm ref}^{(m)}\rangle\langle \Psi_{\rm ref}^{(m)} |\Psi_{\rm mrci}^{(n)} \rangle = \sum_m |\Psi_{\rm ref}^{(m)}\rangle d_{mn}\end{align}$$ with $$\begin{align} d_{mn} &=& \langle \Psi_{\rm ref}^{(m)}|\Psi_{\rm mrci}^{(n)} \rangle = \sum_R C_{Rm}^{(0)} C_{Rn}.\end{align}$$ These projected functions are not orthonormal. The overlap is $$\begin{align} \langle \Psi_{\rm prj}^{(m)} | \Psi_{\rm prj}^{(n)} \rangle &=& ({\bf d}^{\dagger} {\bf d})_{mn}.\end{align}$$ Symmetrical orthonormalization, which changes the functions as little as possible, yields $$\begin{align} \Psi_{\rm rot}^{(n)} &=& \sum_m |\Psi_{\rm ref}^{(m)}\rangle u_{mn}, \\ {\bf u} &=& {\bf d} ({\bf d}^{\dagger} {\bf d})^{-1/2}.\end{align}$$ The overlap of these functions with the MRCI wave functions is $$\begin{align} \langle \Psi_{\rm rot}^{(m)} | \Psi_{\rm mrci}^{(n)} \rangle &=& [({\bf d}^{\dagger} {\bf d}) ({\bf d}^{\dagger} {\bf d})^{-1/2}]_{mn} = [({\bf d}^{\dagger} {\bf d})^{1/2}]_{mn}.\end{align}$$ Thus, in this case we use for the Davidson correction \begin{align} c_n &=& [({\bf d}^{\dagger} {\bf d})^{1/2}]_{nn}. \label{eq:crot} \end{align} The final question is which reference energy to use to compute the correlation energy used in eq. \eqref{eq:dav}. In older MOLPRO version (to 2009.1) the reference wave function which has the largest overlap with the MRCI wave function was used to compute the reference energy for the corresponding state. But this can lead to steps of the Davidson corrected energies if the order of the states swaps along potential energy functions. In this version there are two options: the default is to use for state $n$ the reference energy $n$, cf. eq. \eqref{eq:ecorr} (assuming the states are ordered according to increasing energy). The second option is to recompute the correlation energies using the rotated reference functions \begin{align} E_{corr}^{(n)} &=& E_{\rm MRCI}^{(n)} - \langle \Psi_{\rm rot}^{(n)} | \hat H | \Psi_{\rm rot}^{(n)} \rangle \label{eq:erot}\end{align} Both should give smooth potentials (unless at conical intersections or crossings of states with different symmetries), but there is no guarantee that the Davidson corrected energies of different states don’t cross. This problem is unavoidable for non-variational energies. The relaxed and rotated Davidson corrections give rather similar results; the rotated one yields somewhat larger cluster corrections and was found to give better results in the case of the F + H$_2$ potential [see J. Chem. Phys. 128, 034305 (2008)].

By default, the different cluster corrections listed in the following table are computed in multi-state MRCI calculations. and stored in variables.

Cluster corrections computed in multi-state MRCI calculations
Name $c_n$ (Eq.) $E_{corr}^{(n)}$ (Eq.) Variable
Using standard reference energies:
Fixed \eqref{eq:cfix} \eqref{eq:ecorr} ENERGD1(n)
Relaxed \eqref{eq:crlx} \eqref{eq:ecorr} ENERGD0(n)
Rotated \eqref{eq:crot} \eqref{eq:ecorr} ENERGD2(n)
Using rotated reference energies:
Relaxed \eqref{eq:crlx} \eqref{eq:erot} ENERGD3(n)
Rotated \eqref{eq:crot} \eqref{eq:erot} ENERGD4(n)

By default, the energies are in increasing order of the MRCI total energy. In single-state calculations only the fixed and relaxed values are available.

By default, ENERGD(n)=ENERGD0(n). This can be changed by setting OPTION,CLUSTER=x; then ENERGD(n)=ENERGDx(n) (default $x=0$). The behaviour of Molpro 2009.1 and older can be retrieved using

MRCI,SWAP,ROTREF=-1.

Explicitly correlated MRCI-F12

The only change needed for including explicitly correlated terms is to append -F12 to the MRCI command. All other options work as described before. It is recommended to use correlation consistent basis sets (aug-cc-pVnZ or VnZ-F12) since for these the appropriate fitting and RI auxiliary basis sets are chosen automatically. Otherwise it max be necessary to specify these basis sets as described for single-reference methods in section explicitly correlated methods.

The following options (to be given on the MRCI-F12 command line) are specific to MRCI-F12:

For a description of the various singles corrections see Mol. Phys. 111, 607 (2013). [sec:rs23]