Geometry-dependent lifetime of Interatomic coulombic decay using equation-of-motioncoupled cluster methodAryya Ghosh and Nayana Vaval Citation: The Journal of Chemical Physics 141, 234108 (2014); doi: 10.1063/1.4903827 View online: http://dx.doi.org/10.1063/1.4903827 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/141/23?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Study of interatomic Coulombic decay of Ne(H2O) n (n = 1,3) clusters using equation-of-motion coupled-clustermethod J. Chem. Phys. 139, 064112 (2013); 10.1063/1.4817966 Communications: Explicitly correlated equation-of-motion coupled cluster method for ionized states J. Chem. Phys. 132, 021101 (2010); 10.1063/1.3291042 Ab initio calculation of interatomic decay rates of excited doubly ionized states in clusters J. Chem. Phys. 129, 244102 (2008); 10.1063/1.3043437 Addition by subtraction in coupled cluster theory. II. Equation-of-motion coupled cluster method for excited,ionized, and electron-attached states based on the n CC ground state wave function J. Chem. Phys. 127, 024106 (2007); 10.1063/1.2747245 The active-space equation-of-motion coupled-cluster methods for excited electronic states: Full EOMCCSDt J. Chem. Phys. 115, 643 (2001); 10.1063/1.1378323

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THE JOURNAL OF CHEMICAL PHYSICS 141, 234108 (2014)

Geometry-dependent lifetime of Interatomic coulombic decayusing equation-of-motion coupled cluster method

Aryya Ghosh and Nayana VavalPhysical Chemistry Division, CSIR-National Chemical Laboratory, Pune 411008, India

(Received 29 August 2014; accepted 28 November 2014; published online 16 December 2014)

Electronically excited atom or molecule in an environment can relax via transferring its excess energyto the neighboring atoms or molecules. The process is called Interatomic or Intermolecular coulombicdecay (ICD). The ICD is a fast decay process in environment. Generally, the ICD mechanism pre-dominates in weakly bound clusters. In this paper, we have applied the complex absorbing potentialapproach/equation-of-motion coupled cluster (CAP/EOMCCSD) method which is a combination ofCAP and EOMCC approach to study the lifetime of ICD at various geometries of the molecules.We have applied this method to calculate the lifetime of ICD in Ne-X; X = Ne, Mg, Ar, sys-tems. We compare our results with other theoretical and experimental results available in literature.© 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4903827]

I. INTRODUCTION

Interatomic coulombic decay (ICD) is a efficient relax-ation pathway of electronically excited atom or molecule inan environment. ICD is proposed by Cederbaum et al.1 in1997. The electronically excited states which can relax viaICD mechanism can be generated in various ways, e.g., fol-lowing the Auger decay2 of core excited state or through cre-ating a vacancy in the inner valence state or outer valencestate. The important characteristic of ICD3–6 is its fast decay.Generally, it occurs in femto-second time scale. The ICD isa completely environmental phenomena. The efficient energyexchange with the neighboring atoms or molecules plays thekey role in this decay process. Thus, the ICD decay7–12 ratestrongly depends on the number of environmental species aswell as internuclear distances between them. Energetically,ICD is possible when the binding energy of the excited statelies above the double ionization threshold of the correspond-ing cluster.

Electronically excited states of atom or molecule can re-lax via various radiative decay mechanism, such as photonemission, radiative charge transfer (RCT), etc. However, theseare slow processes. Generally, they occur in nano-second (ns)time scale. Another non-radiative decay mechanism is opera-tive for the core excited states of atom or molecule is calledAuger decay. In Auger decay, a core level vacancy of a par-ticular atom or molecule is replaced by two outer valence va-cancy of the same atom or molecule. Auger decay is also avery fast decay process. It occurs in femto-second or evenatto-second time domain. The electronically excited statespreferably undergoes ICD mechanism when the intramolec-ular auto-ionization is not energetically favorable.

Historically, ICD has been studied in various weaklybound systems, such as hydrogen bonded clusters,13 van derWaals clusters,4 etc. The existence of ICD has also beenproved in most weakly bound He2 cluster in nature.14 Re-cently, Cederbaum and co-workers15 have shown that the siteand energy of the ICD electron can efficiently controlled by

spectator resonance Auger decay. It has also been proved thatcomplex absorbing potential approach is highly efficient tocalculate the lifetime of inner valence excited states. Santraet al.16, 17 have applied the CAP/CI approach to calculate thelifetime of ICD decay mode. The CAP/ADC method18 hasalso been developed to study the ICD decay rate. Recently, ahighly efficient CAP/EOMCC method19 has been developedby Vaval and co-workers and it has been applied successfullyto calculate the lifetime of 2s inner valence excited states ofNe atom in Ne(H2O)n (n = 1,3) clusters. ICD mechanism hasbeen observed experimentally for the NeNe20, 21 and (H2O)2systems.22, 23

Recently, it has been proved that the low energy electronsof the order of 2-3 electron volts (eV) are highly efficient tobreak the single DNA stand and the electrons of the order of5-6 eV are extremely useful to break the double DNAstand.24, 25 One of the most amazing features of ICD is it au-tomatically produces low energy electrons of the order of 4-5eV. Thus, the ICD might be act as an important source of lowenergy electrons which can cause severe damage to the singleand double DNA stand. Therefore, the accurate descriptionof ICD mechanism is highly important to convert this decaymode to a useful radiotherapy scheme.

The ICD process mainly depends on the initial ionizedexcited state and the double ionized final state. Therefore, todescribe the ICD process effectively, the accurate descriptionof both the ionized states is extremely important. The accu-rate measurement of initial ionized excited state is possibleusing the EOMCC method. One of the most amazing fea-tures of EOMCC method is the capability of including elec-tron correlation and relaxation effects in an effective man-ner. The electron correlation and relaxation effects play thesubstantial role in the accurate description of ionized excitedstate. Another advantage is that it gives direct intensive energydifference. Therefore, the EOMCC approach is very promis-ing to calculate the lifetime of ICD process in an accuratemanner.

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234108-2 A. Ghosh and N. Vaval J. Chem. Phys. 141, 234108 (2014)

In this paper, we have applied the CAP/EOMCCSD ap-proach to study the lifetime of 2s inner valence excited stateof Ne atom in Ne-X; X = Ne, Mg, Ar, systems at variousinternuclear distances. The results are compared with othertheoretical results available in literature.

In the Penning ionization process,26 an electronically ex-cited atom (A∗) collides with the target atom or molecule (B).After collision, the electronically excited atom (A∗) comesinto its neutral ground state (A) and the target atom ormolecule becomes a positively charged ion (B+),

A∗ + B → A + B+ + e−. (1)

In this process, the emitted electron goes into continuum.Therefore, the Penning ionization process is a kind of phe-nomena which is closely related with the ICD process. It hasbeen proved that any local complex potential approach is validin the description of Penning ionization process. Therefore,the CAP/EOMCCSD approach will also be generalized to de-scribe the penning ionization process provided excitation en-ergies (EE) EOMCC is used instead of ionization potential(IP) EOMCC. Thus, while ICD and Penning ionization areindeed closely related, there is an essential mechanistic dif-ference between the two processes. The Penning ionizationprocess is mainly governed via electron transfer rather thanenergy transfer. However, ICD is purely an energy transferprocess. This is the reason why at a large internuclear dis-tance (R), Penning decay width (�) exponentially decreaseswith R, while ICD decay width (�) decreases as 1/R6. TheCAP/EOMCC method can also be generalized to describethe electronic decay of double ionized states27 provided dou-ble ionization potential (DIP) EOMCC is used instead of IP-EOMCC.

The paper is organized as follows. In Sec. II, we brieflydiscuss the equation-of-motion coupled cluster theory alongwith the CAP approach. Computational details are given inSec. III. Results and discussion on them are presented inSec IV. In Sec V we conclude our findings.

II. THEORY

In this section, we briefly discuss the CAP/EOMCCSDmethod. The CAP28–30 is known to be a powerful approachto describe the resonance states effectively. The main idea ofCAP approach is to absorb the outgoing electron without dis-turbing the target system. In this way, the wave function ofthe outgoing electron becomes square integrable. In the CAPapproach, the modified Hamiltonian can be written as

H (η) = H − iηW, (2)

where η represents the CAP strength and W is the real softbox like potential. The addition of CAP makes the Hamil-tonian operator non-Hermitian. The resonance energies areobtained by solving the complex eigenvalue problem corre-sponding to the matrix representation of H(η).

The resonance energy is obtained when

|η∂E/∂η| (3)

becomes minimum.

According to Siegert and Gamow, the resonance energycan be expressed as

Er = ER − iΓ /2, (4)

where ER represents the resonance position and Γ is the decaywidth. Γ is inversely related to the lifetime of the resonancestate via, τ = ¯/Γ .

The starting point for the EOMCC method is a coupledcluster (CC) ground state wave function. In CC method, theground state wave function can be defined as

|ψ0〉 = eT |φ0〉, (5)

where φ0 is the N-electron close shell reference determinant,e.g., the restricted Hartree-Fock determinant (RHF) and T isthe cluster operator. In the coupled cluster singles and doubles(CCSD) approximation, T operator can be defined as follows:

T =∑ia

tai a+a ai + 1/4

∑ab

∑ij

tabij a+

a a+b aiaj + . . . , (6)

where the standard convention for the indices is used, i.e., in-dices a, b, . . . , refer to the virtual spin orbitals and indices i,j, . . . , refer to the occupied spin orbitals.

In the EOMCCSD approach,31–34 the wave function forthe μ th ionized states ψμ can be expressed as

|ψμ〉 = R(μ)|ψ0〉, (7)

where R(μ) is the ionization operator.The R(μ) operator can be defined via creation-

annihilation operator as follows:

R(μ)IP =∑

i

ri(μ)ai + 1/2∑

a

∑ij

raij (μ)a+

a ajai + . . . .

(8)The Schrödinger equation for the ionized states can be

expressed as

HNR(μ)|ψ0〉 = ΔEμR(μ)|ψ0〉, (9)

where HN is the normal ordered Hamiltonian and it can bewritten as

HN = H − 〈φ0|H |φ0〉. (10)

The final form of EOMCC equation is

HNR(μ)|φ0〉 = wμR(μ)|φ0〉, (11)

where wμ is the energy change connected with the ionizationprocess. The HN is the similarity transformed Hamiltonian, interms of connected diagrams and it can be defined as

HN = e−T HeT − 〈φ0|e−T HeT |φ0〉. (12)

In a matrix form Eq. (11) is

HNR(μ) = wμR(μ). (13)

The HN matrix is diagonalized in the sub space of 1h and2h1p space to get the required ionization potential (IP) values.

In the CAP/EOMCC method,35, 36 the CAP term is addedto the CC method. After addition of CAP to the CC method,the ground state wave function |ψ0〉 for the CC method canbe written as

|0(η)〉 = eT (η)|φ0〉. (14)

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234108-3 A. Ghosh and N. Vaval J. Chem. Phys. 141, 234108 (2014)

The T(η) amplitudes become complex. These complex T(η)amplitudes have been used latter to construct the HN (η)matrix.

Then, the CAP term is added to the one body particle-particle ( ¯fpp) part of HN . The other terms of the HN matrixare altered via the appearance of the complex T(η). Thus, thenew form of the HN matrix is

HN (η) = e−T (η)HN (η)eT (η) − 〈φ0|e−T (η)HN (η)eT (η)|φ0〉,(15)

HN (η)Rη(μ) = wμ(η)Rη(μ). (16)

Finally, the resulting complex HN (η) matrix is diagonal-ized for the different η values. However to obtain the reso-nance energies we need to use following equation since theground state energies are suppose to be CAP free,

Eres(η) = wμ(η) + ECC(η) − ECC(η = 0). (17)

In this paper, we have made an approximation T(η) ≈ T(η= 0). Thus, the CAP is not added at the CC level. The CAP isadded directly to the one body particle-particle ( ¯fpp) part ofHN . Therefore, the new form of the HN matrix is

HN (η) = e−T (η=0)HN (η)eT (η=0) − 〈φ0|e−T HNeT |φ0〉. (18)

Finally, the resulting complex HN (η) matrix is diagonal-ized for the different η values to get the resonance energies.The resonance states can be identified from the η trajectoriesthat shows stabilization cusps.

The artificial nature of the CAP potential and its appli-cation only to the particle-particle part justify our approxima-tion. The CAP has very less effect on the ground state energy.The main advantage of this approximation is that it reducesthe η trajectory generation time. In this approach CC calcu-lation needs to be done only once. Since the ground state isη independent, resonance energy we get as the direct differ-ence energy obtained as eigenvalues of HN (η) for different η

values,

HN (η)Rη(μ) = wμ(η)Rη(μ). (19)

III. COMPUTATIONAL DETAILS

The aug-cc-pCVTZ basis37 set has been used to calculatethe lifetime of ICD process in Ne-X; X = Ne, Mg, Ar, sys-tems. The first step in the CAP/EOMCCSD computation is aSCF calculation for the neutral Ne-X system. The SCF cal-culation has been performed using the GAMESS-US suite ofprograms.38 The required matrix elements of the EOMCCSDand CAP matrices have been computed using our own codes.For diagonalization purpose, we have implemented the nonhermitian version of Davidson algorithm39 in our EOMCCcode.

The potential W is the soft-box potential and it can bedefined as

W (x; c) =3∑

i=1

Wi(xi ; ci), (20)

TABLE I. Calculated decay widths (Γ ) for the 2�+u inner valence hole of

Ne atom in Ne–Ne.

Bond distance (Å) Γ (meV) lifetime (fs)

2.8 9.52 692.9 8.27 793.0 7.21 913.1 6.72 983.2 6.53 1003.3 6.35 1033.4 6.20 106

where

Wi(xi ; ci) ={

0, |xi | ≤ ci,

(|xi | − ci)2, |xi | > ci.

(21)

Here, ci, i = 1, 3 are the real, non-negative parame-ters which define the size of a rectangular box. The targetmolecule is placed in the center of the box. The matrix ele-ments of W (x; c) are calculated within a Gaussian basis set.

IV. RESULTS AND DISCUSSION

In this paper, we have implemented the CAP/EOMCCSDmethod to study the lifetime of 2s inner valence excited stateof Ne atom in Ne-X; X = Ne, Mg, Ar, systems. The life-time has been studied at various internuclear distances. In theCAP/EOMCCSD calculations, all the molecules are placedin a cartesian coordinate system at (0.0, 0.0, ±R/2 a.u.),where R is the bond distance between the two atoms. In theCAP/EOMCC computations, the CAP box side lengths arechosen to be cx = cy = δc and cz = δc + R/2, where cx, cy,cz are the distances from the center of the coordinate systemalong the x, y, and z axis, respectively, and δc is a non-negativenumber, all in a.u. The δc value we have chosen for the Ne–Neis 3.0 a.u and for the Ne–Mg system value is 5.0 a.u. The δcvalue for the Ne–Ar system is 4.0 a.u.

The ICD decay process in Ne–Ne can be explained asfollows: the Ne 2s vacancy is localized on one of the Neatom. An electron from the 2p level of the same Ne atomcomes and fills up the Ne 2s vacancy and the excess en-ergy is used to eject an electron of the Ne 2p level fromthe neighboring Ne atom. Therefore, the final state of ICDprocess in NeNe is characterized by Ne+(2p−1)Ne+(2p−1)state. The ICD channel is open in Ne–Ne system becausethe energy of Ne+(2s−1)Ne state lies above the energy ofNe+(2p−1)Ne+(2p−1) state. At equilibrium bond length ofneutral Ne–Ne molecule, the energy of Ne+(2s−1)Ne state is48.38 electron volts (eV). Here, we have calculated the life-time of 2�+

u inner valence excited state of neon dimer at vari-ous inter nuclear distances. Starting from 2.8 Å we have sym-metrically stretch the Ne–Ne bond distance up to 3.5 Å. Thelifetimes for the 2�+

u inner valence excited state in variousinternuclear distances are presented in Table I. Starting fromthe Ne–Ne bond distance 2.8 Å the lifetime increases rapidlywhen we stretch the Ne–Ne bond distance. Other importantaspect is the ICD decay channel is open for the 2�+

u inner va-lence excited state at bond distance 〉 2.70 Å. When the Ne–Ne

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234108-4 A. Ghosh and N. Vaval J. Chem. Phys. 141, 234108 (2014)

2.8 2.9 3 3.1 3.2 3.3R (Ang)

6

7

8

9W

idth

(m

eV)

FIG. 1. Calculated decay widths (Γ ) for the 2s inner valence hole of Ne atomin Ne–Ne.

bond distance is 〈 2.70 Å the ICD decay channel for the 2�+u

state is energetically forbidden. The schematic representationof lifetimes for the 2�+

u inner valence excited state of neondimer in various internuclear distances are presented in Fig. 1.

The lifetime for the 2�+u state is compared with the

other theoretical approaches available in the literature. Thecomputed lifetime for the 2�+

u state at equilibrium bonddistance (3.2 Å) is 100 fs. The calculated lifetime usingthe CAP/ADC method is 92 fs.18 The d-aug-cc-pV5Z ba-sis set is used in the CAP/ADC calculation. The CAP/CI17

method predicts lifetime of 64 fs using d-aug-cc-pVDZ ba-sis augmented by three diffuse s, p, and d functions each.The ICD lifetimes for the 2�+

u state of Ne2 in variousNe–Ne bond distances are calculated by Vitali et al.40 us-ing the Fano-ADC(2e) method. The ICD lifetime obtainedusing the CAP/EOMCCSD method show close agreementwith the Fano-ADC(2e) method. The computed ICD life-time of 2�+

u state at various internuclear distances usingthe CAP/EOMCCSD method follow the qualitatively simi-lar trend reported in Ref. 4. In a recent experiment it is foundthat the 2s inner valence excited state of Ne atom in neondimer can have lifetime of the order of (150 ± 50) fs.21

Therefore, the result obtained in CAP/EOMCCSD methodshow excellent agreement with the experimental result.

We have studied the basis set convergence at equilibriumbond length of Ne2 to investigate how the lifetime of ICD pro-cess changes in various basis sets. The results for the differentbasis sets are collected in Table II. Starting from the aug-cc-pCVTZ basis set we have gradually added up to three diffuses functions, three diffuse p functions and three d functionson each neon atom. The exponent of the s, p, d functions aregenerated by scaling the factor 3.0 starting from the expo-nent of the last s, p, and d functions of the aug-cc-pCVTZ

TABLE II. Calculated decay widths (Γ ) for the 2�+u inner valence hole of

Ne atom in Ne–Ne.

Basis set Γ (meV) lifetime (fs)

aug-cc-pCVTZ 6.53 100aug-cc-pCVTZ + 1s1p1d 7.06 92aug-cc-pCVTZ + 2s2p2d 7.07 92aug-cc-pCVTZ + 3s3p3d 7.16 91

TABLE III. Calculated decay widths (Γ ) for the 2s inner valence hole ofNe atom in Ne–Mg.

Bond distance (Å) Γ (meV) lifetime (fs)

4.0 30.24 224.2 24.25 274.4 17.25 384.6 9.87 664.8 3.83 171

basis. When we go from aug-cc-pCVTZ basis to aug-cc-pCVTZ +3s3p3d decay width changes by 0.6 meV.

The 2s inner valence excited state of Ne atom in Ne–Mgcan relax through ICD mechanism to a Ne+(2p−1)Mg+(3s−1)final state. In this process, one 2p electron fills up the 2svacancy of Ne atom and excess energy is used to eject the3s outer valence electron from the Mg atom. At equilibriumbond length (4.4 Å) the energy of the Ne+(2s−1)Mg stateis 48.3 eV. The energy of the Ne+(2p−1)Mg+(3s−1) state is32.29 eV. The energy of Ne+(2p−1)Mg+(3s−1) state is 16 eVlower in comparison with the Ne+(2s−1)Mg state. There-fore, the ICD decay channel is energetically open for theNe+(2s−1)Mg state. The Ne+(2s−1)Mg state can also relax toa final state NeMg2 +(3s−2) via Electron transfer mediated de-cay mechanism (ETMD).41 The energy of the NeMg2 +(3s−2)state is 22.5 eV. The two decay channels are open for theNe+(2s−1)Mg state due to very low energy of 3s orbital ofMg atom. However, the only decay channel open for Ne-Ne isICD. The separate calculation of lifetime for ICD and ETMDprocess is not possible using the CAP/EOMCCSD method.Here, We have calculated the total lifetime of Ne+(2s−1)Mgstate at various internuclear distances. Starting from Ne-Mgbond distance 4.0 Å, the lifetime of Ne+(2s−1)Mg state iscalculated up to the bond distance 5.0 Å. The calculatedlifetime at various internuclear distances are presented inTable III. Starting from equilibrium bond distance, the life-time of Ne+(2s−1)Mg state increases strongly with increasingNe–Mg bond distance. The schematic representation of life-time for the 2s inner valence excited state of NeMg at variousinternuclear distances are presented in Fig. 2.

Cederbaum and Averbukh42 have calculated the total de-cay width of Ne+(2s−1)Mg state in various Ne–Mg bond

4 4.2 4.4 4.6 4.8R (Ang)

0

10

20

30

Wid

th (

meV

)

FIG. 2. Calculated decay widths (Γ ) for the 2s inner valence hole of Ne atomin Ne–Mg.

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234108-5 A. Ghosh and N. Vaval J. Chem. Phys. 141, 234108 (2014)

TABLE IV. Calculated decay widths (Γ ) for the 2s inner valence hole of Neatom in Ne–Ar.

Bond distance (Å) Γ (meV) lifetime (fs)

2.8 124.15 53.0 108.52 63.2 84.90 83.4 47.63 143.5 37.40 173.6 33.89 193.8 26.22 25

distances. The Fano-ADC(2) approach is used in their cal-culations (see Ref. 42). The total decay widths obtained usingthe CAP/EOMCCSD method at equilibrium bond distance aswell as large Ne–Mg bond distance are higher compared to thetotal decay widths obtained using the Fano-ADC(2) approach.However, the calculated potential curve for the ICD lifetimefrom bond length 4.0 Å to 5.0 Å using the CAP/EOMCCSDmethod follow the qualitatively similar trend reported usingthe Fano-ADC(2) approach. It is worth discussing why thecalculated decay rate using the CAP/EOMCCSD method isfaster compared to the Fano-ADC(2) approach. One possiblereason behind the calculated faster decay rate using the EOM-CCSD method is that the EOMCC method includes moreelectron correlation compared to the ACD(2) method. Theelectron correlation plays an important role in the accuratedescription of interatomic decay rate.

We have also calculated the lifetime of 2s inner valenceexcited state of Ne atom in Ne–Ar cluster at various in-ternuclear distances between Ne and Ar atom. The calcu-lated lifetime at various internuclear distances are presentedin Table IV. The schematic representation of lifetime forthe 2s inner valence excited state of NeAr at various inter-nuclear distances is presented in Fig. 3. The energy of theNe+(2s−1)Ar state is 48.26 eV. The two decay channels areopen for the Ne+(2s−1)Ar state. It can decay to the finalNe+(2p−1)Ar+(3p−1) state through ICD process. The ICD de-cay channel is open because Ne+(2p−1)Ar+(3p−1) state (atequilibrium bond length 3.5 Å) has energy about 7 eV lowercompare to the Ne+(2s−1)Ar state. Further, Ne+(2s−1)Ar statecan relax to NeAr2 +(3p−2) state via ETMD pathway. Here,we have calculated the total lifetime of Ne+(2s−1)Ar stateusing the CAP/EOMCCSD method. However, at equilibriumbond length of NeAr system ETMD process is suppressed byICD decay mode.

The interatomic decay rate for the Ne–Ar system is com-pared with the other theoretical methods. The calculated life-time for the Ne+(2s−1)Ar state at equilibrium bond length(3.5 Å) using the CAP/EOMCCSD method is 17 fs. Inearlier theoretical study, Cederbaum and co-workers6 havecalculated the lifetime of Ne+(2s−1)Ar state in various inter-nuclear distances between Ne and Ar atom. In their calcu-lations, they have used Fano theory of resonances, Green’sfunction ab initio technique and Stieltjes imaging. The cal-culated lifetime at equilibrium bond length using Fano-ADCapproach is about 38 fs. The decay widths (Γ ) obtained usingthe CAP/EOMCCSD method overestimate the decay widths

2.8 3 3.2 3.4 3.6 3.8R (Ang)

50

100

150

Wid

th (

meV

)

FIG. 3. Calculated decay widths (Γ ) for the 2s inner valence hole of Ne atomin Ne–Ar.

obtained using the Fano-ADC approach at equilibrium bondlength (3.5 Å) as well as larger internuclear distances betweenNe and Ar atom.

V. CONCLUSION

The CAP/EOMCCSD approach is used for the study ofthe lifetime of 2s inner valence excited state of Ne atom in Ne-X; X = Ne, Mg, Ar, system at various inter nuclear distances.The ICD decay rate decreases rapidly when we stretch thebond distance in Ne–Ne, Ne–Mg, and Ne–Ar systems fromtheir equilibrium bond length. The reason behind decreasingthe decay rate is that with increasing the bond distance be-tween two atoms energy transfer process becomes slow. An-other important aspect is at equilibrium bond length whenwe go from Ne–Ne to Ne–Mg the decay rate increases. Fur-ther, the decay rate increases when we go from Ne–Mg toNe–Ar. The reason for increasing the decay rate when we gofrom Ne–Mg to Ne–Ar is that the equilibrium bond lengthfor the Ne–Mg system is 4.4 Å. However, the equilibriumbond length for Ne–Ar system is 3.5 Å. Therefore, the bonddistance between two atoms play an important role to makedifference in ICD decay rate. Apart from the different bonddistance, number of decay channels also play an importantrole. Mg has only two outer valence electrons, while Ar hassix outer valence electrons that could be ionized in the ICDprocess. We are not counting the ETMD channels as theseare very weak. Thus, the more number of decay channels inNe–Ar leads to increase in the decay rate. The reason for thechange of lifetime is the change in the electronic structure aswe go from Ne–Ne to Ne–Mg. In case of Ne–Mg the doubleionization threshold is much less compare to the Ne–Ne. Toapply our approach for the biologically relevant systems willbe the direction of our future work. We hope our approachmight be helpful in further development of efficient radioon-cology scheme to understand the radiation damage in biolog-ical systems in a more accurate manner.

ACKNOWLEDGMENTS

The authors acknowledge the facilities of the Centerof Excellence in Scientific Computing at NCL. A. Ghosh

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234108-6 A. Ghosh and N. Vaval J. Chem. Phys. 141, 234108 (2014)

acknowledges the Council of Scientific and Industrial Re-search (CSIR) for Fellowship. N. Vaval acknowledges theCSIR MSM project for the financial support. N. Vaval ac-knowledges the Department of Science and Technology, In-dia for financial support. The paper is dedicated to ProfessorSourav Pal in honor of his 60th birthday.

1L. S. Cederbaum, J. Zobeley, and F. Tarantelli, Phys. Rev. Lett. 79, 4778(1997).

2L. S. Cederbaum, Y. C. Chiang, P. V. Demekhin, and N. Moiseyev, Phys.Rev. Lett. 106, 123001 (2011).

3N. Moiseyev, R. Santra, J. Zobeley, and L. S. Cederbaum, J. Chem. Phys.114, 7351 (2001).

4R. Santra, J. Zobeley, L. S. Cederbaum, and N. Moiseyev, Phys. Rev. Lett.85, 4490 (2000).

5S. Scheit, V. Averbukh, H. D. Meyer, N. Moiseyev, R. Santra, T. Sommer-feld, J. Zobeley, and L. S. Cederbaum, J. Chem. Phys. 121, 8393 (2004).

6S. Scheit, V. Averbukh, H. D. Meyer, J. Zobeley, and L. S. Cederbaum, J.Chem. Phys. 124, 154305 (2006).

7S. Barth, S. Joshi, S. Marburger, V. Ulrich, A. Lindblas, G. Öhrwall, O.Björneholm, and U. Hergenhahn, J. Chem. Phys. 122, 241102 (2005).

8P. V. Demekhin, S. D. Stoychev, A. I. Kuleff, and L. S. Cederbaum, Phys.Rev. Lett. 107, 273002 (2011).

9I. B. Müller and L. S. Cederbaum, J. Chem. Phys. 125, 204305 (2006).10V. Averbukh, I. B. Müller, and L. S. Cederbaum, Phys. Rev. Lett. 93,

263002 (2004).11R. Santra and L. S. Cederbaum, Phys. Rep. 368, 1 (2002).12V. Averbukh and L. S. Cederbaum, Phys. Rev. Lett. 96, 053401 (2006).13S. D. Stoychev, A. I. Kuleff, and L. S. Cederbaum, J. Am. Chem. Soc. 133,

6817 (2011).14N. Sisourat, N. V. Kryzhevoi, P. Kolorenc, S. Scheit, T. Jahnke, and L. S.

Cederbaum, Nat. Phys. 6, 508 (2010).15K. Gokhberg, P. Kolorenc, A. I. Kuleff, and L. S. Cederbaum, Nature 505,

661 (2014).16R. Santra, L. S. Cederbaum, and H. D. Meyer, Chem. Phys. Lett. 303, 413

(1999).17R. Santra and L. S. Cederbaum, J. Chem. Phys. 115, 6853 (2001).18N. Vaval and L. S. Cederbaum, J. Chem. Phys. 126, 164110 (2007).19A. Ghosh, S. Pal, and N. Vaval, J. Chem. Phys. 139, 064112 (2013); Mol.

Phys. 112, 669 (2014).20T. Jahnke, A. Czasch, M. S. Schöffler, S. Schössler, A. Knapp, M. Käsz,

J. Titze, C. Wimmer, K. Kreidi, R. E. Grisenti, A. Staudte, O. Jagutzki,U. Hergenhahn, H. Schmidt-Böcking, and R. Dörner, Phys. Rev. Lett. 93,163401 (2004).

21K. Schnorr, A. Senftleben, M. Kurka, A. Rudenko, L. Foucar, G. Schmid,A. Broska, T. Pfeifer, K. Meyer, D. Anielski, R. Boll, D. Rolles, M. Kübel,

M. F. Kling, Y. H. Jiang, S. Mondal, T. Tachibana, K. Ueda, T. Marchenko,M. Simon, G. Brenner, R. Treusch, S. Scheit, V. Averbukh, J. Ullrich,C. D. Schröter, and R. Moshammer, Phys. Rev. Lett. 111, 093402 (2013).

22T. Jahnke, H. Sann, T. Havermeier, K. Kreidi, C. Stuck, M. Meckel, M.Schöffler, N. Neumann, R. Wallauer, S. Voss, A. Czasch, O. Jagutzki, A.Malakzadeh, F. Afaneh, Th. Weber, H. Schmidt-Böcking, and R. Dörner,Nat. Phys. 6, 139 (2010).

23M. Mucke, M. Braune, S. Barth, M. Förstel, T. Lischke, V. Ulrich, T. Arion,U. Becker, A. Bradshaw, and U. Hergenhahn, Nat. Phys. 6, 143 (2010).

24F. Trinter, M. S. Schöffler, H.-K. Kim, F. P. Sturm, K. Cole, N. Neumann,A. Vredenborg, J. Williams, I. Bocharova, R. Guillemin, M. Simon, A.Belkacem, A. L. Landers, Th. Weber, H. Schmidt-Böcking, R. Dörner, andT. Jahnke, Nature 505, 664 (2014).

25B. Boudaïffa, P. Cloutier, D. Hunting, M. A. Huels, and L. Sanche, Science287(5458), 1658 (2000).

26H. Morgner, Chem. Phys. 145, 239 (1990).27P. Kolorenc, V. Averbukh, K. Gokhberg, and L. S. Cederbaum, J. Chem.

Phys. 129, 244102 (2008).28T. Sommerfeld, U. V. Riss, H. D. Meyer, L. S. Cederbaum, B. Engels, and

H. U. Suter, J. Phys. B 31, 4107 (1998); G. Jolicard and E. J. Austin, Chem.Phys. Lett. 121, 106 (1985); W. P. Reinhardt, Annu. Rev. Phys. Chem. 33,223 (1982); N. Moiseyev, Phys. Rep. 302, 212 (1998).

29U. V. Riss and H. D. Meyer, J. Phys. B 26, 4503 (1993); J. G. Muga, J. P.Palao, B. Navarro, and I. L. Egusquiza, Phys. Rep. 395, 357 (2004).

30N. Moiseyev, J. Phys. B 31, 1431 (1998); U. V. Riss and H. D. Meyer, J.Phys. B 31, 2279 (1998).

31M. Musial, S. A. Kucharski, and R. J. Bartlett, J. Chem. Phys. 118, 1128(2003).

32R. J. Bartlett and M. Musial, Rev. Mod. Phys. 79, 291 (2007).33D. I. Lyakh, M. Musial, V. F. Lotrich, and R. J. Bartlett, Chem. Rev. 112,

182 (2012).34H. Pathak, B. K. Sahoo, B. P. Das, N. Vaval, and S. Pal, Phys. Rev. A 89,

042510 (2014).35A. Ghosh, N. Vaval, and S. Pal, J. Chem. Phys. 136, 234110 (2012); A.

Ghosh, N. Vaval, S. Pal, and R. J. Bartlett, ibid. 141, 164113 (2014).36A. Ghosh, A. Karne, S. Pal, and N. Vaval, Phys. Chem. Chem. Phys. 15,

17915 (2013); Y. Sajeev, A. Ghosh, N. Vaval, and S. Pal, Int. Rev. Phys.Chem. 33, 397 (2014).

37T. H. Dunning, Jr., J. Chem. Phys. 90, 1007 (1989).38M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon,

J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Win-dus, M. Dupuis, and J. A. Montgomery, “GAMESS: General atomic andmolecular electronic structure system,” J. Comput. Chem. 14, 1347 (1993).

39E. R. Davidson, J. Comput. Phys. 17, 87 (1975).40V. Averbukh and L. S. Cederbaum, J. Chem. Phys. 125, 094107 (2006).41I. B. Müller and L. S. Cederbaum, J. Chem. Phys. 122, 094305 (2005).42V. Averbukh and L. S. Cederbaum, J. Chem. Phys. 123, 204107

(2005).

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