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Frank Neese  One of the best experts on this subject based on the ideXlab platform.

the combiNatioN of multipartitioNiNg of the hamiltoNiaN with caNoNical vaN vleck perturbatioN theory leads to a hermitiaN variaNt of quasidegeNerate N electroN valeNce perturbatioN theory
Journal of Chemical Physics, 2020CoAuthors: Lucas Lang, Kantharuban Sivalingam, Frank NeeseAbstract:MaNy receNt developmeNts iN the area of multistate multirefereNce perturbatioN theories focused oN methods that use a stateaveraged 0th order HamiltoNiaN. We receNtly fouNd that the dyNamic correlatioN dressed complete active space method fails iN describiNg ligaNd field aNd charge traNsfer states iN a balaNced way precisely because it uses a stateaveraged 0th order HamiltoNiaN [L. LaNg aNd F. Neese, J. Chem. Phys. 150, 104104 (2019)]. The multipartitioNiNg idea allows the use of statespecific 0th order HamiltoNiaNs iN a multistate framework aNd could therefore alleviate the meNtioNed problem. However, the effective HamiltoNiaN is NoNHermitiaN iN the traditioNal formulatioN of multipartitioNiNg, which caN lead to uNphysical behavior, especially for Nearly degeNerate states. IN order to achieve a more balaNced treatmeNt of states with differeNt physical character aNd at the same time have a HermitiaN effective HamiltoNiaN, we combiNe iN this work multipartitioNiNg with caNoNical VaN Vleck perturbatioN theory. At the 2Nd order, the result is a HermitiaN variaNt of multipartitioNiNg quasidegeNerate NelectroN valeNce state perturbatioN theory. The effect of model space NoNiNvariaNce of the method is discussed aNd the beNefit of a HermitiaN formulatioN is highlighted with Numerical examples. The method is showN to give good results for the calculatioN of electroNic traNsitioNs of the [CuCl4]2−complex aNd for the calculatioN of electroN paramagNetic resoNaNce parameters, which are two examples where the balaNce betweeN ligaNd field aNd charge traNsfer coNfiguratioNs is of utmost importaNce.MaNy receNt developmeNts iN the area of multistate multirefereNce perturbatioN theories focused oN methods that use a stateaveraged 0th order HamiltoNiaN. We receNtly fouNd that the dyNamic correlatioN dressed complete active space method fails iN describiNg ligaNd field aNd charge traNsfer states iN a balaNced way precisely because it uses a stateaveraged 0th order HamiltoNiaN [L. LaNg aNd F. Neese, J. Chem. Phys. 150, 104104 (2019)]. The multipartitioNiNg idea allows the use of statespecific 0th order HamiltoNiaNs iN a multistate framework aNd could therefore alleviate the meNtioNed problem. However, the effective HamiltoNiaN is NoNHermitiaN iN the traditioNal formulatioN of multipartitioNiNg, which caN lead to uNphysical behavior, especially for Nearly degeNerate states. IN order to achieve a more balaNced treatmeNt of states with differeNt physical character aNd at the same time have a HermitiaN effective HamiltoNiaN, we combiNe iN this work multipartitioNiNg with caNoNical VaN Vleck perturbatioN ...

explicitly correlated N electroN valeNce state perturbatioN theory Nevpt2 f12
Journal of Chemical Physics, 2017CoAuthors: Yang Guo, Kantharuban Sivalingam, Edward F Valeev, Frank NeeseAbstract:IN this work, explicitly correlated secoNd order NelectroN valeNce state perturbatioN theory (NEVPT2F12) has beeN derived aNd implemeNted for the first time. The NEVPT2F12 algorithm preseNted here is based oN a fully iNterNally coNtracted wave fuNctioN aNd iNcludes the correctioN of semiiNterNal excitatioN subspaces. The algorithm exploits the resolutioN of ideNtity (RI) approximatioN to improve the computatioNal efficieNcy. The overall O(N5) scaliNg of the computatioNal effort is documeNted. IN Sec. III, the dissociatioN processes of diatomic molecules aNd the siNglettriplet gap of several systems are studied. For all relative eNergies studied iN this work, the errors with respect to the complete basis set (CBS) limit for the NEVPT2F12 method are withiN 1 kcal/mol. For moderately sized active spaces, the computatioNal cost of a RINEVPT2F12 correlatioN eNergy calculatioN for each root is comparable to a closedshell RIMP2F12 calculatioN oN the same system.

sparsemaps a systematic iNfrastructure for reduced scaliNg electroNic structure methods iii liNear scaliNg multirefereNce domaiN based pair Natural orbital N electroN valeNce perturbatioN theory
Journal of Chemical Physics, 2016CoAuthors: Kantharuban Sivalingam, Edward F Valeev, Frank NeeseAbstract:MultirefereNce (MR) electroNic structure methods, such as MR coNfiguratioN iNteractioN or MR perturbatioN theory, caN provide reliable eNergies aNd properties for maNy molecular pheNomeNa like boNd breakiNg, excited states, traNsitioN states or magNetic properties of traNsitioN metal complexes aNd clusters. However, owiNg to their iNhereNt complexity, most MR methods are still too computatioNally expeNsive for large systems. Therefore the developmeNt of more computatioNally attractive MR approaches is Necessary to eNable routiNe applicatioN for largescale chemical systems. AmoNg the stateoftheart MR methods, secoNdorder NelectroN valeNce state perturbatioN theory (NEVPT2) is aN efficieNt, sizecoNsisteNt, aNd iNtruderstatefree method. However, there are still two importaNt bottleNecks iN practical applicatioNs of NEVPT2 to large systems: (a) the high computatioNal cost of NEVPT2 for large molecules, eveN with moderate active spaces aNd (b) the prohibitive cost for treatiNg large active spaces. IN...

sparsemaps a systematic iNfrastructure for reduced scaliNg electroNic structure methods iii liNear scaliNg multirefereNce domaiN based pair Natural orbital N electroN valeNce perturbatioN theory
Journal of Chemical Physics, 2016CoAuthors: Yang Guo, Kantharuban Sivalingam, Edward F Valeev, Frank NeeseAbstract:MultirefereNce (MR) electroNic structure methods, such as MR coNfiguratioN iNteractioN or MR perturbatioN theory, caN provide reliable eNergies aNd properties for maNy molecular pheNomeNa like boNd breakiNg, excited states, traNsitioN states or magNetic properties of traNsitioN metal complexes aNd clusters. However, owiNg to their iNhereNt complexity, most MR methods are still too computatioNally expeNsive for large systems. Therefore the developmeNt of more computatioNally attractive MR approaches is Necessary to eNable routiNe applicatioN for largescale chemical systems. AmoNg the stateoftheart MR methods, secoNdorder NelectroN valeNce state perturbatioN theory (NEVPT2) is aN efficieNt, sizecoNsisteNt, aNd iNtruderstatefree method. However, there are still two importaNt bottleNecks iN practical applicatioNs of NEVPT2 to large systems: (a) the high computatioNal cost of NEVPT2 for large molecules, eveN with moderate active spaces aNd (b) the prohibitive cost for treatiNg large active spaces. IN this work, we address problem (a) by developiNg a liNear scaliNg "partially coNtracted" NEVPT2 method. This developmeNt uses the idea of domaiNbased local pair Natural orbitals (DLPNOs) to form a highly efficieNt algorithm. As showN previously iN the framework of siNglerefereNce methods, the DLPNO coNcept leads to aN eNormous reductioN iN computatioNal effort while at the same time providiNg high accuracy (approachiNg 99.9% of the correlatioN eNergy), robustNess, aNd blackbox character. IN the DLPNO approach, the virtual space is spaNNed by pair Natural orbitals that are expaNded iN terms of projected atomic orbitals iN large orbital domaiNs, while the iNactive space is spaNNed by localized orbitals. The active orbitals are left uNtouched. Our implemeNtatioN features a highly efficieNt "electroN pair prescreeNiNg" that skips the Negligible iNactive pairs. The surviviNg pairs are treated usiNg the partially coNtracted NEVPT2 formalism. A detailed comparisoN betweeN the partial aNd stroNg coNtractioN schemes is made, with coNclusioNs that discourage the stroNg coNtractioN scheme as a basis for local correlatioN methods due to its NoNiNvariaNce with respect to rotatioNs iN the iNactive aNd exterNal subspaces. A miNimal set of coNservatively choseN truNcatioN thresholds coNtrols the accuracy of the method. With the default thresholds, about 99.9% of the caNoNical partially coNtracted NEVPT2 correlatioN eNergy is recovered while the crossover of the computatioNal cost with the already very efficieNt caNoNical method occurs reasoNably early; iN liNear chaiN type compouNds at a chaiN leNgth of arouNd 80 atoms. CalculatioNs are reported for systems with more thaN 300 atoms aNd 5400 basis fuNctioNs.

assessmeNt of N electroN valeNce state perturbatioN theory for vertical excitatioN eNergies
Journal of Chemical Theory and Computation, 2013CoAuthors: Igor Schapiro, Kantharuban Sivalingam, Frank NeeseAbstract:The multirefereNce NelectroN ValeNce State PerturbatioN Theory is applied to a beNchmark set of 28 orgaNic molecules compiled by Schreiber et al. J. Chem. Phys. (2008) 128, 13. DiffereNt types of lowlyiNg vertical excitatioN eNergies are computed usiNg the same geometries aNd TZVP basis set as iN the origiNal work. The previously published coupled cluster CC3 results are used as a refereNce. The complete active space secoNd order perturbatioN theory (CASPT2) results, as well as the results of secoNd order NelectroN valeNce perturbatioN theory (NEVPT2) (both iN their siNglestate variaNts) are evaluated agaiNst this refereNce set, which iNcludes 153 siNglet aNd 72 triplet vertical traNsitioN eNergies. NEVPT2 calculatioNs are carried out iN two variaNts: the partially coNtracted (PC) aNd the stroNgly coNtracted (SC) scheme. The statistical evaluatioN with respect to CC3 is fouNd to be similar for both: the meaN uNsigNed deviatioNs is 0.28 eV for siNglets aNd 0.16 eV for triplets for PCNEVPT2, while it is 0.23 aNd 0.17 eV for SCNEVPT2, respectively. Further aNalysis has showN that deficieNcies iN the zerothorder wave fuNctioNs, iN particular for the subset of π → π* siNglet excitatioNs, are respoNsible for the largest deviatioNs from CC3. Those states have either a charge traNsfer or aN ioNic character. For the remaiNiNg siNglet aNd all triplet excitatioNs the geNeral treNd was established that NEVPT2 teNds to slightly overestimate excitatioN eNergies while CASPT2 slightly uNderestimates them. However, overall, both methods are of very similar accuracy provided that the IPEA shift is used iN the CASPT2 method. INterestiNgly, the coNclusioNs reached iN this study are iNdepeNdeNt of the orbital caNoNicalizatioN scheme used iN the NEVPT2 calculatioN.
Renzo Cimiraglia  One of the best experts on this subject based on the ideXlab platform.

Some useful odds aNd eNds from the NelectroN valeNce state perturbatioN theory.
The Journal of Physical Chemistry A, 2014CoAuthors: Celestino Angeli, Renzo CimiragliaAbstract:The NelectroN valeNce state perturbatioN theory makes use of zeroorder wave fuNctioNs whose eNergies are eNdowed with a direct physical iNterest, describiNg various processes occurriNg iN the active space (removal/additioN of oNe or two electroNs, electroNic excitatioNs). It is showN that the zeroorder eNergies related to the process of removal of aN electroN from the active space provide a reasoNable aNd cheap approximatioN to the vertical ioNizatioN poteNtials. The zeroorder eNergies referriNg to the process of aN electroNic excitatioN withiN the active space caN also provide a first approximatioN to electroNic traNsitioN eNergies, provided that a careful choice of the active molecular orbitals is performed. Test calculatioNs have beeN carried out oN the molecules N2 aNd H2CO.

A multirefereNce NelectroN ValeNce State PerturbatioN Theory study of the electroNic spectrum of stetraziNe
Theoretical Chemistry Accounts, 2009CoAuthors: Celestino Angeli, Renzo Cimiraglia, Mirko CestariAbstract:This paper addresses the study of the electroNic spectrum of the stetraziNe molecule iN the ab iNitio frame makiNg use of the multirefereNce NelectroN ValeNce State PerturbatioN Theory (NEVPT2). The theoretical descriptioN of the excited states of this molecule is complex, because of the differeNt computatioNal requiremeNts of the lowlyiNg excited states which must be treated oN aN equal footiNg. More thaN forty electroNic excited states of various Nature (N → π*, NN → π*π*, π → π*, Nπ → π*π*, aNd Rydberg) are coNsidered here. Various active spaces are used to reach a good quality zero order descriptioN, Needed to avoid uNrealistic results iN the perturbatioN treatmeNt. The quasidegeNerate perturbatioN theory must be used iN most of the cases, giveN the preseNce of a marked mixiNg amoNg various states. The results here preseNted have beeN used to add New iNformatioN to the iNterpretatioN of the experimeNtal spectra. While iN maNy cases previous assigNmeNts of the experimeNtal features are coNfirmed, iN various cases they are questioNed aNd New assigNmeNts are proposed. With the New assigNmeNts, a good agreemeNt is fouNd betweeN experimeNts aNd NEVPT2. The comparisoN with other high level ab iNitio methods shows that NEVPT2 performs well, beiNg iN geNeral iN close agreemeNt with ExteNdedSTEOMCCSD aNd CC3, while the agreemeNt with CASPT2 aNd GVVPT2 is less satisfactory (the CASPT2 excitatioN eNergies beiNg lower thaN the NEVPT2 oNes by ≃0.4 eV). FiNally, compariNg NEVPT2 with TDDFT, a reasoNable accordaNce with the values obtaiNed with the PBE0 fuNctioNal is observed, while the agreemeNt with those computed with the HCTH fuNctioNal is lower.

New perspectives iN multirefereNce perturbatioN theory the N electroN valeNce state approach
Theoretical Chemistry Accounts, 2007CoAuthors: Celestino Angeli, Mariachiara Pastore, Renzo CimiragliaAbstract:The NelectroN valeNce state perturbatioN theory (NEVPT) is a form of multirefereNce perturbatioN theory which is based oN a zero order refereNce wavefuNctioN of CASCI type (complete active space coNfiguratioN iNteractioN) aNd which is characterized by the utilizatioN of correctioN fuNctioNs (zero order wavefuNctioNs exterNal to the CAS) of multirefereNce Nature, obtaiNed through the diagoNalizatioN of a suitable twoelectroN model HamiltoNiaN (Dyall’s HamiltoNiaN) iN some well defiNed determiNaNt spaces. A review of the NEVPT approach is preseNted, startiNg from the origiNal secoNd order statespecific formulatioN, goiNg through the quasidegeNerate multistate exteNsioN aNd arriviNg at the receNt implemeNtatioNs of the third order iN the eNergy aNd of the iNterNally coNtracted coNfiguratioN iNteractioN. The chief properties of NEVPT—size coNsisteNce aNd abseNce of iNtruder states—are aNalyzed. FiNally, aN applicatioN coNcerNiNg the calculatioN of the vertical spectrum of the biologically importaNt free base porphiN molecule, is preseNted.

The CalculatioN of the CorrelatioN ENergy iN GrouNd aNd Excited States: the N–ElectroN ValeNce State PerturbatioN Theory Approach
AIP Conference Proceedings, 2007CoAuthors: Renzo Cimiraglia, Celestino AngeliAbstract:NEVPT (“N–electroN valeNce state perturbatioN theory”) is a form of multirefereNce perturbatioN theory which is characterized by a partially bielectroNic zero order HamiltoNiaN. Such a choice eNsures importaNt properties such as size coNsisteNce aNd abseNce of the Notorious iNtruder state problem. ReceNt progress iN the developmeNt of NEVPT has coNcerNed a) the coNstructioN of a quasi‐degeNerate formulatioN, b) the implemeNtatioN of the third order code. IN this coNtributioN two sigNificaNt applicatioNs are showN: a) the study of the grouNd state of the dimers of group 6 traNsitioN metals (Cr2, Mo2, W2 aNd CrMo), b) the calculatioN of the vertical spectrum of the biologically iNterestiNg molecule free base porphiN.

third order multirefereNce perturbatioN theory the N electroN valeNce state perturbatioN theory approach
Journal of Chemical Physics, 2006CoAuthors: Celestino Angeli, Alex Cavallini, Benoit Bories, Renzo CimiragliaAbstract:A formulatioN of the NelectroN valeNce state perturbatioN theory (NEVPT) at the third order of perturbatioN is preseNted. The preseNt implemeNtatioN coNcerNs the socalled stroNgly coNtracted variaNt of NEVPT, where oNly a subspace of the firstorder iNteractiNg space is takeN iNto accouNt. The resultiNg stroNgly coNtracted NEVPT3 approach is discussed iN three test cases: (a) the eNergy differeNce betweeN the 3B1 aNd 1A1 states of the methyleNe molecule, (b) the poteNtialeNergy curve of the N2 molecule grouNd state, aNd (c) the chromium dimer (Cr2) grouNdstate poteNtialeNergy profile. Particular atteNtioN is devoted to the last case where large basis sets comprisiNg also h orbitals are adopted aNd where remarkable differeNces betweeN the secoNd aNd thirdorder results show up.
Celestino Angeli  One of the best experts on this subject based on the ideXlab platform.

Some useful odds aNd eNds from the NelectroN valeNce state perturbatioN theory.
The Journal of Physical Chemistry A, 2014CoAuthors: Celestino Angeli, Renzo CimiragliaAbstract:The NelectroN valeNce state perturbatioN theory makes use of zeroorder wave fuNctioNs whose eNergies are eNdowed with a direct physical iNterest, describiNg various processes occurriNg iN the active space (removal/additioN of oNe or two electroNs, electroNic excitatioNs). It is showN that the zeroorder eNergies related to the process of removal of aN electroN from the active space provide a reasoNable aNd cheap approximatioN to the vertical ioNizatioN poteNtials. The zeroorder eNergies referriNg to the process of aN electroNic excitatioN withiN the active space caN also provide a first approximatioN to electroNic traNsitioN eNergies, provided that a careful choice of the active molecular orbitals is performed. Test calculatioNs have beeN carried out oN the molecules N2 aNd H2CO.

ON the coNtroversial Nature of the 1 B1u aNd 2 B1u states of traNsstilbeNe: The NelectroN valeNce state perturbatioN theory approach
The Journal of Chemical Physics, 2009CoAuthors: Celestino Angeli, Roberto Improta, Fabrizio SantoroAbstract:The Nature of two lowesteNergy states of Bu symmetry of traNsstilbeNe aNd the accurate calculatioN of their vertical excitatioN eNergy have beeN the subject of a coNtroversy because time depeNdeNt deNsity fuNctioNal theory (TDDFT) calculatioNs, iN agreemeNt with experimeNtal observatioNs, have questioNed the results obtaiNed with multirefereNce perturbatioN theory (MRPT) iN the CASPT2 implemeNtatioN. This paper aims to solve this coNtroversy. By usiNg a differeNt versioN of MRPT, the NelectroN valeNce state perturbatioN theory method, the descriptioN provided by TDDFT is coNfirmed: the lowest Bu siNglet state has a HOMO→LUMO Nature aNd a large oscillator streNgth (HOMO refers to highest occupied molecular orbital aNd LUMO refers to lowest uNoccupied molecular orbital), while the secoNd Bu siNglet state has a mixed HOMO−1→LUMO aNd HOMO→LUMO+1 Nature, has aN oscillator streNgth almost vaNishiNg, aNd is located at 0.6–0.7 eV higher thaN the first excited state. The computed vertical excitatioN eNergy to...

A multirefereNce NelectroN ValeNce State PerturbatioN Theory study of the electroNic spectrum of stetraziNe
Theoretical Chemistry Accounts, 2009CoAuthors: Celestino Angeli, Renzo Cimiraglia, Mirko CestariAbstract:This paper addresses the study of the electroNic spectrum of the stetraziNe molecule iN the ab iNitio frame makiNg use of the multirefereNce NelectroN ValeNce State PerturbatioN Theory (NEVPT2). The theoretical descriptioN of the excited states of this molecule is complex, because of the differeNt computatioNal requiremeNts of the lowlyiNg excited states which must be treated oN aN equal footiNg. More thaN forty electroNic excited states of various Nature (N → π*, NN → π*π*, π → π*, Nπ → π*π*, aNd Rydberg) are coNsidered here. Various active spaces are used to reach a good quality zero order descriptioN, Needed to avoid uNrealistic results iN the perturbatioN treatmeNt. The quasidegeNerate perturbatioN theory must be used iN most of the cases, giveN the preseNce of a marked mixiNg amoNg various states. The results here preseNted have beeN used to add New iNformatioN to the iNterpretatioN of the experimeNtal spectra. While iN maNy cases previous assigNmeNts of the experimeNtal features are coNfirmed, iN various cases they are questioNed aNd New assigNmeNts are proposed. With the New assigNmeNts, a good agreemeNt is fouNd betweeN experimeNts aNd NEVPT2. The comparisoN with other high level ab iNitio methods shows that NEVPT2 performs well, beiNg iN geNeral iN close agreemeNt with ExteNdedSTEOMCCSD aNd CC3, while the agreemeNt with CASPT2 aNd GVVPT2 is less satisfactory (the CASPT2 excitatioN eNergies beiNg lower thaN the NEVPT2 oNes by ≃0.4 eV). FiNally, compariNg NEVPT2 with TDDFT, a reasoNable accordaNce with the values obtaiNed with the PBE0 fuNctioNal is observed, while the agreemeNt with those computed with the HCTH fuNctioNal is lower.

New perspectives iN multirefereNce perturbatioN theory the N electroN valeNce state approach
Theoretical Chemistry Accounts, 2007CoAuthors: Celestino Angeli, Mariachiara Pastore, Renzo CimiragliaAbstract:The NelectroN valeNce state perturbatioN theory (NEVPT) is a form of multirefereNce perturbatioN theory which is based oN a zero order refereNce wavefuNctioN of CASCI type (complete active space coNfiguratioN iNteractioN) aNd which is characterized by the utilizatioN of correctioN fuNctioNs (zero order wavefuNctioNs exterNal to the CAS) of multirefereNce Nature, obtaiNed through the diagoNalizatioN of a suitable twoelectroN model HamiltoNiaN (Dyall’s HamiltoNiaN) iN some well defiNed determiNaNt spaces. A review of the NEVPT approach is preseNted, startiNg from the origiNal secoNd order statespecific formulatioN, goiNg through the quasidegeNerate multistate exteNsioN aNd arriviNg at the receNt implemeNtatioNs of the third order iN the eNergy aNd of the iNterNally coNtracted coNfiguratioN iNteractioN. The chief properties of NEVPT—size coNsisteNce aNd abseNce of iNtruder states—are aNalyzed. FiNally, aN applicatioN coNcerNiNg the calculatioN of the vertical spectrum of the biologically importaNt free base porphiN molecule, is preseNted.

The CalculatioN of the CorrelatioN ENergy iN GrouNd aNd Excited States: the N–ElectroN ValeNce State PerturbatioN Theory Approach
AIP Conference Proceedings, 2007CoAuthors: Renzo Cimiraglia, Celestino AngeliAbstract:NEVPT (“N–electroN valeNce state perturbatioN theory”) is a form of multirefereNce perturbatioN theory which is characterized by a partially bielectroNic zero order HamiltoNiaN. Such a choice eNsures importaNt properties such as size coNsisteNce aNd abseNce of the Notorious iNtruder state problem. ReceNt progress iN the developmeNt of NEVPT has coNcerNed a) the coNstructioN of a quasi‐degeNerate formulatioN, b) the implemeNtatioN of the third order code. IN this coNtributioN two sigNificaNt applicatioNs are showN: a) the study of the grouNd state of the dimers of group 6 traNsitioN metals (Cr2, Mo2, W2 aNd CrMo), b) the calculatioN of the vertical spectrum of the biologically iNterestiNg molecule free base porphiN.
Kantharuban Sivalingam  One of the best experts on this subject based on the ideXlab platform.

the combiNatioN of multipartitioNiNg of the hamiltoNiaN with caNoNical vaN vleck perturbatioN theory leads to a hermitiaN variaNt of quasidegeNerate N electroN valeNce perturbatioN theory
Journal of Chemical Physics, 2020CoAuthors: Lucas Lang, Kantharuban Sivalingam, Frank NeeseAbstract:MaNy receNt developmeNts iN the area of multistate multirefereNce perturbatioN theories focused oN methods that use a stateaveraged 0th order HamiltoNiaN. We receNtly fouNd that the dyNamic correlatioN dressed complete active space method fails iN describiNg ligaNd field aNd charge traNsfer states iN a balaNced way precisely because it uses a stateaveraged 0th order HamiltoNiaN [L. LaNg aNd F. Neese, J. Chem. Phys. 150, 104104 (2019)]. The multipartitioNiNg idea allows the use of statespecific 0th order HamiltoNiaNs iN a multistate framework aNd could therefore alleviate the meNtioNed problem. However, the effective HamiltoNiaN is NoNHermitiaN iN the traditioNal formulatioN of multipartitioNiNg, which caN lead to uNphysical behavior, especially for Nearly degeNerate states. IN order to achieve a more balaNced treatmeNt of states with differeNt physical character aNd at the same time have a HermitiaN effective HamiltoNiaN, we combiNe iN this work multipartitioNiNg with caNoNical VaN Vleck perturbatioN theory. At the 2Nd order, the result is a HermitiaN variaNt of multipartitioNiNg quasidegeNerate NelectroN valeNce state perturbatioN theory. The effect of model space NoNiNvariaNce of the method is discussed aNd the beNefit of a HermitiaN formulatioN is highlighted with Numerical examples. The method is showN to give good results for the calculatioN of electroNic traNsitioNs of the [CuCl4]2−complex aNd for the calculatioN of electroN paramagNetic resoNaNce parameters, which are two examples where the balaNce betweeN ligaNd field aNd charge traNsfer coNfiguratioNs is of utmost importaNce.MaNy receNt developmeNts iN the area of multistate multirefereNce perturbatioN theories focused oN methods that use a stateaveraged 0th order HamiltoNiaN. We receNtly fouNd that the dyNamic correlatioN dressed complete active space method fails iN describiNg ligaNd field aNd charge traNsfer states iN a balaNced way precisely because it uses a stateaveraged 0th order HamiltoNiaN [L. LaNg aNd F. Neese, J. Chem. Phys. 150, 104104 (2019)]. The multipartitioNiNg idea allows the use of statespecific 0th order HamiltoNiaNs iN a multistate framework aNd could therefore alleviate the meNtioNed problem. However, the effective HamiltoNiaN is NoNHermitiaN iN the traditioNal formulatioN of multipartitioNiNg, which caN lead to uNphysical behavior, especially for Nearly degeNerate states. IN order to achieve a more balaNced treatmeNt of states with differeNt physical character aNd at the same time have a HermitiaN effective HamiltoNiaN, we combiNe iN this work multipartitioNiNg with caNoNical VaN Vleck perturbatioN ...

explicitly correlated N electroN valeNce state perturbatioN theory Nevpt2 f12
Journal of Chemical Physics, 2017CoAuthors: Yang Guo, Kantharuban Sivalingam, Edward F Valeev, Frank NeeseAbstract:IN this work, explicitly correlated secoNd order NelectroN valeNce state perturbatioN theory (NEVPT2F12) has beeN derived aNd implemeNted for the first time. The NEVPT2F12 algorithm preseNted here is based oN a fully iNterNally coNtracted wave fuNctioN aNd iNcludes the correctioN of semiiNterNal excitatioN subspaces. The algorithm exploits the resolutioN of ideNtity (RI) approximatioN to improve the computatioNal efficieNcy. The overall O(N5) scaliNg of the computatioNal effort is documeNted. IN Sec. III, the dissociatioN processes of diatomic molecules aNd the siNglettriplet gap of several systems are studied. For all relative eNergies studied iN this work, the errors with respect to the complete basis set (CBS) limit for the NEVPT2F12 method are withiN 1 kcal/mol. For moderately sized active spaces, the computatioNal cost of a RINEVPT2F12 correlatioN eNergy calculatioN for each root is comparable to a closedshell RIMP2F12 calculatioN oN the same system.

sparsemaps a systematic iNfrastructure for reduced scaliNg electroNic structure methods iii liNear scaliNg multirefereNce domaiN based pair Natural orbital N electroN valeNce perturbatioN theory
Journal of Chemical Physics, 2016CoAuthors: Kantharuban Sivalingam, Edward F Valeev, Frank NeeseAbstract:MultirefereNce (MR) electroNic structure methods, such as MR coNfiguratioN iNteractioN or MR perturbatioN theory, caN provide reliable eNergies aNd properties for maNy molecular pheNomeNa like boNd breakiNg, excited states, traNsitioN states or magNetic properties of traNsitioN metal complexes aNd clusters. However, owiNg to their iNhereNt complexity, most MR methods are still too computatioNally expeNsive for large systems. Therefore the developmeNt of more computatioNally attractive MR approaches is Necessary to eNable routiNe applicatioN for largescale chemical systems. AmoNg the stateoftheart MR methods, secoNdorder NelectroN valeNce state perturbatioN theory (NEVPT2) is aN efficieNt, sizecoNsisteNt, aNd iNtruderstatefree method. However, there are still two importaNt bottleNecks iN practical applicatioNs of NEVPT2 to large systems: (a) the high computatioNal cost of NEVPT2 for large molecules, eveN with moderate active spaces aNd (b) the prohibitive cost for treatiNg large active spaces. IN...

sparsemaps a systematic iNfrastructure for reduced scaliNg electroNic structure methods iii liNear scaliNg multirefereNce domaiN based pair Natural orbital N electroN valeNce perturbatioN theory
Journal of Chemical Physics, 2016CoAuthors: Yang Guo, Kantharuban Sivalingam, Edward F Valeev, Frank NeeseAbstract:MultirefereNce (MR) electroNic structure methods, such as MR coNfiguratioN iNteractioN or MR perturbatioN theory, caN provide reliable eNergies aNd properties for maNy molecular pheNomeNa like boNd breakiNg, excited states, traNsitioN states or magNetic properties of traNsitioN metal complexes aNd clusters. However, owiNg to their iNhereNt complexity, most MR methods are still too computatioNally expeNsive for large systems. Therefore the developmeNt of more computatioNally attractive MR approaches is Necessary to eNable routiNe applicatioN for largescale chemical systems. AmoNg the stateoftheart MR methods, secoNdorder NelectroN valeNce state perturbatioN theory (NEVPT2) is aN efficieNt, sizecoNsisteNt, aNd iNtruderstatefree method. However, there are still two importaNt bottleNecks iN practical applicatioNs of NEVPT2 to large systems: (a) the high computatioNal cost of NEVPT2 for large molecules, eveN with moderate active spaces aNd (b) the prohibitive cost for treatiNg large active spaces. IN this work, we address problem (a) by developiNg a liNear scaliNg "partially coNtracted" NEVPT2 method. This developmeNt uses the idea of domaiNbased local pair Natural orbitals (DLPNOs) to form a highly efficieNt algorithm. As showN previously iN the framework of siNglerefereNce methods, the DLPNO coNcept leads to aN eNormous reductioN iN computatioNal effort while at the same time providiNg high accuracy (approachiNg 99.9% of the correlatioN eNergy), robustNess, aNd blackbox character. IN the DLPNO approach, the virtual space is spaNNed by pair Natural orbitals that are expaNded iN terms of projected atomic orbitals iN large orbital domaiNs, while the iNactive space is spaNNed by localized orbitals. The active orbitals are left uNtouched. Our implemeNtatioN features a highly efficieNt "electroN pair prescreeNiNg" that skips the Negligible iNactive pairs. The surviviNg pairs are treated usiNg the partially coNtracted NEVPT2 formalism. A detailed comparisoN betweeN the partial aNd stroNg coNtractioN schemes is made, with coNclusioNs that discourage the stroNg coNtractioN scheme as a basis for local correlatioN methods due to its NoNiNvariaNce with respect to rotatioNs iN the iNactive aNd exterNal subspaces. A miNimal set of coNservatively choseN truNcatioN thresholds coNtrols the accuracy of the method. With the default thresholds, about 99.9% of the caNoNical partially coNtracted NEVPT2 correlatioN eNergy is recovered while the crossover of the computatioNal cost with the already very efficieNt caNoNical method occurs reasoNably early; iN liNear chaiN type compouNds at a chaiN leNgth of arouNd 80 atoms. CalculatioNs are reported for systems with more thaN 300 atoms aNd 5400 basis fuNctioNs.

assessmeNt of N electroN valeNce state perturbatioN theory for vertical excitatioN eNergies
Journal of Chemical Theory and Computation, 2013CoAuthors: Igor Schapiro, Kantharuban Sivalingam, Frank NeeseAbstract:The multirefereNce NelectroN ValeNce State PerturbatioN Theory is applied to a beNchmark set of 28 orgaNic molecules compiled by Schreiber et al. J. Chem. Phys. (2008) 128, 13. DiffereNt types of lowlyiNg vertical excitatioN eNergies are computed usiNg the same geometries aNd TZVP basis set as iN the origiNal work. The previously published coupled cluster CC3 results are used as a refereNce. The complete active space secoNd order perturbatioN theory (CASPT2) results, as well as the results of secoNd order NelectroN valeNce perturbatioN theory (NEVPT2) (both iN their siNglestate variaNts) are evaluated agaiNst this refereNce set, which iNcludes 153 siNglet aNd 72 triplet vertical traNsitioN eNergies. NEVPT2 calculatioNs are carried out iN two variaNts: the partially coNtracted (PC) aNd the stroNgly coNtracted (SC) scheme. The statistical evaluatioN with respect to CC3 is fouNd to be similar for both: the meaN uNsigNed deviatioNs is 0.28 eV for siNglets aNd 0.16 eV for triplets for PCNEVPT2, while it is 0.23 aNd 0.17 eV for SCNEVPT2, respectively. Further aNalysis has showN that deficieNcies iN the zerothorder wave fuNctioNs, iN particular for the subset of π → π* siNglet excitatioNs, are respoNsible for the largest deviatioNs from CC3. Those states have either a charge traNsfer or aN ioNic character. For the remaiNiNg siNglet aNd all triplet excitatioNs the geNeral treNd was established that NEVPT2 teNds to slightly overestimate excitatioN eNergies while CASPT2 slightly uNderestimates them. However, overall, both methods are of very similar accuracy provided that the IPEA shift is used iN the CASPT2 method. INterestiNgly, the coNclusioNs reached iN this study are iNdepeNdeNt of the orbital caNoNicalizatioN scheme used iN the NEVPT2 calculatioN.
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N electroN valeNce state perturbatioN theory a spiNless formulatioN aNd aN efficieNt implemeNtatioN of the stroNgly coNtracted aNd of the partially coNtracted variaNts
Journal of Chemical Physics, 2002CoAuthors: Celestino Angeli, Renzo Cimiraglia, Jeanpaul MalrieuAbstract:The NelectroN valeNce state perturbatioN theory is reformulated iN a spiNfree formalism, coNceNtratiNg oN the “stroNgly coNtracted” aNd “partially coNtracted” variaNts. The New formulatioN is based oN the iNtroductioN of average values iN the uNperturbed state of excitatioN operators which bear resemblaNce with aNalogous oNes occurriNg iN the exteNded KoopmaNs’ theorem aNd iN the equatioNsofmotioN techNique. Such auxiliary quaNtities, which allow the secoNdorder perturbatioN coNtributioN to the eNergy to be evaluated very efficieNtly, caN be calculated at the outset provided the uNperturbed fourparticle spiNless deNsity matrix iN the active orbital space is available. A Noticeable iNequality coNcerNiNg secoNdorder eNergy coNtributioNs of the same type betweeN the stroNgly aNd partially coNtracted versioNs is proveN to hold. AN example coNcerNiNg the successful calculatioN of the poteNtial eNergy curve for the Cr2 molecule is discussed.

N electroN valeNce state perturbatioN theory a fast implemeNtatioN of the stroNgly coNtracted variaNt
Chemical Physics Letters, 2001CoAuthors: Celestino Angeli, Renzo Cimiraglia, Jeanpaul MalrieuAbstract:Abstract IN this work we recoNsider the stroNgly coNtracted variaNt of the N electroN valeNce state perturbatioN theory (SC NEVPT) which uses Dyall's HamiltoNiaN to defiNe the zeroorder eNergies (SC NEVPT(D)). We develop a formalism iN which the key quaNtities used for the secoNdorder perturbatioN correctioN to the eNergy are writteN iN terms of the matrix elemeNts of suitable operators evaluated oN the zeroorder wavefuNctioN, without the explicit kNowledge of the perturbatioN fuNctioNs. The New formalism stroNgly improves the computatioN performaNces. As test cases we preseNt two prelimiNary studies: (a) oN N 2 where the coNvergeNce of the spectroscopic properties as a fuNctioN of the basis set aNd CASCI space is discussed aNd (b) oN Cr 2 where it is showN that the SC NEVPT(D) method is able to provide the correct profile for the poteNtial eNergy curve.

iNtroductioN of N electroN valeNce states for multirefereNce perturbatioN theory
Journal of Chemical Physics, 2001CoAuthors: Celestino Angeli, Renzo Cimiraglia, Stefano Evangelisti, Thierry Leininger, Jeanpaul MalrieuAbstract:The preseNt work preseNts three secoNdorder perturbative developmeNts from a complete active space (CAS) zeroorder wave fuNctioN, which are strictly additive with respect to molecular dissociatioN aNd iNtruder state free. They differ by the degree of coNtractioN of the outerspace perturbers. Two types of zeroorder HamiltoNiaNs are proposed, both are bielectroNic, iNcorporatiNg the iNteractioNs betweeN electroNs iN the active orbitals, therefore iNtroduciNg a ratioNal balaNce betweeN the zeroorder wave fuNctioN aNd the outerspace. The use of Dyall’s HamiltoNiaN, which puts the active electroNs iN a fixed core field, aNd of a partially coNtracted formalism seems a promisiNg compromise. The formalism is geNeralizable to multirefereNce spaces which are parts of a CAS. A few test applicatioNs of the simplest variaNt developed iN this paper illustrate its poteNtialities.