Pilot reported observing a target on his cockpit display on departure but not seeing it out the wind...

Narrative:

I was waiting for an IFR release from tower. There was lots of inbound VFR traffic. I requested a VFR climb but tower said they would have our IFR release soon so we waited about 5 minutes while VFR traffic landed. There was one RV6 inbound who said he was on the east side of the valley. We talked about this but thought it would not be a problem because it would be on the east side of the valley. I set up the mfd (multi function display) for short range to get the best detail of the traffic which was showing up on the TCAS.it was a normal takeoff with runway to spare and a climb to 12000 feet. On intial climbout I noticed the RV6 target on the TCAS had moved right onto our route. The RV6 who said he was on the east side of the valley was not any more. I increased the rate of climb but I think the RV6 may have also climbed because it looked like it was going to be close. I scanned for traffic but it was not in sight. I pointed out the traffic on the mfd to the non flying pilot (nfp). It now looked like we might not outclimb the rv-6 by much so I again checked the mfd but the nfp had changed it from the stick-graphic of the departure with TCAS display to the jepesen departure chart with no TCAS display. I could see the target on my pfd inside the HSI I had set up but it was not easy to judge from that because the scale was wrong and I could not read the altitude difference in all the clutter. Since I couldn't see the rv-6 out the windscreen or on the TCAS and it looked like we were going to merge very soon; I turned right to avoid. The nfp asked me what I was doing and I told him we were about to merge with the traffic on the TCAS which was no longer displayed. He was slightly upset so I decided to talk about it later when we weren't so busy. I got back onto the departure and continued the climb uneventfully. We then talked about it later and he got the idea.factors leading up to this. I overestimated our ability to climb based on previous experience there. The nfp changing the display and not briefing about what to do about the RV6. I thought the short range high detail on the mfd would have been enough. Also; I like to make a practice of departing VFR when there is lots of VFR traffic because of the added flexibility in ground track and altitude. I was flying but not the PIC (pilot in command) on this flight and went along with the PIC; but if I told him my reasoning about the VFR departure he would have easily agreed.how it could have been avoided. Brief with nfp about the display and why I had it set that way. Depart VFR with an IFR squawk from center like I usually do with lots of traffic. The plane climbs so well you can make a very early right turn and climb over the hills instead of flying down the valley where all the traffic is; and also keep your scan outside because you do not have to follow a specific track.

Original NASA ASRS Text

Title: Pilot reported observing a target on his cockpit display on departure but not seeing it out the window. Pilot turned off course to avoid traffic resulting in a NMAC.

Narrative: I was waiting for an IFR release from Tower. There was lots of inbound VFR traffic. I requested a VFR climb but Tower said they would have our IFR release soon so we waited about 5 minutes while VFR traffic landed. There was one RV6 inbound who said he was on the east side of the valley. We talked about this but thought it would not be a problem because it would be on the east side of the valley. I set up the MFD (Multi Function Display) for short range to get the best detail of the traffic which was showing up on the TCAS.It was a normal takeoff with runway to spare and a climb to 12000 feet. On intial climbout I noticed the RV6 target on the TCAS had moved right onto our route. The RV6 who said he was on the east side of the valley was not any more. I increased the rate of climb but I think the RV6 may have also climbed because it looked like it was going to be close. I scanned for traffic but it was not in sight. I pointed out the traffic on the MFD to the non flying pilot (NFP). It now looked like we might not outclimb the RV-6 by much so I again checked the MFD but the NFP had changed it from the stick-graphic of the departure with TCAS display to the Jepesen departure chart with no TCAS display. I could see the target on my PFD inside the HSI I had set up but it was not easy to judge from that because the scale was wrong and I could not read the altitude difference in all the clutter. Since I couldn't see the RV-6 out the windscreen or on the TCAS and it looked like we were going to merge very soon; I turned right to avoid. The NFP asked me what I was doing and I told him we were about to merge with the traffic on the TCAS which was no longer displayed. He was slightly upset so I decided to talk about it later when we weren't so busy. I got back onto the departure and continued the climb uneventfully. We then talked about it later and he got the idea.Factors leading up to this. I overestimated our ability to climb based on previous experience there. The NFP changing the display and not briefing about what to do about the RV6. I thought the short range high detail on the MFD would have been enough. Also; I like to make a practice of departing VFR when there is lots of VFR traffic because of the added flexibility in ground track and altitude. I was flying but not the PIC (Pilot in Command) on this flight and went along with the PIC; but if I told him my reasoning about the VFR departure he would have easily agreed.How it could have been avoided. Brief with NFP about the display and why I had it set that way. Depart VFR with an IFR squawk from center like I usually do with lots of traffic. The plane climbs so well you can make a very early right turn and climb over the hills instead of flying down the valley where all the traffic is; and also keep your scan outside because you do not have to follow a specific track.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.

Attributes
ACN	1753042
Time
Date	202007
Local Time Of Day	1201-1800
Environment
Flight Conditions	VMC
Light	Daylight
Aircraft 1
Make Model Name	Citationjet (C525/C526) - CJ I / II / III / IV
Operating Under FAR Part	Part 91
Flight Phase	Initial Climb
Route In Use	SID AURELIA 3
Flight Plan	IFR
Aircraft 2
Make Model Name	RV-6
Operating Under FAR Part	Part 91
Flight Plan	VFR
Person 1
Function	Pilot Flying
Qualification	Flight Crew Instrument Flight Crew Multiengine Flight Crew Flight Instructor Flight Crew Air Transport Pilot (ATP)
Experience	Flight Crew Last 90 Days 70 Flight Crew Total 9393 Flight Crew Type 1374
Events
Anomaly	Conflict NMAC Deviation - Altitude Excursion From Assigned Altitude Deviation - Procedural Clearance Deviation - Procedural Published Material / Policy
Miss Distance	Horizontal 100 Vertical 200

Pilot reported observing a target on his cockpit display on departure but not seeing it out the window. Pilot turned off course to avoid traffic resulting in a near midair collision.