The Journal of Physical Chemistry
Benchmark studies on the building blocks of DNA: I.
Superiority of Coupled Cluster methods in describing the
excited states of nucleobases in the Franck-Condon region
Journal:
Manuscript ID:
Manuscript Type:
Date Submitted by the
Author:
Complete List of Authors:
The Journal of Physical Chemistry
Draft
Article
n/a
Szalay, Peter; Institute of Chemistry, Eoetvoes Lorand University
Watson, Thomas; University of Florida,
Perera, Ajiith; University of Florida, Department of Chemistry
Lotrich, Victor; University of Florida, Quantum Theory Project
Bartlett, Rodney; University of Florida, Department of Chemistry
Note: The following files were submitted by the author for peer review, but cannot be converted to
PDF. You must view these files (e.g. movies) online.
paper1_submitted.pdf
ACS Paragon Plus Environment
Page 1 of 27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
The Journal of Physical Chemistry
Benchmark studies on the building blocks of DNA: I.
Superiority of Coupled Cluster methods in
describing the excited states of nucleobases in the
Franck-Condon region
Péter G. Szalay,∗,† Thomas Watson,‡ Ajith Perera,‡ Victor F. Lotrich,‡ and Rod J.
Bartlett‡
Institute of Chemistry, Eötvös University, H-1518 Budapest, P.O.Box 32, Hungary, and Quantum
Theory Project, University of Florida, Gainesville, FL
E-mail: [email protected]
∗ To
whom correspondence should be addressed
of Chemistry, Eötvös University, H-1518 Budapest, P.O.Box 32, Hungary
‡ Quantum Theory Project, University of Florida, Gainesville, FL
† Institute
1
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Abstract
Equation of Motion Excitation Energy Coupled-Cluster (EOMEE-CC) methods including
perturbative triple excitations have been used to set benchmark results for the excitation energy and oscillator strength of the building units of DNA, i.e. cytosine, guanine, adenine and
thymine. In all cases the lowest twelve states have been considered including valence and
Rydberg ones. Triple-ζ basis sets with diffuse functions have been used and the results are
compared to CC2, CASPT2, TDDFT and DFT/MRCI results from the literature. The results
clearly show that it is only the EOMEE-CCSD(T) which is capable to provide accuracy of
about 0.1 eV. EOMEE-CCSD systematically overshoots all type of excited states by 0.1-0.3
eV, while CC2 is surprisingly accurate for π → π ∗ excited states but fails (often badly) for
n → π ∗ and Rydberg states. DFT and CASPT2 seems to give reliable results for the lowest
state but the error increases fast with the excitation level. The differences in the excitation
energies often change the energy ordering of the states which should even influence the conclusions of excited state dynamics obtained with these approximate methods. The results call
for further benchmark calculations on larger building blocks of DNA (nucleosides, basis pairs)
at the CCSD(T) level.
Introduction
Electronic properties of DNA and RNA lies at the focus of biochemical research. 1–4 The basic
building blocks of these systems are the nucleobases. Therefore it is important to obtain detailed
information on the structure, excitation energy, and the associated spectra of these molecules. For
earlier results we refer to the detailed review by Shukla and Leszczynski. 5 Recent results include
the accurate determination of the ground state geometry of uracil, 6 the simulation of the spectra of
cytosine, 7–9 potential energy surfaces of excited states to locate minima, conical intersections and
relaxation pathways for several of the nucleobases. 10–21 There are also several studies reporting
simulations of the excited state dynamics. 3,21–39
Due to the size of nucleobases, mostly lower level approaches such as MCSCF, CASPT2, 40–43
2
ACS Paragon Plus Environment
Page 2 of 27
Page 3 of 27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
The Journal of Physical Chemistry
CC2, 43,44 TDDFT, 45,46 eventually MR-CI with limited reference or excitation space 3,14,47 have
been used to describe the excitation spectrum, but higher level calculations with different versions
of EOM-CC methods 7,9,13,43,48 are also available. To answer the question what happens with DNA
after excitation, dynamics simulations in the excited states need to be performed. These simulations can supply additional information on how the relaxation of excited molecules takes place
and what are the structural changes associated with this process. 3 Because of the high computational demand, however, these simulations are usually based on lower level calculations, like
CASSCF, 3,24,25,31 MR-CIS, 3,30 TDDFT 22,27,35 or even semi-empirical methods. 27,29,33,34,36 The
reliability of these calculations depends on the quality of the underlying potential energy surfaces,
and without accurate account of the relative energies of the electronic states involved, the picture
obtained from the simulation can be unreliable. Therefore it is very important to know how accurately the methods describe details of the surfaces, such as the order of excited states, location of
conical intersections etc. To that end calibration against high level calculations is important.
It is clear that in order to understand the electronic and spectral properties of DNA and RNA,
larger fragments than the monomers of nucleobases need to be studied. Such calculations are,
however, very expensive and approximate methods, provided they are accurate enough, can be
quite useful. In this respect, too, benchmarking by reliable and accurate methods is unavoidable.
EOMEE-CC (Equation of Motion Excitation Energy Coupled Cluster) method 49 (see also
Ref 50 ) is a powerful tool for calculating excitation energy within CC theory. In particular, the
version limited to single and double excitation (EOM-CCSD) 51,52 and the related linear response
CCSD-LR method 53 provide accurate results for excitation energies. 54,55 Extension to triple excitation have been done in different versions. The full EOM-CCSDT was presented by Kucharski,
et al. 56 and serves as the benchmark for triples methods. 54 However, in practice CCSDT is an ∼n8
method, and building its EOM matrix is also ∼n8 , to give a matrix of rank ∼n6 , which will require
partial, iterative diagonalization. Consequently, simplified methods reminiscent of the ground state
hierarchy, CCSDT-n 57 have been developed, EOMEE-CCSDT-1, 58 EOMEE-CCSDT-3, 59 along
with CC3-LR. 60 In these methods the triple excitation amplitudes are formally obtained from
3
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
an ∼n7 iterative procedure. However, they still suffer from the matrix diagonalization of rank
∼n6 . Hence, it is very important to formulate non-iterative versions, and two have been proposed,
EOMEE-CCSD(T) 58 and EOM-CCSD(Te). 59 Both add a single non-iterative evaluation of triples,
analogous to CCSD(T) 61,62 and only require an iterative diagonalization of a matrix of the same
size as that for EOM-CCSD, i.e. ∼n4 . Hence, they are vastly faster than the iterative triples models.
Recently, one of us 9 presented EOM-CC (Equation of Motion Coupled Cluster) simulation of
the UV spectrum of cytosine and compared it to a newly measured matrix-isolation (MI) spectrum.
After considering several tautomers, excellent agreement between the measured and calculated
spectra has been obtained. It was concluded that at the EOM-CCSD level the discrepancy in
excitation energy can be as large as 0.1-0.3 eV and inclusion of triple excitations are necessary to
get an accuracy of 0.1 eV. 9
The aim of this paper is to present a detailed analysis of the performance of different methods
by studying the excited states of nucleobases. In particular, the molecular building blocks of DNA,
i.e. cytosine, adenine, guanine, and thymine, will be investigated. The methods applied are all from
the Coupled-Cluster family, i.e. EOMEE-CC methods. The primary CCSD approximation will
be extended with triple excitations using the iterative EOMEE-CCSDT-3, 59 and CC3 60 methods
as well as the non-iterative EOMEE-CCSD(T) variant 58 which is based on perturbation theory
arguments (for more detail see below). (In what follows, for brevity, just EOM will be used for
EOMEE and even the EOM prefix will some times be omitted in the text and tables.)
The Coupled Cluster results will also be compared with various literature data. For studying
nucleobases, the most often used methods are TDDFT, CC2 and CASSCF; for review see Ref. 5
Since there are quite a large number of calculations with these methods, we have chosen those
which are in our opinion representative for the given method, available for most nucleobases and
represent a solid ground for an unbiased comparison. In particular we compare our CC results to
the CC2 results of Fleig et al., 44 to TDDFT results by Shukla and Leszczynski, 45 to the DFT/MRCI
results by Silva-Junior et al. 46 and the CASPT2 results from a large benchmark study by Schreiber
et al. 43 The later paper does not discuss guanine, therefore for this one molecule we compare with
4
ACS Paragon Plus Environment
Page 4 of 27
Page 5 of 27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
The Journal of Physical Chemistry
the CASPT2 results by Yamazaki et al. 26
The large CC calculations presented in this paper should therefore serve as benchmarks and
a methodological guide for future studies on larger pieces of DNA. Thus, we include up to 12
excited states, both valence and Rydberg, in the calculations, because, in our opinion, an accurate
description of the valence states requires the inclusion of the proper interaction with Rydberg states,
as well (see discussion below). Description of Rydbeg states requires the inclusion of diffuse
functions in the basis sets. To that end aug-pVDZ and aug-pVTZ basis sets will be used. 63 Careful
assignment of the calculated states based on the characteristics of the wave function (dominant
excitations and form of corresponding orbitals; natural orbitals of the density differences) will be
performed to obtain relationship between the accuracy and types of the excitation.
We note in passing that the methodological conclusion will in some cases differ from that
obtained for small molecules in earlier benchmark studies. 58,59
Methodology
Two program systems have been used in the calculations, namely ACES III 64,65 and CFOUR. 66
CFOUR was used for the calculation on cytosine at all levels, except EOM-CCSD(T), while all
other calculations have been performed with ACES III.
To maintain compatibility with earlier and following projects, the geometries of the four nucleobases have been obtained at slightly different levels of theory. In the cases of cytosine and adenine
the optimization was performed at the CCSD level using cc-pVDZ basis, 63 for guanine MBPT(2)
(MP2) level using cc-pVDZ basis sets, 63 while for thymine the MBPT(2)/aug-cc-pVDZ level was
used. The slight difference in the geometry caused by the different methods, should not influence
the results. Only the biologically relevant, canonical tautomers of the four nucleobases have been
included in this study. The optimization of cytosine and adenine have been performed by CFOUR
using internal coordinates 67 and the GDIIS algorithm. 68 The other structures were optimized with
ACES III using redundant internal coordinates. 69,70
5
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 6 of 27
Excitation energies are the main focus of this paper and the calculations have been performed at
different levels of EOM-CC theory. These include the singles-doubles level (EOM-CCSD) 51,52 and
various levels including triple excitations: EOM-CCSDT-3, 59 CC3-LR 60 with iterative and EOMCCSD(T) 58 with non-iterative triples. EOM-CCSDT-3, CC3-LR as well as CC2-LR 71 calculations
have been performed with CFOUR, while all EOM-CCSD(T) calculations were done with ACES
III. Two basis sets are used in the excitation energy calculations, the aug-cc-pVDZ and aug-ccpVTZ. 63 While both basis sets are used in the EOM-CCSD and EOM-CCSD(T) calculations, only
the smaller bases are used in conjunction with the iterative triple methods.
Oscillator strengths have been calculated from transition moments obtained according to Ref. 51
at the EOM-CCSD level. We also report the CC3-LR oscillator strength 60 for cytosine.
A detailed description of the EOM-CCSD(T) method and its implementation in ACES III will
be presented separately. 72 For the sake of fully documenting the results we give here the formula
used to calculate the correction of the excitation energy (ωk ) with respect to the CCSD one:
CCSD(T )
ωk
(1)
(1)
(2)
(2)
(2)
(2)
= hLk3 | f (0) |Rk3 i + hLk3 |V (1) |Rk i + hLk |V (1) |Rk3 i
with f (0) = ∑ f pp {p† p}, V (1) = ∑ fai {a† i} + {i† a} +
p
ai
∑ hpq||rsi{p†q†sr}.
pqrs
(1)
Rk
(1)
(1)
and Lk
are the EOM-CCSD right and left eigenvectors of state k, respectively, being necessarily first order
(2)
(2)
quantities in V (1) (superscripts in parenthesis stand for the order of the quantity). Rk3 and Lk3
are the second order contributions to the eigenvectors in the triples space and calculated from:
(2)
(1)
(2)
Lk3 D3 = Lk V (1) Q3
(3)
D3 Rk3
= Q3V (1) Rk
(2)
(1)
with Q3 being a projection onto the triply excited state, D3 is the corresponding difference of the
occupied and virtual orbital energies. With this the final correction to the excitation energy reads:
CCSD(T )
ωk
(1)
(1)
(1)
(1)
(0) −1
(1)
= hLk |V (1) Q3 D−1
D3 Q3V (1) |Rk i + hLk |V (1) Q3 D−1
|Rk i
3 f
3 V
6
ACS Paragon Plus Environment
Page 7 of 27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
The Journal of Physical Chemistry
(1)
(1)
(1)
+hLk |V (1) D−1
|Rk i
3 Q3V
(4)
Originally, Watts and Bartlett 58 presented this correction as ’second-order’ with respect to the
EOM-CCSD eigenvalue. Here an other choice was preferred: to be consistent with the treatment
of the ground state Λ-CCSD(T) method 61,73 henceforth, we consider it as a “fourth-order” triples
correction in the perturbation V (1) . We are also free to incorporate the ω CCSD value in the previous
expression into H0 , since it simply accounts for a shift. Numerically, there is virtually no difference in the answers. With these choices, we have analogous diagrams for the fourth-order triples
corrections in the ground state and the EOM excited states. We also retain the occupied-occupied
and virtual-virtual orbital rotation invariance for the approximation and the final equations can be
viewed as generalization of the so called Λ-CCSD(T) correction 54,61,62,73,74 for the ground state
using instead of the ground state quantities T3 , Λ1 and Λ2 the corresponding excited state quantities
R3 , R1 , R2 , and L3 , L1 and L2 , respectively. 72
ACES III was essential for the success of this study and those following this paper on larger
fragments of the DNA. 75,76 ACES III 64,77 is a newly written program to perform high level quantum chemical calculations with many-body methods. The program operates on blocks of numbers,
instead of individual floating point numbers, and parallelizes over these blocks. This offers a high
degree of tune-ability resulting in superior scaling across thousands to hundreds of thousands of
computing cores. 77 For more details see Refs. 64,77,78
Results
The choice of basis set is essential to get reliable and accurate results. It is generally assumed
that valence excitation energies are less sensitive to the basis set choice, and diffuse functions
are required only to describe the Rydberg states. However, description of the proper interaction
of the valence states with Rydberg ones might be also important which again necessitate diffuse
basis functions. For example, it has been shown for cytosine 7 that valence excitations energies are
7
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
influenced up to 0.2 eV by diffuse functions, due to some interaction of valence and Rydberg states.
Of the results obtained with the two basis sets (see previos section), only the aug-cc-pVTZ results
are presented below, while the aug-cc-pVDZ results can be found in supplementary materials.
The comparison of the results obtained by these two basis sets shows that they are essentially
the same for valence states (deviation is in the range of 0.01-0.03 eV), and even for the lowenergy Rydberg states only a small difference could be noticed: the triple-ζ excitation energies
are larger by up to 0.15-0.17 eV only. This means that valence-Rydberg interactions are already
well described with the aug-cc-pVDZ basis and in later studies on larger systems the smaller basis
can be used. Methodological comparison with calculations that do not include diffuse functions
should, however, be handled with care (see below).
It has been shown in Ref. 7 that the triple excitations have an effect of 0.1-0.3 eV on the excitation energies of cytosine. This means that if one seeks an accuracy of about 0.1 eV, inclusion
of triple excitations is an absolute necessity. There is no reason to doubt that this conclusion is
valid for the other nucleobases, as well. In Ref. 7 the CC3-LR method 60 was used to include triples
effect. It is an iterative method, and like the other ∼n7 methods we use, the storage of the triple
excitation amplitudes is not necessary, but the large matrix diagonalization remains making such
calculations substantially more expensive than CCSD calculations. Therefore we prefer the noniterative methods like CCSD(T) 58 but to document their accuracy, we also consider the iterative
CCSDT-3 method 59 in the case of cytosine. The results obtained by the various methods and the
aug-cc-pVDZ basis are listed in Table Table 1.
All three triples methods give very similar results, the excitation energies are lower by 0.2-0.3
eV if triple excitations are considered. CC3 always gives the lowest energy, but the difference
between CCSDT-3 and CC3 is no larger than 0.1 eV. As there is no variational bound on any of
these results for excitation energies, the only way to assess accuracy is calibration to experiment,
or in the cases where they are not available, to EOM-CCSDT or full CI. Due to the size of the
molecule these later calculations are not possible, but we know the excellent agreement of the CC3
excitation energy is for the π → π ∗ states of cytosine. 9 The non-iterative CCSD(T) results in most
8
ACS Paragon Plus Environment
Page 8 of 27
Page 9 of 27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
The Journal of Physical Chemistry
cases fall between the CCSDT-3 and CC3 results. Considering the fact the CCSD(T) method is
non-iterative and therefore the most cost-effective, it seems to be reasonable to use it in the further
studies.
Tables Table 2-Table 5 present EOM-CCSD, EOM-CCSD(T) results with aug-cc-pVTZ basis
set obtained for cytosine, adenine, guanine and thymine, respectively along with the results from
the literature. Unfortunately different basis sets have been used in these latter studies: while the
results of the CC2 calculations 44 have also been obtained by the aug-cc-pVTZ basis set (allowing
direct comparison), the 6-311++(d,p) basis was used in the TDDFT study, while the TZVP basis
was used in the CASPT2 calculations. It is expected that the 6-311++(d,p) basis gives results of
similar quality as the aug-cc-pVTZ (both being valence triple zeta with polarization functions),
but the TZVP basis is certainly not capable of describing Rydberg states due to the lack of diffuse
functions. Yamazaki et al. 26 also use a tripel-ζ basis with polarization factions, so comparison is
appropriate in the case of guanine. These facts need to be kept in mind during the course of the
discussion below.
Beside the calculated excitation energies and oscillator strengths, Tables Table 2-Table 5 also
list the assignment of the excited states. Our assignment is based on the inspection of the EOMEE
vectors and orbitals as well as difference densities. Literature data are listed according to the
assignment given in the original papers (if not noted otherwise).
Now we start a systematic discussion of the results on the various nucleobases.
Cytosine
In a recent study by Bazsó et al. 7 it has been shown that the MI/UV spectrum of cytosine can
only be explained if the three lowest energy tautomers are included in the spectrum simulation. In
the present study we include only the canonical form, which is not the lowest energy conformer
in the gas phase, 79 but it is the only conformer in solid phase and it is the only one considered in
biological systems. The reason for the stability difference in gas and condensed phase is the larger
stabilization of the canonical form by hydrogen bonds. 80
A first inspection of Table Table 2 reveals that all methods predict the π → π ∗ state to be the
9
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
lowest followed by the n → π ∗ . According to our CC calculations, there are three more π → π ∗ and
two other n → π ∗ type excitations below 7 eV. The strongest excitation is the π → 2π ∗ transition
at 6.53 eV (CCSD) and 6.33 (CCSD(T)), respectively. CASPT2 gives similar results. The CC2
calculation of Ref. 44 does not include this latter state. According to our own CC2/aug-cc-pVDZ
calculations (see supplementary materials), CC2 gives similar excitation energy as CCSD(T) for
this state, the oscillator strength is, however, somewhat lower (0.294). TDDFT excitation energies
for the first two π → π ∗ states are similar to the other methods, the oscillator strength are, however,
substantially smaller. In the case of the third π → π ∗ excitation, two states appear with substantial
oscillator strength, as a result of a pronounced interaction between valence and Rydberg states, not
shown by the other methods. The excitation energy corresponding to the stronger one of these two
transitions appears to be too high. Even considering these differences one can conclude that all
methods would give very similar (dipole-allowed) spectrum with some differences in the details.
It is particularly striking to see how well CC2 and EOM-CCSD(T) results agree for valence
π → π ∗ states. Since theoretically CC2 is an approximation to CCSD and does not include any
triple excitation effect, the results suggest that there is some kind of error compensation. CC2
excitation energies are always lower than CCSD, as are results with triple excitations. While in
the latter case the lowering comes from the additional contribution of the triple excitations, in case
of CC2 the lowering is caused by some approximations introduced with respect to CCSD. Since
EOM-CC methods (including CC2-LR) can be viewed as direct methods to obtain excitation energies (i.e. energy differences), one could argue that the good agreement of CC2 is a result of
providing a better balanced description of ground and excited states than in CCSD. When considering also the n → π ∗ states, CC2 results differ considerably from the CCSD(T) results which
makes the latter argument weak. In fact, CC2 energies for these n → π ∗ states are again lower than
the CCSD ones but the amount is much larger: while it is about 0.2-0.3 eV for the π → π ∗ sates,
it is 0.3-0.8 eV for the n → π ∗ states. Since triples corrections remain in the range of 0.2-0.3 eV
for the latter case as well, as a result, CC2 highly underestimates the excitation energy of these
states. One does not find good agreement between the CC2 and CCSD(T) results for the Rydberg
10
ACS Paragon Plus Environment
Page 10 of 27
Page 11 of 27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
The Journal of Physical Chemistry
states, either. Here again CC2 excitation energies are consistently lower than the CCSD(T) ones,
the difference is about 0.1-0.3 eV. Therefore, it does not seem to be proven that the good agreement observed between CCSD(T) and CC2 results for the π → π ∗ states comes from a balanced
description of ground and excited states; rather it appears that there is fortunate error cancelation in
this case which does not happen for states with other character, in particular not for n → π ∗ states.
Finding the reasons for this different performance is out of the scope of present paper and will be
investigated in a separate one where other model systems and other second order methods will be
investigated.
Note that this unbalanced description of the states with different character has the unwanted
effect that CC2 gives a different ordering of some of the states than CCSD and CCSD(T). In the
case of cytosine, the states designated as π−1 → π ∗ and n, n−1 → 2π ∗ are flipped by CC2. Possible
consequences are discussed below.
TDDFT gives very good agreement for the first excited state (π → π ∗ ), however, all other
excitation energies seem to be underestimated, considerably for some of the states. While the
resulting TDDFT spectrum would show some resemblance with the coupled-cluster spectra for
the lower states (in particular with CC2), for higher states it does not seem to be correct even
qualitatively.
Quite good agreement can be observed between CASPT2 and coupled cluster results for the
valence states listed in Table Table 2. Again, the n → π ∗ states are somewhat underestimated.
One has to remember, however, that the inclusion of the diffuse function would further lower the
excitation energies by about 0.2 eV resulting in too low values for the entire spectrum. Note also
that very different CASPT2 numbers are available in the literature for the states of cytosine. 41,41
The good agreement found in Ref. 43 was a result of a systematic procedure (selection of reference
space, choice of the denominator shift) used for a series of molecules. The present results suggest,
however, that this good agreement between calculated CASPT2 values 43 and experiment could be
worse if diffuse functions are also included in the basis.
Adenine
11
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Results for adenine are listed in Table Table 3. Here again, only the canonical tautomer (known
as adenine-N9H 5 ) has been investigated. See Guerra et al. 81 for a discussion of other tautomers.
The lowest three states, two π → π ∗ and an n → π ∗ states, are very close in energy. Beside several
π → R states there is another n → π ∗ around 6 eV. At the higher energy end of the studied region
there are again one n → π ∗ and two π → π ∗ states close in energy. Unfortunately, Ref. 44 does not
report CC2 energies above 6.14 eV, and the n → π ∗ state is missing from the CASPT2 list. 43
The difficulty with adenine’s spectrum is that there is a pair of close lying π → π ∗ states (first
and second excited states with CCSD and CCSD(T)). CC2 cannot separate them with the aug-ccpVTZ basis giving a pair of complex eigenvalues (see Ref.; 44 we have found the same problem
with aug-cc-pVDZ basis, see supplements). In case of TDDFT the lowest excited state is n → π ∗
but the energy of the two π → π ∗ excited states agree well with the CCSD(T) results. Note,
however, that the order of the two states are reversed: in the TDDFT case the brighter one is lower
in energy. CASPT2 43 gives a splitting of 0.1 eV of the two π → π ∗ states, but both states come out
with similar oscillator strength, a discrepancy to the CC results. Note that the oscillator strength
reported in Ref. 43 comes from a MCSCF calculation, so it does not include dynamic correlation.
Of the overall performance of the different methods, one can draw similar conclusions as for
cytosine: for π → π ∗ states CC2 excitation energies are close to the CCSD(T) ones, but that of
the n → π ∗ states are far too low. Except for the first two π → π ∗ states the TDDFT excitation
energies are too low with discrepancy as much as 0.5 eV. CASPT2 energies for the valence states
are in good agreement with CCSD(T). Note again, inclusion of diffuse functions might change this
conclusion.
Underestimation of the n → π ∗ excitation energies has the consequence that both CC2 and
TDDFT incorrectly give the n → π ∗ state as the lowest excited state contrary to CCSD and
CCSD(T) where both π → π ∗ states are below the n → π ∗ one. This can have severe consequences on relaxation dynamics where conical interactions between these states are of crucial
importance. 30
Guanine
12
ACS Paragon Plus Environment
Page 12 of 27
Page 13 of 27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
The Journal of Physical Chemistry
In the case of guanine, the biologically relevant canonical form is the keto-N9H. 5 Table Table 4
shows that the lowest excited state predicted by all but the CCSD method is a π → π ∗ state; in
case of the CCSD, the first and second states are practically degenerate. There is, however, a
discrepancy in the assignment of the other component of this pair of states: while the CC methods
(CCSD, CCSD(T) and CC2) predict substantial π → R character for this state (A”symmetry), the
assignment based on the CASPT2 26 and also on the TDDFT 45 calculations is given as π → σ ∗ .
Note that the CASPT2 calculations by Yamazaki, Domcke and Sobolewski 26 reported in Table
Table 4 uses a triple-ζ basis with polarization functions, so the description of Rydberg states are
possible in this case. Nevertheless, all methods agree that the two lowest states for guanine are
close in energy, the brighter one is a π → π ∗ state, while the other one is weak. The largest gap
between them is at the CASPT2 level, in fact the energy of the π → π ∗ state seems to be far too
low.
It is interesting to note that CCSD(T) and CC2 results compare somewhat differently than
for cytosine: we cannot find a perfect agreement between CC2 and CCSD(T) excitation energies
for the π → π ∗ states, while for the π → R states CC2 and CCSD results almost match. The
n → π ∗ excitations energies are again too low at the CC2 level: while for the first n → π ∗ state
the underestimation with respect to CCSD(T) is small (0.05 eV), it is as much as 0.30 eV for the
n → 2π ∗ state (in Ref. 44 this state is assigned as n → R, along with another close lying state at 6.13
eV). As a result, CC2 does not seem to predict the order of the n → π ∗ and second π → π ∗ states
correctly. Note that these later two states are very close in energy even at the CCSD level; it is only
the CCSD(T) which pulls them somewhat more apart. Due to near-degeneracy, CC2 distributes
the oscillator strength of the π → 2π ∗ state between this and a π → R state. No such effect can be
observed for CCSD where these two states are further apart.
As mentioned already, the CASPT2 study by Yamazaki et al. 26 used a basis set which can describe Rydberg sates. Unfortunately, only valence states are reported in Ref. 26 The results for these
show, however, a different pattern from what we observed for other molecules by comparing to the
CASPT2 results of Schreiber et al. 43 The reason can be assigned to the fact that CASPT2 results
13
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
largely depend on several choices such as reference space, level shift, etc. and these have been
carefully chosen by Schreiber et al., 43 therefore their results seem to be more systematic. Another
important difference is that there are no diffuse functions included in the basis in Ref., 43 while
diffuse functions are included in the calculations of Ref.; 26 as stated above and in Ref., 9 diffuse
functions lower the excitation energy of the valence states by about 0.2 eV, as well. Therefore, it
seems to be proven that CASPT2 excitation energies are too low.
Thymine
Finally, the results on thymine are summarized in Table Table 5. It is seen there that all methods
predict the n → π ∗ state to be lowest followed by the π → π ∗ state. Comparison of CC2 and
CCSD(T) results shows much better overall agreement than before: while for π → π ∗ states one
does not find the perfect agreement observed for the other molecules (maximum discrepancy is less
than 0.1 eV though), the excitation energy of the first n → π ∗ state agrees perfectly and even in
case of the n−1 → 2π ∗ state the underestimation by the CC2 method is only 0.1 eV. All of TDDFT
excitation energies are too low. For higher states the discrepancy grows fast, for the π → 2π ∗ it is
already more than 0.3 eV. Thus, TDDFT does not seem to be very useful to predict the spectrum
of thymine. As before, CASPT2 results are reasonable for all valence states, although the splitting
of the n−1 → 2π ∗ and π → 2π ∗ states are largely overestimated in this case. One should not
forget about the possible effect of diffuse functions which presumably would lower all valence
state energies resulting in poorer agreement.
Discussion and Conclusions
The results presented above can be summarized as follows. The excited states of nucleobases
can be described by EOM-CC methods including triple excitations very accurately. The error of
the vertical excitation energies is assumed to be about 0.1 eV or less (aug-cc-pVTZ or aug-ccpVDZ basis) in this case. Among the methods including triple effects, the most cost effective,
non-iterative CCSD(T) performs well. In the case of cytosine we have found between the non-
14
ACS Paragon Plus Environment
Page 14 of 27
Page 15 of 27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
The Journal of Physical Chemistry
iterative EOM-CCSD(T) and the iterative versions (CC3, CCSDT-3) a perfect agreement. EOMCCSD excitation energies are too high by about 0.1-0.3 eV. No relation between the size of this
discrepancy and the character of the states could be found. Therefore it seems to be essential to
include triple excitations in the wave function if accuracy of about 0.1 eV is required.
Concerning the accuracy of the approximate CC2 method we observed very good agreement
with the CCSD(T) results for the π → π ∗ excited states for all four molecules. In most cases, however, both n → π ∗ and π → R excitation energies are underestimated, sometimes by as much as 0.4
eV. In other cases, like thymine, there is good agreement even for the n → π ∗ states. Such reduced
accuracy of CC2 for n → π ∗ states has not been observed for other molecules. For example, in
the comprehensive study by Schreiber et al. 43 CC2 works equally well for n → π ∗ and π → π ∗
states of a large number of molecules including heterocycles. Note that in case of the nucleobases
Ref. 43 does not report triples results, however, CCSD and CC2 excitation energies agree very well.
This contradicts our findings, since we observe substantial differences between CCSD and CC2
excitation energies in most cases. We could not find any explanation for this discrepancy, but we
note that one important difference between the two studies is the lack of diffuse function in Ref. 43
It is out of the scope of the present paper to explain the failure of CC2, in particular for n →
π ∗ states. However, a quick analysis of the character of the excited states shows that for most
nucleobases the n → π ∗ states arise either from a nitrogen or an oxygen lone pair. They are the
two states of cytosine (showing the largest discrepancy) where strong interaction of the N and O
lone pairs could be observed for the hole orbital. On the other hand, in case of thymine, where
the error of CC2 seems to be the smallest, both n → π ∗ excitations are localized on one of the CO
fragments. More detailed analysis involving other model systems will be presented elsewhere.
TDDFT/B3LYP gives good excitation energies for the lowest π → π ∗ states (cytosine, adenine
and guanine) but it fails already if there is another lower state, like in case of thymine where there
is an n → π ∗ state close by. The discrepancy to CCSD(T) grows with the excitation energy so
TDDFT/B3LYP does not seem to be good enough to predict even the observable UV spectrum
of the nucleobases. Note that we compare only with one set of results obtained by the B3LYP
15
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
functional and we do not investigate whether other functionals are more reliable. In this respect
the recent paper of Silva-Junior et al. 46 states that B3LYP clearly outperforms other functionals
like BP86 and BHLYP. Since this conclusion is based on a large number of exited states (same
set as the one used by Schreiber et al. 43 ), this conclusion supports the representativeness of the
TDDFT/B3LYP numbers. Note that according to the Table III of Ref., 46 DFT/MRCI 82 results
also are no better than the TDDFT/B3LYP results for singlet states. Tables Table 2-Table 5 of the
present paper confirm this findings.
The data presented in this paper suggest that only the EOM-CC methods with the triple excitation correction can give a balanced description of all of the states of these four nucleobases. If the
goal is to obtain very precise results with uncertainty of about 0.1 eV, triple excitations in the form
of the EOM-CCSD(T) method needs to be included. The often used CC2, TDDFT and CASPT2
methods do not seem to fullfil this requirement.
In our forthcoming papers 75,76 we will investigate the effect of hydration, the effect of sugar
bound in nucleotides, and that of nearby nucleobases either as Watson-Crick base pairs, or in
stacked configurations. To gain unambiguous information on the electronic properties of these
systems the EOM-CCSD(T) method will be used. These calculation even at the CCSD(T) level
are, however, very expensive but considering the above describe uncertainty of the lower level
methods, one has to go into this endeavor and establish a benchmark set for these systems, as well.
These can then be used to evaluate the cheaper methods like CC2 and various TDDFT variants. A
detailed understanding of the phenomenon like electron and charge transfer certainly requires this
kind of precision at least in the early stage of the research.
Acknowledgements
P.G.S. acknowledges financial support by the Hungarian American Enterprise Scholarship Fund
(HAESF) during his sabbatical stay at the University of Florida. Contribution from Orszagos
Tudomanyos Kutatasi Alap (OTKA; Grant No. F72423) and TAMOP, supported by the European
16
ACS Paragon Plus Environment
Page 16 of 27
Page 17 of 27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
The Journal of Physical Chemistry
Union and cofinanced by the European Social Fund (Grant Agreement No. TAMOP 4.2.1/B09/1/KMR-2010-0003) is also acknowledged. Most of the calculations have been performed on
DoD computer Chugach at the Arctic Region Supercomputer Center and financed by the U.S.
ARO, grant No.: 54344CH.
References
(1) Crespo-Hernandez, C.; Cohen, B.; Hare, P.; Kohler, B. Chem. Rev. 2004, 104, 1977–2019.
(2) Middleton, C. T.; de La Harpe, K.; Su, C.; Law, Y. K.; Crespo-Hernandez, C. E.; Kohler, B.
Annu. Rev. Phys. Chem. 2009, 60, 217–239.
(3) Barbatti, M.; Aquino, A. J. A.; Szymczak, J. J.; Nachtigallova, D.; Hobza, P.; Lischka, H.
Proc. Natl. Acad. Sci. USA 2010, 107, 21453–21458.
(4) Shukla, M.; Leszczynski, J. Radiation Induced Molecular Phenomena in Nucleic Acids,
Springer; 2008.
(5) Shukla, M. K.; Leszczynski, J. J. Biomol. Struct. Dyn. 2007, 25, 93–118.
(6) Puzzarini, C.; Barone, V. Phys. Chem. Chem. Phys. 2011, 13, 7158–7166.
(7) Tajti, A.; Fogarasi, G.; Szalay, P. G. ChemPhysChem 2009, 10, 1603–1606.
(8) Barbatti, M.; Aquino, A. J. A.; Lischka, H. Phys. Chem. Chem. Phys. 2010, 12, 4959–4967.
(9) Bazso, G.; Tarczay, G.; Fogarasi, G.; Szalay, P. G. Phys. Chem. Chem. Phys. 2011, 13, 6799–
6807.
(10) Chen, H.; Li, S. J. Phys. Chem. A 2005, 109, 8443–8446.
(11) Perun, S.; Sobolewski, A.; Domcke, W. Chem. Phys. 2005, 313, 107–112.
(12) Perun, S.; Sobolewski, A.; Domcke, W. J. Am. Chem. Soc 2005, 127, 6257–6265.
17
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
(13) Zgierski, M.; Patchkovskii, S.; Fujiwara, T.; Lim, E. J. Phys. Chem. A 2005, 109, 9384–9387.
(14) Tomic, K.; Tatchen, J.; Marian, C. J. Phys. Chem. A 2005, 109, 8410–8418.
(15) Marian, C. J. Chem. Phys. 2005, 122, 104314.
(16) Gustavsson, T.; Banyasz, A.; Lazzarotto, E.; Markovitsi, D.; Scalmani, G.; Frisch, M.;
Barone, V.; Improta, R. J. Am. Chem. Soc 2006, 128, 607–619.
(17) Serrano-Andres, L.; Merchan, M.; Borin, A. Proc. Natl. Acad. Sci. USA 2006, 103, 8691–
8696.
(18) Chung, W. C.; Lan, Z.; Ohtsuki, Y.; Shimakura, N.; Domcke, W.; Fujimura, Y. Phys. Chem.
Chem. Phys. 2007, 9, 2075–2084.
(19) Marian, C. M. J. Phys. Chem. A 2007, 111, 1545–1553.
(20) Zechmann, G.; Barbatti, M. J. Phys. Chem. A 2008, 112, 8273–8279.
(21) Asturiol, D.; Lasorne, B.; Robb, M. A.; Blancafort, L. J. Phys. Chem. A 2009, 113, 10211–
10218.
(22) Langer, H.; Doltsinis, N.; Marx, D. ChemPhysChem 2005, 6, 1734–1737.
(23) Merchan, M.; Gonzalez-Luque, R.; Climent, T.; Serrano-Andres, L.; Rodriuguez, E.;
Reguero, M.; Pelaez, D. J. Phys. Chem. B 2006, 110, 26471–26476.
(24) Groenhof, G.; Schaefer, L. V.; Boggio-Pasqua, M.; Goette, M.; Grubmueller, H.; Robb, M. A.
J. Am. Chem. Soc 2007, 129, 6812–6819.
(25) Hudock, H. R.; Levine, B. G.; Thompson, A. L.; Satzger, H.; Townsend, D.; Gador, N.;
Ullrich, S.; Stolow, A.; Martinez, T. J. J. Phys. Chem. A 2007, 111, 8500–8508.
(26) Yamazaki, S.; Domcke, W.; Sobolewski, A. L. J. Phys. Chem. A 2008, 112, 11965–11968.
(27) Lei, Y.; Yuan, S.; Dou, Y.; Wang, Y.; Wen, Z. J. Phys. Chem. A 2008, 112, 8497–8504.
18
ACS Paragon Plus Environment
Page 18 of 27
Page 19 of 27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
The Journal of Physical Chemistry
(28) Hudock, H. R.; Martinez, T. J. ChemPhysChem 2008, 9, 2486–2490.
(29) Fabiano, E.; Thiel, W. J. Phys. Chem. A 2008, 112, 6859–6863.
(30) Barbatti, M.; Lischka, H. J. Am. Chem. Soc 2008, 130, 6831–6839.
(31) Szymczak, J. J.; Barbatti, M.; Hoo, J. T. S.; Adkins, J. A.; Windus, T. L.; Nachtigallova, D.;
Lischka, H. J. Phys. Chem. A 2009, 113, 12686–12693.
(32) Mitric, R.; Werner, U.; Wohlgemuth, M.; Seifert, G.; Bonacic-Koutecky, V. J. Phys. Chem. A
2009, 113, 12700–12705.
(33) Lan, Z.; Fabiano, E.; Thiel, W. ChemPhysChem 2009, 10, 1225–1229.
(34) Lan, Z.; Fabiano, E.; Thiel, W. J. Phys. Chem. B 2009, 113, 3548–3555.
(35) Improta, R.; Barone, V.; Lami, A.; Santoro, F. J. Phys. Chem. B 2009, 113, 14491–14503.
(36) Alexandrova, A. N.; Tully, J. C.; Granucci, G. J. Phys. Chem. B 2010, 114, 12116–12128.
(37) Barbatti, M.; Szymczak, J. J.; Aquino, A. J. A.; Nachtigallova, D.; Lischka, H. J. Chem. Phys.
2011, 134, 014304.
(38) Barbatti, M.; Aquino, A. J. A.; Szymczak, J. J.; Nachtigallova, D.; Lischka, H. Phys. Chem.
Chem. Phys. 2011, 13, 6145–6155.
(39) Nachtigallova, D.; Aquino, A. J. A.; Szymczak, J. J.; Barbatti, M.; Hobza, P.; Lischka, H. J.
Phys. Chem. A 2011, 115, 5247–5255.
(40) Lorentzon, J.; Fulscher, M.; Roos, B. O. J. Am. Chem. Soc 1995, 117, 9265–9273.
(41) Fulscher, M.; Roos, B. O. J. Am. Chem. Soc 1995, 117, 2089–2095.
(42) Fulscher, M.; SerranoAndres, L.; Roos, B. O. J. Am. Chem. Soc 1997, 119, 6168–6176.
(43) Schreiber, M.; Silva, M. R. J.; Sauer, S. P. A.; Thiel, W. J. Chem. Phys. 2008, 128, 134110.
19
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
(44) Fleig, T.; Knecht, S.; Haettig, C. J. Phys. Chem. A 2007, 111, 5482–5491.
(45) Shukla, M.; Leszczynski, J. J. Comput. Chem. 2004, 25, 768–778.
(46) Silva-Junior, M. R.; Schreiber, M.; Sauer, S. P. A.; Thiel, W. J. Chem. Phys. 2008, 129,
104103.
(47) Matsika, S. J. Phys. Chem. A 2004, 108, 7584–7590.
(48) Kowalski, K.; Valiev, M. J. Phys. Chem. A 2008, 112, 5538–5541.
(49) Sekino, H.; Bartlett, R. J. Int. J. Quantum Chem. 1984, S18, 255.
(50) Monkhorst, H. J. Int. J. Quantum Chem. 1977, S11, 421.
(51) Stanton, J. F.; Bartlett, R. J. J. Chem. Phys. 1993, 98, 7029–7039.
(52) Comeau, D. C.; Bartlett, R. J. Chem. Phys. Lett. 1993, 207, 414.
(53) Koch, H.; Jørgensen, P. J. Chem. Phys. 1990, 93, 3333.
(54) Bartlett, R. J.; Musial, M. Rev. Mod. Phys. 2007, 79, 291–352.
(55) Bartlett, R. J. WIREs Comput. Mol. Sci. 2012, 2, 126–138.
(56) Kucharski, S.; Wloch, M.; Musial, M.; Bartlett, R. J. J. Chem. Phys. 2001, 115, 8263–8266.
(57) Noga, J.; Bartlett, R. J.; Urban, M. Chem. Phys. Lett. 1987, 134, 126–132.
(58) Watts, J. D.; Bartlett, R. J. Chem. Phys. Lett. 1995, 233, 81–87.
(59) Watts, J. D.; Bartlett, R. J. Chem. Phys. Lett. 1996, 258, 581–588.
(60) Christiansen, O.; Koch, H.; Jørgensen, P. J. Chem. Phys. 1995, 103, 7429–7441.
(61) Taube, A. G.; Bartlett, R. J. J. Chem. Phys. 2008, 128, 044110.
(62) Bartlett, R. J. Mol. Phys. 2010, 108, 2905–2920.
20
ACS Paragon Plus Environment
Page 20 of 27
Page 21 of 27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
The Journal of Physical Chemistry
(63) Dunning, T. H. J. Chem. Phys. 1989, 90, 1007.
(64) Lotrich, V.; Flocke, N.; Ponton, M.; Yau, A. D.; Perera, A.; Deumens, E.; Bartlett, R. J. J.
Chem. Phys. 2008, 128, 194104.
(65) ACES III is a massively parallel program for coupled-cluster and MBPT calculations
for molecular structure and spectra. Authors, V. Lotrich, M. Ponton, A. Perera, T. Watson, N. Jindal, T. Hughes, D. Lyakh, R. Bhoj, E. Deumens, B. Sanders, and R. J.
Bartlett, Quantum Theory Project, University of Florida. The program is available at
http://www.qtp.ufl.edu/ACES/index.shtml.
(66) CFOUR, a quantum chemical program package written by J.F. Stanton, J. Gauss, M.E. Harding, P.G. Szalay with contributions from A.A. Auer, R.J. Bartlett, U. Benedikt, C. Berger,
D.E. Bernholdt, O. Christiansen, M. Heckert, O. Heun, C. Huber, D. Jonsson, J. Jusélius, K.
Klein, W.J. Lauderdale, D. Matthews, T. Metzroth, D.P. O’Neill, D.R. Price, E. Prochnow, K.
Ruud, F. Schiffmann, S. Stopkowicz, A. Tajti, M.E. Varner, J. Vázquez, F. Wang, J.D. Watts
and the integral packages MOLECULE (J. Almlöf and P.R. Taylor), PROPS (P.R. Taylor),
ABACUS (T. Helgaker, H.J. Aa. Jensen, P. Jørgensen, and J. Olsen), and ECP routines by A.
V. Mitin and C. van Wüllen. For the current version, see http://www.cfour.de.
(67) Fogarasi, G.; Zhou, X. F.; Taylor, P. W.; Pulay, P. J. Am. Chem. Soc 1992, 114, 8191–8201.
(68) Császár, P.; Pulay, P. J. Mol. Struct. 1984, 114, 31.
(69) Pulay, P.; Fogarasi, G. J. Chem. Phys. 1992, 96, 2856–2860.
(70) Bakken, V.; Helgaker, T. J. Chem. Phys. 2002, 117, 9160–9174.
(71) Christiansen, O.; Koch, H.; Jørgensen, P. Chem. Phys. Lett. 1995, 243, 409–418.
(72) Watson, T.; Lotrich, V. F.; Szalay, P. G.; Bartlett, R. J. 2012, Triple Excitations in EOM-CC
methods, to be bulished.
21
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
(73) Kucharski, S.; Bartlett, R. J. J. Chem. Phys. 1998, 108, 5243–5254.
(74) Crawford, T. D.; Stanton, J. F. Int. J. Quantum Chem. 1998, 70, 601–611.
(75) Szalay, P. G.; Watson, T.; Lotrich, V. F.; Perera, A.; Fogarasi, G.; Bartlett, R. J. 2012, Effect
of biological environment on the excitation spectrum of cytosine, to be submitted.
(76) Szalay, P. G.; Watson, T.; Lotrich, V. F.; Perera, A.; Bartlett, R. J. 2012, Systematic Coupled
Cluster study of Watson-Crick and stacked base pairs, to be submitted.
(77) Lotrich, V. F.; Ponton, J. M.; Perera, A. S.; Deumens, E.; Bartlett, R. J.; Sanders, B. A. Mol.
Phys. 2010, 108, 3323–3330.
(78) Deumens, E.; Lotrich, V. F.; Perera, A.; Ponton, M. J.; Sanders, B. A.; Bartlett, R. J. WIREs
Comput. Mol. Sci. 2011, 1, 895–901.
(79) Fogarasi, G. J. Phys. Chem. A 2002, 106, 1381–1390.
(80) Fogarasi, G.; Szalay, P. G. Chem. Phys. Lett. 2002, 356, 383–390.
(81) Guerra, C.; Bickelhaupt, F.; Saha, S.; Wang, F. J. Phys. Chem. A 2006, 110, 4012–4020.
(82) Grimme, S.; Waletzke, M. J. Chem. Phys. 1999, 111, 5645–5655.
22
ACS Paragon Plus Environment
Page 22 of 27
Page 23 of 27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
The Journal of Physical Chemistry
Table 1: Comparsion of various triples methods for the excitation energy (eV) and oscillator
strength of cytosine. All calculations with aug-pVDZ bases, frozen core
2A0
3A0
4A0
5A0
6A0
7A0
1A”
2A”
3A”
4A”
5A”
6A”
7A”
8A”
CCSD
4.94 0.064
5.86 0.164
6.50 0.508
6.70 0.026
6.88 0.181
7.05 0.007
5.56 0.004
5.46 0.003
6.04 0.002
6.06 0.005
6.19 0.007
6.34 0.000
6.51 0.005
6.82 0.000
CC3
4.71 0.065
5.55 0.138
6.30 0.426
6.43 0.025
6.62
5.46
5.18
5.94
5.97
5.60
CCSD(T)
4.74
5.62
6.35
6.57
6.69
6.93
5.49
5.25
5.91
5.96
6.08
5.90
6.43
6.73
23
ACS Paragon Plus Environment
CCSDT-3
4.79
5.65
6.38
6.57
6.7
5.52
5.29
6.00
6.05
5.79
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
π → π∗
n → π∗
π →R
π−1 → π ∗
n, n−1 → 2π ∗
π−1 → R
π →R
n−1 → π ∗
π → 2π ∗
π →R
n→R
π−1 → 2π ∗
EOMEE-CCSD
EOMEE-CCSD(T)
CC2-LRa
TDDFTb
aug-cc-pVTZ
aug-cc-pVTZ
aug-cc-pVTZ
B3LYP/6-311++(d,p)
4.96
0.066
4.69
4.66 0.052
4.63
0.046
5.44
0.003
5.18
4.87 0.002
4.73
0.003
5.73
0.004
5.59
5.53 0.005
5.11
0.001
5.89
0.171
5.60
5.61 0.138
5.44
0.074
6.06
0.000
5.82
5.26 0.002
5.28e
0.005
6.23
0.006
6.10
6.08 0.026
5.65
0.001
e
6.35
0.007
6.18
5.70
0.015
6.40
0.000
5.88
5.83 0.000
6.40 f
0.023
f
6.53
0.507
6.33
6.25
0.149
f
6.65
0.004
6.50
6.62
0.419
6.87
0.026
6.68
5.95 0.031
6.90
0.127
6.69
a Ref. 44 b Ref. 45 c Ref. 46 d Ref. 43 e Strong π → π ∗ component. f π → σ ∗ .
5.54 0.352
5.54 0.002
6.40
6.98
5.43
5.32
6.38
6.74
ACS Paragon Plus Environment
24
0.366
0.623
CASPT2d
TZVP
4.68 0.093
5.12 0.003
DFT/MRCIc
TZVP
4.62
4.86
Table 2: Comparsion of various methods for the excitation energy (eV) and oscillator strength of cytosine
The Journal of Physical Chemistry
Page 24 of 27
π → π∗
π → 2π ∗
n → 2π ∗
π →R
π →R
n → π∗
π →R
n−1 → 2π ∗
π−1 → π ∗ + 2π ∗
π−2 → π ∗ + 2π ∗
n→R
EOMEE-CCSD
EOMEE-CCSD(T)
CC2-LRa
TDDFTb
DFT/MRCIc
aug-cc-pVTZ
aug-cc-pVTZ
aug-cc-pVTZ
B3LYP/6-311++(d,p)
TZVP
5.30
0.021
5.04
5.25
–
4.98
0.205
4.99
5.47
0.275
5.23
5.25 0.302
5.21
0.023
5.15
5.54
0.001
5.28
5.12 0.007
4.88
0.013
5.11
5.70
0.009
5.58
5.53 0.011
5.28
0.008
6.04
0.001
5.91
5.86 0.004
5.59
0.007
6.10
0.003
5.84
5.75 0.003
5.55
0.002
5.72
6.49
0.001
6.38
6.52
0.002
6.27
6.14 0.001
5.82
0.001
6.58
0.478
6.36
6.14
0.095
6.29
6.68
0.035
6.53
6.20
0.200
6.19
–e
6.08 0.030
a Ref. 44 b Ref. 45 c Ref. 46 d Ref. 43 e n → R state has not been found among the first 12 states.
0.002
6.35 0.538
6.64 0.001
5.97
CASPT2d
TZVP
5.20 0.146
5.30 0.201
5.21 0.001
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Table 3: Comparsion of various methods for the excitation energy (eV) and oscillator strength of adenine
Page 25 of 27
The Journal of Physical Chemistry
ACS Paragon Plus Environment
25
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
EOMEE-CCSD
EOMEE-CCSD(T)
CC2-LRa
TDDFTb
CASPT2c
aug-cc-pVTZ
aug-cc-pVTZ
aug-cc-pVTZ
B3LYP/6-311++(d,p)
TZ with diffuse
π →R
5.07
0.002
4.91
5.08 0.028
5.08d
0.008
4.89d 0.005
π → π∗
5.10
0.160
4.86
4.98 0.132
4.88
0.122
4.51
0.164
π →R
5.47
0.005
5.32
5.43 0.141
π → 2π ∗ + R 5.61
0.366
5.37
5.47 0.179
5.18
0.224
5.25
0.080
∗
n→π
5.64
0.000
5.43
5.38 0.003
5.30
0.002
5.22
0.001
π →R
5.98
0.001
5.84
5.99 0.003
5.69
0.002
π →R
6.11
0.001
5.98
5.75
0.000
π →R
6.29
0.010
6.15
5.92
0.002
π → R(π)
6.41
0.000
6.28
6.67
0.038
π → 3π ∗
6.49
0.024
6.26
n → 2π ∗
6.59
0.003
6.37
6.07 0.006
6.06
0.005
π →R
6.79
0.001
6.51
n→R
6.13
0.008
a Ref. 44 b Ref. 45 c Ref., 26 (10s6p1d/5s1p)/[5s3p1d/3s1p] basis set of triple-ζ plus polarization quality. d Assigned as π → σ ∗
Table 4: Comparsion of various methods for the excitation energy (eV) and oscillator strength of guanine
The Journal of Physical Chemistry
ACS Paragon Plus Environment
26
Page 26 of 27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
n → π∗
π → π∗
π →R
n−1 → 2π ∗
π → 2π ∗
π →R
π → 3π ∗
π →R
π →R
n→R
π−1 → R
n−1 → π ∗
EOMEE-CCSD
aug-cc-pVTZ
5.09
0.000
5.36
0.213
5.90
0.001
6.46
0.00
6.59
0.060
6.68
0.001
6.76
0.236
6.84
0.000
7.11
0.029
7.30
0.010
7.47
0.000
7.51
0.001
EOMEE-CCSD(T)
CC2-LRa
TDDFTb
aug-cc-pVTZ
aug-cc-pVTZ
B3LYP/6-311++(d,p)
4.85
4.82 0.000
4.71
0.000
5.15
5.20 0.182
4.95
0.138
5.77
5.74 0.000
5.44
0.000
6.27
6.16 0.000
5.82
0.000
6.26
6.27 0.037
5.92
0.068
6.54
6.49 0.000
6.15
0.000
6.46
6.53 0.178
6.22
0.130
6.70
6.97
7.08
6.39 0.061
7.29
6.96
6.20
0.000
a Ref. 44 b Ref. 45 c Ref. 46 d Ref. 43
6.38
6.15
6.52
6.86
6.42
6.43
ACS Paragon Plus Environment
27
0.000
0.356
0.000
0.067
CASPT2d
TZVP
4.94 0.000
5.06 0.334
5.93
5.98
DFT/MRCIc
TZVP
4.48
5.18
Table 5: Comparsion of various methods for the excitation energy (eV) and oscillator strength of thymine
Page 27 of 27
The Journal of Physical Chemistry